Properties

Label 23.10
Level 23
Weight 10
Dimension 187
Nonzero newspaces 2
Newforms 3
Sturm bound 440
Trace bound 1

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Defining parameters

Level: \( N \) = \( 23 \)
Weight: \( k \) = \( 10 \)
Nonzero newspaces: \( 2 \)
Newforms: \( 3 \)
Sturm bound: \(440\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_1(23))\).

Total New Old
Modular forms 209 207 2
Cusp forms 187 187 0
Eisenstein series 22 20 2

Trace form

\( 187q - 11q^{2} - 11q^{3} - 11q^{4} - 11q^{5} - 11q^{6} - 11q^{7} - 11q^{8} - 11q^{9} + O(q^{10}) \) \( 187q - 11q^{2} - 11q^{3} - 11q^{4} - 11q^{5} - 11q^{6} - 11q^{7} - 11q^{8} - 11q^{9} - 11q^{10} - 11q^{11} - 11q^{12} - 11q^{13} - 11q^{14} + 969023q^{15} - 478731q^{16} - 1054867q^{17} + 1519925q^{18} + 1526459q^{19} + 3198965q^{20} - 3575231q^{21} - 5153654q^{22} - 3650823q^{23} + 6167018q^{24} + 8299797q^{25} + 9664149q^{26} + 3875311q^{27} - 21469195q^{28} - 10200751q^{29} - 24330955q^{30} + 9969839q^{31} + 46627317q^{32} - 21902947q^{33} - 8377589q^{34} + 57736239q^{35} - 30672686q^{36} - 107778935q^{37} - 92052576q^{38} + 23347753q^{39} + 213344989q^{40} + 62844639q^{41} + 178280179q^{42} - 29184023q^{43} - 225229796q^{44} - 270641272q^{45} - 311125331q^{46} - 54389346q^{47} + 183376413q^{48} + 341786995q^{49} + 511328114q^{50} + 237700969q^{51} + 138729679q^{52} - 103750977q^{53} - 1104475251q^{54} - 96640643q^{55} + 210507990q^{56} + 59318281q^{57} + 513967300q^{58} - 118047545q^{59} - 1153719721q^{60} + 344711653q^{61} + 980989141q^{62} + 882717759q^{63} + 986185717q^{64} + 158418557q^{65} - 747426636q^{66} - 378627887q^{67} - 2822341654q^{68} - 1069913031q^{69} - 1006270870q^{70} + 56718519q^{71} + 1971614260q^{72} + 582788437q^{73} + 699926392q^{74} + 3594630963q^{75} + 4934994042q^{76} + 832730437q^{77} - 4315286437q^{78} - 4249645807q^{79} - 10615143550q^{80} - 5321334799q^{81} + 416976439q^{82} + 3425248739q^{83} + 14370912435q^{84} + 7253042687q^{85} + 779636011q^{86} + 2829378673q^{87} - 671992739q^{88} - 2402723741q^{89} - 12214147682q^{90} - 6034596590q^{91} - 6333894578q^{92} - 5895816058q^{93} - 1344916188q^{94} - 1504040945q^{95} + 17191683300q^{96} + 11525413603q^{97} + 12597404941q^{98} + 10210410199q^{99} + O(q^{100}) \)

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_1(23))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
23.10.a \(\chi_{23}(1, \cdot)\) 23.10.a.a 7 1
23.10.a.b 10
23.10.c \(\chi_{23}(2, \cdot)\) 23.10.c.a 170 10