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Properties

Label 27.36
Level 27
Weight 36
Dimension 739
Nonzero newspaces 3
Sturm bound 1944
Trace bound 1

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Defining parameters

Level: \( N \) = \( 27 = 3^{3} \)
Weight: \( k \) = \( 36 \)
Nonzero newspaces: \( 3 \)
Sturm bound: \(1944\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{36}(\Gamma_1(27))\).

Total New Old
Modular forms 960 755 205
Cusp forms 930 739 191
Eisenstein series 30 16 14

Trace form

\( 739 q + 131067 q^{2} - 6 q^{3} + 228033693823 q^{4} - 1862764974639 q^{5} + 61112258396154 q^{6} - 281013594003055 q^{7} - 21744479954175237 q^{8} - 92558698165628316 q^{9} + O(q^{10}) \) \( 739 q + 131067 q^{2} - 6 q^{3} + 228033693823 q^{4} - 1862764974639 q^{5} + 61112258396154 q^{6} - 281013594003055 q^{7} - 21744479954175237 q^{8} - 92558698165628316 q^{9} + 470275449101921775 q^{10} + 6793321410385665075 q^{11} + 50827737260050253103 q^{12} - 16280706345122488669 q^{13} + 149582403213165849015 q^{14} + 1326324051834349967649 q^{15} + 7333545933355965286051 q^{16} - 18803949467879673127359 q^{17} + 49753007276535004780845 q^{18} - 44963840546895954647302 q^{19} + 44732659978935288426951 q^{20} + 542025847818179977432200 q^{21} - 906264905612960443468053 q^{22} + 1056640685264915011574580 q^{23} + 12238950686660372529489474 q^{24} + 11624285761023881151899530 q^{25} - 65433936211174620596372022 q^{26} - 74953413209760394038555177 q^{27} - 97625460549868855409787478 q^{28} - 57044184956280648449764416 q^{29} + 655818943733073852098117139 q^{30} - 219001083148345656027776425 q^{31} + 3363258973724149889246471289 q^{32} - 2747820125176015727147638536 q^{33} + 1922366028583518908997091635 q^{34} - 6676034356776002410116365688 q^{35} - 10338591511381146778689128352 q^{36} - 6504921125110202537805182818 q^{37} - 14076642583728386691107890455 q^{38} - 6374951920141782304277103231 q^{39} + 9612609986250916344773908899 q^{40} + 50085520666124623917479444151 q^{41} - 260129701656375156656618451318 q^{42} + 135584429200449089944715870075 q^{43} - 665869579478379936503465962581 q^{44} - 230842815651025385052720142575 q^{45} - 222167323828709655467920054791 q^{46} - 1288153386819625709164943957751 q^{47} + 3151639404745034986096619512233 q^{48} + 625492123437787102317591309366 q^{49} + 7404828742106660642331995298900 q^{50} - 1168477047338956886581984233774 q^{51} + 4168923698408971992414140421479 q^{52} + 3658114902526109891903215365642 q^{53} - 22295461656609894581219069090370 q^{54} + 5982280044782251302977893280076 q^{55} + 21550383913776121667742441777981 q^{56} - 22059243300699983925278965437627 q^{57} + 23963300946564505984863212100387 q^{58} - 40153097506994866674741797967924 q^{59} - 44126954678312503901384729508486 q^{60} - 90033986175931545630654395764729 q^{61} + 93950990902885873693511227665870 q^{62} - 26105116001889431833232389064415 q^{63} - 810837165925021134352524296324831 q^{64} - 628189953969260301664210272703665 q^{65} + 610112287132537597146483820232589 q^{66} + 487025798620561783765988531553290 q^{67} - 2391464054828059576872614863381224 q^{68} + 1241715194716715642713333843282455 q^{69} - 652669122428499516661810471234845 q^{70} - 1647529304352268808440531583149941 q^{71} + 1961195150704043840295103392081492 q^{72} - 1322511597797508775380293000939509 q^{73} - 567624228437440829886332152381245 q^{74} - 504012592791124028824131417439581 q^{75} - 1565969767817140943726740412268025 q^{76} + 182502995286158223519611628603459 q^{77} - 2160250957292522455710353430741078 q^{78} + 1869766166674053378821099558089295 q^{79} - 10836805351908521304352991333716722 q^{80} + 2927417255022310257090668624116992 q^{81} - 17276913670306767422941868433832590 q^{82} - 6321899169134764660258400163660561 q^{83} + 44842827761253883752116599549595562 q^{84} - 40676586582195848565667910485668087 q^{85} - 47751492749121596893956986836709955 q^{86} + 72390490584971387073625386971858097 q^{87} - 113156886483632202748339062057402885 q^{88} - 44665670943268608006160689464855163 q^{89} + 222335784634720362097517452589858550 q^{90} + 36764351127119394461410677585428185 q^{91} + 89410547841153742699486827118077969 q^{92} - 193453490961228090083914927757230401 q^{93} - 186546084780610861396065068394619713 q^{94} - 137322594902900333660372883987952545 q^{95} - 421772031527882998842101007315780750 q^{96} - 34980872076659995554445992838596214 q^{97} - 113183740837818831355513895786019552 q^{98} - 101864853634760610787428229886191839 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{36}^{\mathrm{new}}(\Gamma_1(27))\)

We only show spaces with even parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
27.36.a \(\chi_{27}(1, \cdot)\) 27.36.a.a 1 1
27.36.a.b 10
27.36.a.c 12
27.36.a.d 12
27.36.a.e 12
27.36.c \(\chi_{27}(10, \cdot)\) 27.36.c.a 68 2
27.36.e \(\chi_{27}(4, \cdot)\) n/a 624 6

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{36}^{\mathrm{old}}(\Gamma_1(27))\) into lower level spaces

\( S_{36}^{\mathrm{old}}(\Gamma_1(27)) \cong \) \(S_{36}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{36}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 3}\)\(\oplus\)\(S_{36}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 2}\)\(\oplus\)\(S_{36}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 1}\)