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Properties

Label 13.11
Level 13
Weight 11
Dimension 64
Nonzero newspaces 2
Newform subspaces 2
Sturm bound 154
Trace bound 1

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Defining parameters

Level: \( N \) = \( 13 \)
Weight: \( k \) = \( 11 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 2 \)
Sturm bound: \(154\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{11}(\Gamma_1(13))\).

Total New Old
Modular forms 76 76 0
Cusp forms 64 64 0
Eisenstein series 12 12 0

Trace form

\( 64 q - 6 q^{2} - 6 q^{3} - 6 q^{4} - 6 q^{5} - 6 q^{6} - 7456 q^{7} + 147450 q^{8} - 157470 q^{9} + O(q^{10}) \) \( 64 q - 6 q^{2} - 6 q^{3} - 6 q^{4} - 6 q^{5} - 6 q^{6} - 7456 q^{7} + 147450 q^{8} - 157470 q^{9} - 37926 q^{10} + 294228 q^{11} - 1227738 q^{13} - 756108 q^{14} + 1892478 q^{15} + 5242874 q^{16} + 2121648 q^{17} - 13319952 q^{18} + 8292890 q^{19} + 7233522 q^{20} - 32239044 q^{21} - 3943716 q^{22} + 14209650 q^{23} + 66932778 q^{24} - 58420476 q^{26} - 94603764 q^{27} - 42152960 q^{28} + 360834 q^{29} + 386524746 q^{30} + 86481376 q^{31} - 246646872 q^{32} - 358403904 q^{33} - 238255806 q^{34} + 270086184 q^{35} + 862663626 q^{36} - 89948216 q^{37} - 114371022 q^{39} - 1495270404 q^{40} - 40860516 q^{41} + 989137560 q^{42} + 484189248 q^{43} + 755584044 q^{44} - 689980446 q^{45} - 1182412266 q^{46} - 462398580 q^{47} - 384517494 q^{48} + 1432995756 q^{49} + 3784343496 q^{50} - 3761020508 q^{52} - 1251117528 q^{53} - 188393808 q^{54} - 990869016 q^{55} - 784908372 q^{56} + 414004128 q^{57} + 2654091402 q^{58} + 1581718176 q^{59} + 4463727732 q^{60} - 2668039476 q^{61} - 480851634 q^{62} - 7749794544 q^{63} + 10048236228 q^{65} + 11380456848 q^{66} - 7736869390 q^{67} - 13241644584 q^{68} - 8061602724 q^{69} - 10860187908 q^{70} - 2690760114 q^{71} + 21419991744 q^{72} + 15932767610 q^{73} + 17420705862 q^{74} + 2520930528 q^{75} - 2849673610 q^{76} - 15349151712 q^{78} + 947674896 q^{79} - 32231060508 q^{80} - 22109338842 q^{81} - 40275130626 q^{82} - 222571212 q^{83} + 25211545620 q^{84} + 48229514352 q^{85} + 27564684060 q^{86} + 8360182926 q^{87} + 41091238308 q^{88} + 19174360266 q^{89} - 9908224924 q^{91} - 62579932164 q^{92} - 47597893944 q^{93} - 27308083914 q^{94} - 20960240478 q^{95} - 80477408808 q^{96} + 29400101014 q^{97} - 1133576070 q^{98} + 98659951308 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{11}^{\mathrm{new}}(\Gamma_1(13))\)

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
13.11.d \(\chi_{13}(5, \cdot)\) 13.11.d.a 20 2
13.11.f \(\chi_{13}(2, \cdot)\) 13.11.f.a 44 4