Properties

Label 13.10
Level 13
Weight 10
Dimension 57
Nonzero newspaces 4
Newform subspaces 5
Sturm bound 140
Trace bound 1

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Defining parameters

Level: \( N \) = \( 13 \)
Weight: \( k \) = \( 10 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 5 \)
Sturm bound: \(140\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_1(13))\).

Total New Old
Modular forms 69 67 2
Cusp forms 57 57 0
Eisenstein series 12 10 2

Trace form

\( 57 q - 6 q^{2} - 6 q^{3} - 6 q^{4} - 6 q^{5} - 6 q^{6} - 2058 q^{7} - 36870 q^{8} - 6 q^{9} + O(q^{10}) \) \( 57 q - 6 q^{2} - 6 q^{3} - 6 q^{4} - 6 q^{5} - 6 q^{6} - 2058 q^{7} - 36870 q^{8} - 6 q^{9} + 153354 q^{10} - 18426 q^{11} - 414732 q^{12} - 108438 q^{13} + 363828 q^{14} + 596802 q^{15} - 6 q^{16} - 1407705 q^{17} + 996060 q^{18} - 945954 q^{19} + 47490 q^{20} + 1091994 q^{21} + 7251264 q^{22} + 1079118 q^{23} - 9699510 q^{24} - 5859387 q^{25} - 8735256 q^{26} + 3339312 q^{27} + 14239284 q^{28} + 24371211 q^{29} + 5598570 q^{30} - 21628782 q^{31} - 52435044 q^{32} - 17053806 q^{33} + 38183442 q^{34} + 62746314 q^{35} + 34768494 q^{36} - 53509041 q^{37} - 75064908 q^{38} - 80178942 q^{39} + 106596636 q^{40} + 56747037 q^{41} - 14526420 q^{42} - 80175066 q^{43} + 56834772 q^{44} + 73439469 q^{45} + 170228838 q^{46} - 6163842 q^{47} - 56937270 q^{48} - 34849122 q^{49} - 128608704 q^{50} - 71585676 q^{51} - 288763668 q^{52} - 114189792 q^{53} - 246491784 q^{54} + 163894998 q^{55} + 411453492 q^{56} + 565707582 q^{57} + 537801978 q^{58} + 154378806 q^{59} - 60832368 q^{60} - 782273979 q^{61} - 1008838710 q^{62} + 100702062 q^{63} + 550962348 q^{64} + 106769433 q^{65} - 1355116728 q^{66} - 1242683958 q^{67} - 336262764 q^{68} + 1099685022 q^{69} + 2304349956 q^{70} + 1546925586 q^{71} + 2551405308 q^{72} + 129804042 q^{73} - 504794946 q^{74} - 1302985644 q^{75} - 2241261522 q^{76} - 2326903116 q^{77} - 3971344908 q^{78} - 833767980 q^{79} + 3055272 q^{80} + 714226488 q^{81} + 2614660038 q^{82} + 3843007890 q^{83} + 6813050412 q^{84} + 1267441977 q^{85} + 2993016648 q^{86} + 2516626782 q^{87} - 5351686524 q^{88} - 5347573806 q^{89} - 16198597968 q^{90} - 6798799098 q^{91} - 2717293548 q^{92} + 2392035078 q^{93} + 8666109342 q^{94} + 7621807350 q^{95} + 10009032444 q^{96} + 4709667126 q^{97} + 8696899974 q^{98} + 7410530166 q^{99} + O(q^{100}) \)

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_1(13))\)

We only show spaces with even 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
13.10.a \(\chi_{13}(1, \cdot)\) 13.10.a.a 4 1
13.10.a.b 5
13.10.b \(\chi_{13}(12, \cdot)\) 13.10.b.a 10 1
13.10.c \(\chi_{13}(3, \cdot)\) 13.10.c.a 18 2
13.10.e \(\chi_{13}(4, \cdot)\) 13.10.e.a 20 2