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

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

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