Properties

Label 13.8
Level 13
Weight 8
Dimension 43
Nonzero newspaces 4
Newform subspaces 6
Sturm bound 112
Trace bound 1

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Defining parameters

Level: \( N \) = \( 13 \)
Weight: \( k \) = \( 8 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 6 \)
Sturm bound: \(112\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_1(13))\).

Total New Old
Modular forms 55 53 2
Cusp forms 43 43 0
Eisenstein series 12 10 2

Trace form

\( 43 q - 6 q^{2} - 6 q^{3} - 6 q^{4} - 6 q^{5} - 6 q^{6} - 1520 q^{7} + 4602 q^{8} - 5838 q^{9} + O(q^{10}) \) \( 43 q - 6 q^{2} - 6 q^{3} - 6 q^{4} - 6 q^{5} - 6 q^{6} - 1520 q^{7} + 4602 q^{8} - 5838 q^{9} - 9966 q^{10} + 3948 q^{11} + 34548 q^{12} + 14958 q^{13} - 10860 q^{14} - 41154 q^{15} - 81926 q^{16} - 65769 q^{17} + 249780 q^{18} + 153526 q^{19} - 106302 q^{20} - 342192 q^{21} - 219216 q^{22} + 14958 q^{23} + 502602 q^{24} + 234363 q^{25} + 409464 q^{26} + 154176 q^{27} - 681548 q^{28} + 76953 q^{29} - 626262 q^{30} - 258056 q^{31} - 1050948 q^{32} + 36528 q^{33} + 700050 q^{34} + 399624 q^{35} + 320958 q^{36} - 249245 q^{37} + 1975380 q^{38} - 369030 q^{39} + 2796252 q^{40} + 2173287 q^{41} + 619068 q^{42} - 1491724 q^{43} - 6740220 q^{44} - 7009371 q^{45} - 6362874 q^{46} - 520680 q^{47} + 4751178 q^{48} + 5470856 q^{49} + 7643448 q^{50} + 5202828 q^{51} + 6489628 q^{52} + 5697084 q^{53} + 5023944 q^{54} - 3327552 q^{55} - 12589788 q^{56} - 14632344 q^{57} - 15795486 q^{58} - 7107960 q^{59} - 10369728 q^{60} + 2597415 q^{61} + 213786 q^{62} + 24945120 q^{63} + 42145260 q^{64} + 25073715 q^{65} + 13473096 q^{66} - 10324958 q^{67} - 20309340 q^{68} - 20351532 q^{69} - 38565900 q^{70} - 19914258 q^{71} - 46047252 q^{72} - 12678410 q^{73} + 368070 q^{74} + 25169952 q^{75} + 59478862 q^{76} + 44006880 q^{77} + 85447572 q^{78} + 15844488 q^{79} + 9329784 q^{80} - 27657246 q^{81} - 52917618 q^{82} - 35849820 q^{83} - 80552724 q^{84} - 66082509 q^{85} - 61274616 q^{86} + 12139794 q^{87} + 50076132 q^{88} + 53885130 q^{89} + 128173584 q^{90} + 43758208 q^{91} + 88422900 q^{92} + 601932 q^{93} - 15292674 q^{94} - 80709522 q^{95} - 200332404 q^{96} - 74861486 q^{97} - 47531130 q^{98} - 2915364 q^{99} + O(q^{100}) \)

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_1(13))\)

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
13.8.a \(\chi_{13}(1, \cdot)\) 13.8.a.a 1 1
13.8.a.b 2
13.8.a.c 4
13.8.b \(\chi_{13}(12, \cdot)\) 13.8.b.a 6 1
13.8.c \(\chi_{13}(3, \cdot)\) 13.8.c.a 16 2
13.8.e \(\chi_{13}(4, \cdot)\) 13.8.e.a 14 2