THE UNITED STATES
SECURITIES AND EXCHANGE COMMISSION
Washington, D.C. 20549

SCHEDULE 13G

Under the Securities Exchange Act of 1934

(Amendment No. )*

Trillium Therapeutics, Inc.
(Name of Issuer)

Common Stock, No Par Value
(Title of Class of Securities)

89620X506
(CUSIP Number)

December 31, 2017
(Date of Event Which Requires Filing of this Statement)

Check the appropriate box to designate the rule pursuant to which this
Schedule 13G is filed:

[X] Rule 13d-1(b)
[ ] Rule 13d-1(c)
[ ] Rule 13d-1(d)

*The remainder of this cover page shall be filled out for a reporting person?s initial filing on this form with respect to the subject class of securities, and for any subsequent amendment containing information which would alter the disclosures provided in a prior cover page.

The information required in the remainder of this cover page shall not be deemed to be ?filed? for the purpose of Section 18 of the Securities Exchange Act of 1934 (?Act?) or otherwise subject to the liabilities of that section of the Act but shall be subject to all other provisions of the Act (however, see the Notes).

CUSIP No. 29076N206
(1)     Names of Reporting Persons.  I.R.S. Identification Nos. of
Above Persons (entities only):
        AWM Investment Company, Inc.
(2)     Check the Appropriate Box if a Member of a Group (See
Instructions)   (a)___  b)___

(3)     SEC Use Only
(4)     Citizenship or Place of Organization:  Delaware, United States
Number of Shares Beneficially
Owned by Each Reporting Person
With
(5) Sole Voting Power:
969,138**

(6) Shared Voting Power:         0**

(7) Sole Dispositive Power:
969,138**


(8) Shared Dispositive Power: 0**
(9)     Aggregate Amount Beneficially Owned by Each Reporting
Person:  969,138**
(10)    Check if the Aggregate Amount in Row (9) Excludes Certain Shares
(See Instructions):
(11)    Percent of Class Represented by Amount in Row (9): 9.99%**
(12)    Type of Reporting Person (See Instructions):  IA
**AWM Investment Company, Inc., a Delaware corporation (?AWM?), is the
investment adviser to Special Situations Cayman Fund, L.P. (?CAYMAN?),
Special Situations Fund III QP, L.P. (?SSFQP?), Special Situations
Private Equity Fund, L.P. (?SSPE?) and Special Situations Life
Sciences, L.P. (?SSLS?). (CAYMAN, SSFQP, SSPE and SSLS will hereafter
be referred to as the ?Funds?).  As the investment adviser to the
Funds, AWM holds sole voting and investment power over 107,540 shares
of Common Stock of the Issuer (the ?Shares?), 1,049,786 shares of
Preferred Stock*** convertible into 34,993 Shares and 1,607,143
Warrants*** to purchase 53,571 Shares held by CAYMAN, 323,512 Shares,
3,615,929 shares of Preferred Stock*** convertible into 120,531 Shares
and 5,535,714 Warrants*** to purchase 184,524 held by SSFQP, 145,685
Shares, 2,332,857 shares of Preferred Stock convertible into 77,762
Shares and 3,571,429 Warrants*** to purchase 119,048 held by SSPE and
392,221 Shares, 4,665,714 shares of Preferred Stock*** convertible
into 155,524 Shares and 7,142,857 Warrants*** to purchase 238,095 held
by SSLS. See Items 2 and 4 of this Schedule for additional
information.



*** The Preferred Stock and Warrants described herein may only be
exercised to the extent that the total number of Common Shares then
beneficially owned does not exceed 9.99% of the outstanding shares.


Item 1(a).  Name Of Issuer:  Trillium Therapeutics, Inc.

Item 1(b).  Address of Issuer?s Principal Executive Offices:

2488 Dunwin Drive
Mississauga Ontario L5L 1J9 Canada

Item 2(a).  Name of Person Filing:

The person filing this report is AWM Investment Company, Inc.,
a Delaware corporation (?AWM?), which is the investment adviser
to Special Situations Cayman Fund, L.P., a Cayman Islands
Limited Partnership (?CAYMAN?), Special Situations Fund III QP,
L.P., a Delaware limited partnership (?SSFQP?), Special
Situations Private Equity Fund, L.P., a Delaware limited
partnership (?SSPE?) and Special Situations Life Sciences Fund,
L.P. (?SSLS?), a Delaware limited partnership (?SSLS?),
(CAYMAN, SSFQP, SSPE  and SSLS, will hereafter be referred to
as the ?Funds?).  The principal business of each Fund is to
invest in equity and equity-related securities and other
securities of any kind or nature.

