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

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

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