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Properties

Label 23.31
Level 23
Weight 31
Dimension 649
Nonzero newspaces 2
Newform subspaces 4
Sturm bound 1364
Trace bound 1

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Defining parameters

Level: \( N \) = \( 23 \)
Weight: \( k \) = \( 31 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 4 \)
Sturm bound: \(1364\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{31}(\Gamma_1(23))\).

Total New Old
Modular forms 671 671 0
Cusp forms 649 649 0
Eisenstein series 22 22 0

Trace form

\( 649 q - 11 q^{2} - 11 q^{3} - 11 q^{4} - 11 q^{5} - 11 q^{6} - 11 q^{7} - 11 q^{8} - 11 q^{9} + O(q^{10}) \) \( 649 q - 11 q^{2} - 11 q^{3} - 11 q^{4} - 11 q^{5} - 11 q^{6} - 11 q^{7} - 11 q^{8} - 11 q^{9} - 11 q^{10} - 11 q^{11} - 11 q^{12} - 11 q^{13} - 11 q^{14} + 1888459891557523581 q^{15} + 2916509380352409589 q^{16} + 6141760561475910789 q^{17} + 65954701312060030965 q^{18} - 36626049237336688811 q^{19} + 153392625590529425397 q^{20} - 67988527827441731411 q^{21} - 10062944948858758363 q^{23} + 804951017948341862378 q^{24} - 1203633116603054381387 q^{25} + 3595511311319626547189 q^{26} - 12949494517233482300411 q^{27} + 35662723755297227145205 q^{28} - 16082571446126961483411 q^{29} + 91062982067521035173877 q^{30} - 3183044296527880983011 q^{31} - 280970628939402916659211 q^{32} - 237277788254386285012827 q^{33} - 711619762870908244781681 q^{34} - 943175995009155273437511 q^{35} + 932072938242028262175364 q^{36} + 1428378497900819782983061 q^{37} - 3617801833687586618948886 q^{38} + 3687768017373889749171949 q^{39} - 5957870168741455078125011 q^{40} - 590141217348708622663011 q^{41} + 25797531026218879749894919 q^{42} - 21416374393968676119855011 q^{43} + 40180884460531598750409058 q^{44} - 90982816645799417393676611 q^{46} + 74268461748212250676570050 q^{47} - 56132217870731647098185875 q^{48} - 148251161717805841583331971 q^{49} + 351029448211193084716796864 q^{50} - 118717088916880904292156611 q^{51} - 463609608274004112575301581 q^{52} + 260611453253782029709943589 q^{53} - 1027237204371954132111495171 q^{54} + 676448748769109400234846685 q^{55} + 1527302114039519250092727144 q^{56} - 2216153710596500029006582139 q^{57} + 3679416986248239515743808014 q^{58} - 597503195205096514583961591 q^{59} - 9358529172054253189504869781 q^{60} + 3723303325675088901886213909 q^{61} - 5190879012312157104365568011 q^{62} - 1333681847062858320496711011 q^{63} + 13540911612309357531632762869 q^{64} - 9416014920744143710326484475 q^{65} - 11397420755047451682980548632 q^{66} + 6399352552588353846862571989 q^{67} - 24674352238355035415585564211 q^{69} + 21998348675389581216398966762 q^{70} + 30854441198001257180225501389 q^{71} - 87503470225557869163374129150 q^{72} - 11844282545228742064047873611 q^{73} + 23064324112283654108935114044 q^{74} - 113150713372138400761225690091 q^{75} - 249937659186303259354652498546 q^{76} + 151320355163920448768284272789 q^{77} + 16772290959969974773537607139 q^{78} - 215276382827313017964798894971 q^{79} + 460341399684191274245185573318 q^{80} - 452147212615310124267146328691 q^{81} - 337632308630625749057308798961 q^{82} + 550605915117053147008455933189 q^{83} - 1400507069158520854121147121301 q^{84} - 226458329711397720833214597455 q^{85} + 337048954956812743638921219699 q^{86} + 356116806823636769305335586789 q^{87} - 1388970815891469206414850079875 q^{88} - 54357497501614699345697069711 q^{89} + 4541926083717923921152321341482 q^{90} - 2958973955852359010421060079886 q^{92} - 116456704676556247252701507022 q^{93} + 4079963731342148373414241265000 q^{94} + 1439870139531376874044014669741 q^{95} - 14137712632871027231839316874992 q^{96} - 1361322970673145949919060930495 q^{97} + 7189250272609137391604107804653 q^{98} + 5269803331430526955464508479589 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{31}^{\mathrm{new}}(\Gamma_1(23))\)

We only show spaces with odd 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
23.31.b \(\chi_{23}(22, \cdot)\) 23.31.b.a 1 1
23.31.b.b 2
23.31.b.c 56
23.31.d \(\chi_{23}(5, \cdot)\) 23.31.d.a 590 10