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Properties

Label 41.6
Level 41
Weight 6
Dimension 330
Nonzero newspaces 6
Newform subspaces 8
Sturm bound 840
Trace bound 2

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Defining parameters

Level: \( N \) = \( 41 \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 6 \)
Newform subspaces: \( 8 \)
Sturm bound: \(840\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(41))\).

Total New Old
Modular forms 370 368 2
Cusp forms 330 330 0
Eisenstein series 40 38 2

Trace form

\( 330 q - 20 q^{2} - 20 q^{3} - 20 q^{4} - 20 q^{5} - 20 q^{6} - 20 q^{7} - 20 q^{8} - 20 q^{9} + O(q^{10}) \) \( 330 q - 20 q^{2} - 20 q^{3} - 20 q^{4} - 20 q^{5} - 20 q^{6} - 20 q^{7} - 20 q^{8} - 20 q^{9} - 20 q^{10} - 20 q^{11} - 20 q^{12} - 20 q^{13} - 20 q^{14} - 20 q^{15} - 20 q^{16} - 20 q^{17} - 20 q^{18} - 20 q^{19} - 20 q^{20} - 20 q^{21} - 20 q^{22} - 20 q^{23} - 20 q^{24} - 20 q^{25} - 20 q^{26} - 20 q^{27} - 20 q^{28} - 20 q^{29} - 76020 q^{30} + 200 q^{31} + 71660 q^{32} + 81640 q^{33} + 60980 q^{34} + 30980 q^{35} + 24620 q^{36} - 27080 q^{37} - 40180 q^{38} - 112420 q^{39} - 192040 q^{40} - 31200 q^{41} - 204200 q^{42} - 15400 q^{43} - 9620 q^{44} + 57980 q^{45} + 62220 q^{46} + 137920 q^{47} + 394220 q^{48} + 117780 q^{49} + 124980 q^{50} + 76240 q^{51} - 68340 q^{52} - 90000 q^{53} - 383220 q^{54} - 20 q^{55} - 20 q^{56} - 20 q^{57} - 20 q^{58} - 20 q^{59} - 20 q^{60} - 20 q^{61} - 20 q^{62} - 20 q^{63} - 20 q^{64} - 198430 q^{65} - 834500 q^{66} - 210560 q^{67} + 129080 q^{68} + 344860 q^{69} + 1173780 q^{70} + 500700 q^{71} + 1035160 q^{72} + 367260 q^{73} + 360100 q^{74} + 188620 q^{75} - 210320 q^{76} - 199140 q^{77} - 811820 q^{78} - 424740 q^{79} - 1232860 q^{80} - 1115410 q^{81} - 1554980 q^{82} - 472760 q^{83} - 1169220 q^{84} - 578190 q^{85} - 314220 q^{86} + 42460 q^{87} + 558180 q^{88} + 405660 q^{89} + 2162680 q^{90} + 1443020 q^{91} + 1234900 q^{92} + 863260 q^{93} + 1846960 q^{94} + 673500 q^{95} + 991780 q^{96} - 35940 q^{97} - 815920 q^{98} - 1112960 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(41))\)

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 available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
41.6.a \(\chi_{41}(1, \cdot)\) 41.6.a.a 6 1
41.6.a.b 10
41.6.b \(\chi_{41}(40, \cdot)\) 41.6.b.a 2 1
41.6.b.b 14
41.6.c \(\chi_{41}(9, \cdot)\) 41.6.c.a 34 2
41.6.d \(\chi_{41}(10, \cdot)\) 41.6.d.a 64 4
41.6.f \(\chi_{41}(4, \cdot)\) 41.6.f.a 64 4
41.6.g \(\chi_{41}(2, \cdot)\) 41.6.g.a 136 8