Properties

Label 13.5
Level 13
Weight 5
Dimension 22
Nonzero newspaces 2
Newform subspaces 2
Sturm bound 70
Trace bound 1

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 13 \)
Weight: \( k \) = \( 5 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 2 \)
Sturm bound: \(70\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(\Gamma_1(13))\).

Total New Old
Modular forms 34 34 0
Cusp forms 22 22 0
Eisenstein series 12 12 0

Trace form

\( 22 q - 6 q^{2} - 6 q^{3} - 6 q^{4} - 6 q^{5} - 6 q^{6} + 104 q^{7} - 6 q^{8} - 222 q^{9} + O(q^{10}) \) \( 22 q - 6 q^{2} - 6 q^{3} - 6 q^{4} - 6 q^{5} - 6 q^{6} + 104 q^{7} - 6 q^{8} - 222 q^{9} - 486 q^{10} - 132 q^{11} + 294 q^{13} + 564 q^{14} + 750 q^{15} + 1274 q^{16} + 984 q^{17} + 1632 q^{18} - 766 q^{19} - 3534 q^{20} - 3204 q^{21} - 3156 q^{22} - 1014 q^{23} - 2166 q^{24} + 1524 q^{26} + 3588 q^{27} + 7648 q^{28} + 4998 q^{29} + 9162 q^{30} + 592 q^{31} - 2904 q^{32} - 3312 q^{33} - 7806 q^{34} - 9096 q^{35} - 15750 q^{36} - 3548 q^{37} + 8178 q^{39} + 18108 q^{40} + 9030 q^{41} + 8328 q^{42} - 1368 q^{43} + 6780 q^{44} - 5976 q^{45} - 14730 q^{46} - 5388 q^{47} - 12438 q^{48} - 11820 q^{49} - 13896 q^{50} + 5332 q^{52} + 9312 q^{53} + 13056 q^{54} + 13344 q^{55} + 8124 q^{56} + 6936 q^{57} + 9546 q^{58} + 1992 q^{59} - 5148 q^{60} + 5826 q^{61} + 19614 q^{62} + 11352 q^{63} - 10266 q^{65} - 28464 q^{66} - 14782 q^{67} - 17016 q^{68} + 2412 q^{69} - 27156 q^{70} - 22722 q^{71} + 7440 q^{72} - 9574 q^{73} - 1338 q^{74} + 8280 q^{75} + 14198 q^{76} - 5952 q^{78} - 14448 q^{79} - 9516 q^{80} - 17322 q^{81} - 5346 q^{82} + 32052 q^{83} + 32244 q^{84} + 39546 q^{85} + 96636 q^{86} + 64926 q^{87} + 40836 q^{88} + 19506 q^{89} - 21892 q^{91} - 44580 q^{92} - 88440 q^{93} - 66762 q^{94} - 98574 q^{95} - 73944 q^{96} + 27790 q^{97} + 20058 q^{98} - 4140 q^{99} + O(q^{100}) \)

Decomposition of \(S_{5}^{\mathrm{new}}(\Gamma_1(13))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
13.5.d \(\chi_{13}(5, \cdot)\) 13.5.d.a 6 2
13.5.f \(\chi_{13}(2, \cdot)\) 13.5.f.a 16 4