Austin W. Marxe (?Marxe?), David M. Greenhouse (?Greenhouse?)
and Adam C. Stettner (?Stettner?) are members of: SSCayman,
L.L.C., a Delaware limited liability company (?SSCAY?), the
general partner of CAYMAN; MGP Advisers Limited Partnership, a
Delaware limited partnership (?MGP?), the general partner of
SSFQP; MG Advisers, L.L.C., a New York limited liability
company (?MGA?), the general partner of SSPE; and LS Advisers,
L.L.C., a Delaware limited liability company (?LSA?), the
general partner of SSLS. Marxe, Greenhouse and Stettner are
also controlling principals of AWM.

Item 2(b). Address of Principal Business Office or, if None,
Residence:
The principal business address for AWM is c/o Special
Situations Funds, 527 Madison Avenue, Suite 2600, New York, NY
10022.
Item 2(c).  Citizenship: AWM is a Delaware Corporation.
Item 2(d).  Title of Class of Securities: Common Stock, Par
                                          No Par Value
Item 2(e).  CUSIP No.:  89620X506

Item 3.  If This Statement Is Filed Pursuant to ??240.13d-1(b) or
240.13d-2(b) or (c), check whether the Person Filing is a:
             Not Applicable.


Item 4.  Ownership

        (a)     Amount Beneficially Owned:  969,138**

        (b)     Percent of Class:       9.99%**

        (c)     Number of Shares as to which the person has:

                (i)     sole power to vote or to direct the vote: 969,138**

             (ii)       shared power to vote or to direct the vote: 0**

            (iii)       sole power to dispose or to direct the disposition of:
                   969,138**

             (iv)       shared power to dispose or to direct the disposition
                   of:  0**
______________________________________________________________________

** AWM is the investment adviser to each of the Funds.  As the
investment adviser to the Funds, AWM holds sole voting and investment
power over 107,540 shares of Common Stock of the Issuer (the
?Shares?), 1,049,786 shares of Preferred Stock*** convertible into
34,993 Shares and 1,607,143 Warrants*** to purchase 53,571 Shares held
by CAYMAN, 323,512 Shares, 3,615,929 shares of Preferred Stock***
convertible into 120,531 Shares and 5,535,714 Warrants*** to purchase
184,524 held by SSFQP, 145,685 Shares, 2,332,857 shares of Preferred
Stock convertible into 77,762 Shares and 3,571,429 Warrants*** to
purchase 119,048 held by SSPE and 392,221 Shares, 4,665,714 shares of
Preferred Stock*** convertible into 155,524 Shares and 7,142,857
Warrants*** to purchase 238,095 held by SSLS.  Marxe, Greenhouse and
Stettner are members of: SSCAY, the general partner of CAYMAN; MGP,
the general partner of SSFQP; MGA, the general partner of SSPE; and
LSA, the general partner of SSLS. Marxe, Greenhouse and Stettner are
also controlling principals of AWM.

Item 5.  Ownership of Five Percent or Less of a Class

        If this statement is being filed to report the fact that as of
the date hereof the reporting person has ceased to be the beneficial
owner of more than five percent of the class of securities, check the
following. ___

Item 6. Ownership of More Than Five Percent on Behalf of Another
Person

        Not Applicable.


Item 7. Identification and Classification of the Subsidiary Which
Acquired the Security Being Reported on by the Parent Holding
Company or Control Person

        Not Applicable.




Item 8.  Identification and Classification of Members of the Group

        Not Applicable.

Item 9.  Notice of Dissolution of Group

        Not Applicable.


Item 10.  Certification

        By signing below I certify that, to the best of my knowledge and
belief, the securities referred to above were not acquired and are not
held for the purpose of or with the effect of changing or influencing
the control of the issuer of the securities and were not acquired and
are not held in connection with or as a participant in any transaction
having that purpose or effect.



SIGNATURE

        After reasonable inquiry and to the best of my knowledge and
belief, I certify that the information set forth in this statement is
true, complete and correct.


Dated: February 9, 2018



AWM INVESTMENT COMPANY, INC.


By:/s/ David Greenhouse
   Name:  David Greenhouse
   Title:       Executive Vice President






Attention:  Intentional misstatements or omissions of fact constitute
Federal criminal violations (See 18 U.S.C. 1001)
-6-

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