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Properties

Label 13.7
Level 13
Weight 7
Dimension 36
Nonzero newspaces 2
Newform subspaces 2
Sturm bound 98
Trace bound 1

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Defining parameters

Level: \( N \) = \( 13 \)
Weight: \( k \) = \( 7 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 2 \)
Sturm bound: \(98\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(\Gamma_1(13))\).

Total New Old
Modular forms 48 48 0
Cusp forms 36 36 0
Eisenstein series 12 12 0

Trace form

\( 36 q - 6 q^{2} - 6 q^{3} - 6 q^{4} - 6 q^{5} - 6 q^{6} + 714 q^{7} - 2310 q^{8} - 6 q^{9} + O(q^{10}) \) \( 36 q - 6 q^{2} - 6 q^{3} - 6 q^{4} - 6 q^{5} - 6 q^{6} + 714 q^{7} - 2310 q^{8} - 6 q^{9} + 4674 q^{10} + 1914 q^{11} - 5478 q^{13} - 9132 q^{14} - 7782 q^{15} - 6 q^{16} + 20898 q^{17} + 9624 q^{18} - 12270 q^{19} - 33678 q^{20} + 3114 q^{21} + 66684 q^{22} + 29634 q^{23} + 78762 q^{24} - 57756 q^{26} - 127524 q^{27} - 36480 q^{28} - 89082 q^{29} - 247734 q^{30} - 57102 q^{31} + 115944 q^{32} + 261594 q^{33} + 361794 q^{34} + 263634 q^{35} + 105066 q^{36} - 71682 q^{37} + 166362 q^{39} - 379524 q^{40} - 547632 q^{41} - 984840 q^{42} - 480486 q^{43} - 308340 q^{44} + 312804 q^{45} + 967638 q^{46} + 702474 q^{47} + 1606410 q^{48} + 854562 q^{49} + 839136 q^{50} - 1350204 q^{52} - 887940 q^{53} - 2142480 q^{54} - 1469526 q^{55} - 1461108 q^{56} - 543486 q^{57} + 113826 q^{58} + 573594 q^{59} + 3294612 q^{60} + 1782372 q^{61} + 3741966 q^{62} + 2202042 q^{63} - 2077032 q^{65} - 5495280 q^{66} - 2932278 q^{67} - 2882184 q^{68} - 1475766 q^{69} + 332412 q^{70} + 1481082 q^{71} + 3080544 q^{72} + 2914554 q^{73} + 5533470 q^{74} + 3466008 q^{75} + 1769142 q^{76} - 1496064 q^{78} - 1809660 q^{79} - 7899708 q^{80} - 4789212 q^{81} - 3540426 q^{82} - 2747166 q^{83} - 268140 q^{84} + 3615312 q^{85} + 3572508 q^{86} + 2640762 q^{87} + 4478052 q^{88} - 344622 q^{89} - 1858038 q^{91} + 2026812 q^{92} - 511782 q^{93} - 4686090 q^{94} - 2753718 q^{95} - 3082824 q^{96} + 3241602 q^{97} + 6023610 q^{98} + 7231194 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{7}^{\mathrm{new}}(\Gamma_1(13))\)

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
13.7.d \(\chi_{13}(5, \cdot)\) 13.7.d.a 12 2
13.7.f \(\chi_{13}(2, \cdot)\) 13.7.f.a 24 4