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Properties

Label 41.2
Level 41
Weight 2
Dimension 51
Nonzero newspaces 6
Newform subspaces 6
Sturm bound 280
Trace bound 2

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Defining parameters

Level: \( N \) = \( 41 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 6 \)
Newform subspaces: \( 6 \)
Sturm bound: \(280\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(41))\).

Total New Old
Modular forms 90 90 0
Cusp forms 51 51 0
Eisenstein series 39 39 0

Trace form

\( 51 q - 17 q^{2} - 16 q^{3} - 13 q^{4} - 14 q^{5} - 8 q^{6} - 12 q^{7} - 5 q^{8} - 7 q^{9} + O(q^{10}) \) \( 51 q - 17 q^{2} - 16 q^{3} - 13 q^{4} - 14 q^{5} - 8 q^{6} - 12 q^{7} - 5 q^{8} - 7 q^{9} - 2 q^{10} - 8 q^{11} + 8 q^{12} - 6 q^{13} + 4 q^{14} + 4 q^{15} + 11 q^{16} - 2 q^{17} + 19 q^{18} + 22 q^{20} + 12 q^{21} + 16 q^{22} + 4 q^{23} + 40 q^{24} + 11 q^{25} + 22 q^{26} + 20 q^{27} + 36 q^{28} + 10 q^{29} + 12 q^{30} - 8 q^{31} - 27 q^{32} - 32 q^{33} - 16 q^{34} - 12 q^{35} - 69 q^{36} - 42 q^{37} - 44 q^{39} - 70 q^{40} + q^{41} - 104 q^{42} + 4 q^{43} - 56 q^{44} - 22 q^{45} + 12 q^{46} - 32 q^{47} - 36 q^{48} - 3 q^{49} + 23 q^{50} - 8 q^{51} + 8 q^{52} + 14 q^{53} + 60 q^{54} + 52 q^{55} + 100 q^{56} + 60 q^{57} + 70 q^{58} + 40 q^{59} + 148 q^{60} + 42 q^{61} + 76 q^{62} + 84 q^{63} + 107 q^{64} + 54 q^{65} + 44 q^{66} - 12 q^{67} + 6 q^{68} - 4 q^{69} - 76 q^{70} - 28 q^{71} - 5 q^{72} - 26 q^{73} - 26 q^{74} - 56 q^{75} - 180 q^{76} - 4 q^{77} - 52 q^{78} - 20 q^{79} - 74 q^{80} - 89 q^{81} - 137 q^{82} - 36 q^{83} - 76 q^{84} - 82 q^{85} - 88 q^{86} + 20 q^{87} - 40 q^{88} - 10 q^{89} - 86 q^{90} - 68 q^{91} + 28 q^{92} + 28 q^{93} - 56 q^{94} + 20 q^{95} + 32 q^{96} - 2 q^{97} + 51 q^{98} + 76 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(41))\)

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
41.2.a \(\chi_{41}(1, \cdot)\) 41.2.a.a 3 1
41.2.b \(\chi_{41}(40, \cdot)\) 41.2.b.a 2 1
41.2.c \(\chi_{41}(9, \cdot)\) 41.2.c.a 6 2
41.2.d \(\chi_{41}(10, \cdot)\) 41.2.d.a 8 4
41.2.f \(\chi_{41}(4, \cdot)\) 41.2.f.a 8 4
41.2.g \(\chi_{41}(2, \cdot)\) 41.2.g.a 24 8