Properties

Label 23.7
Level 23
Weight 7
Dimension 121
Nonzero newspaces 2
Newforms 4
Sturm bound 308
Trace bound 1

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Defining parameters

Level: \( N \) = \( 23 \)
Weight: \( k \) = \( 7 \)
Nonzero newspaces: \( 2 \)
Newforms: \( 4 \)
Sturm bound: \(308\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(\Gamma_1(23))\).

Total New Old
Modular forms 143 143 0
Cusp forms 121 121 0
Eisenstein series 22 22 0

Trace form

\( 121q - 11q^{2} - 11q^{3} - 11q^{4} - 11q^{5} - 11q^{6} - 11q^{7} - 11q^{8} - 11q^{9} + O(q^{10}) \) \( 121q - 11q^{2} - 11q^{3} - 11q^{4} - 11q^{5} - 11q^{6} - 11q^{7} - 11q^{8} - 11q^{9} - 11q^{10} - 11q^{11} - 11q^{12} - 11q^{13} - 11q^{14} + 10461q^{15} - 31691q^{16} - 11451q^{17} + 13365q^{18} + 15829q^{19} + 78837q^{20} + 40909q^{21} - 32923q^{23} - 179542q^{24} - 69707q^{25} - 54571q^{26} - 18491q^{27} + 101365q^{28} + 58509q^{29} + 311157q^{30} + 59389q^{31} - 59851q^{32} - 234267q^{33} + 400015q^{34} - 71511q^{35} - 601436q^{36} - 446699q^{37} - 275286q^{38} + 64141q^{39} + 626989q^{40} + 235389q^{41} + 1274119q^{42} + 428989q^{43} + 434434q^{44} - 542531q^{46} - 518430q^{47} - 1390675q^{48} - 1141283q^{49} - 1203136q^{50} - 463331q^{51} - 247181q^{52} + 183909q^{53} + 3219117q^{54} + 1417405q^{55} + 175560q^{56} + 78661q^{57} - 970706q^{58} - 1638087q^{59} - 2858581q^{60} + 495253q^{61} + 1544389q^{62} + 1713789q^{63} + 2973685q^{64} + 2406085q^{65} + 2124936q^{66} + 290389q^{67} - 770451q^{69} - 2392918q^{70} - 2086931q^{71} - 5921630q^{72} - 1024331q^{73} - 1038180q^{74} + 1483669q^{75} - 1754258q^{76} - 2268651q^{77} - 6512781q^{78} - 833723q^{79} + 2796838q^{80} + 138413q^{81} + 3609199q^{82} + 2924229q^{83} + 6932651q^{84} + 4488385q^{85} + 1596771q^{86} + 9184549q^{87} + 5363325q^{88} + 2950849q^{89} + 5004362q^{90} - 2477486q^{92} - 6461422q^{93} - 6892600q^{94} - 3255219q^{95} - 13057616q^{96} - 6375215q^{97} - 11621907q^{98} - 16096091q^{99} + O(q^{100}) \)

Decomposition of \(S_{7}^{\mathrm{new}}(\Gamma_1(23))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
23.7.b \(\chi_{23}(22, \cdot)\) 23.7.b.a 1 1
23.7.b.b 2
23.7.b.c 8
23.7.d \(\chi_{23}(5, \cdot)\) 23.7.d.a 110 10