Properties

Label 58.2
Level 58
Weight 2
Dimension 34
Nonzero newspaces 4
Newform subspaces 6
Sturm bound 420
Trace bound 3

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Defining parameters

Level: \( N \) = \( 58 = 2 \cdot 29 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 6 \)
Sturm bound: \(420\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(58))\).

Total New Old
Modular forms 133 34 99
Cusp forms 78 34 44
Eisenstein series 55 0 55

Trace form

\( 34 q - q^{2} - 4 q^{3} - q^{4} - 6 q^{5} - 4 q^{6} - 8 q^{7} - q^{8} - 13 q^{9} + O(q^{10}) \) \( 34 q - q^{2} - 4 q^{3} - q^{4} - 6 q^{5} - 4 q^{6} - 8 q^{7} - q^{8} - 13 q^{9} - 6 q^{10} - 12 q^{11} - 4 q^{12} - 14 q^{13} - 8 q^{14} - 24 q^{15} - q^{16} - 18 q^{17} - 13 q^{18} - 20 q^{19} + q^{20} + 24 q^{21} + 16 q^{22} + 4 q^{23} + 24 q^{24} + 25 q^{25} + 21 q^{26} + 44 q^{27} - 8 q^{28} + 27 q^{29} + 60 q^{30} + 24 q^{31} - q^{32} + 36 q^{33} + 17 q^{34} + 8 q^{35} + 15 q^{36} - 10 q^{37} + 8 q^{38} + q^{40} - 42 q^{41} - 32 q^{42} - 44 q^{43} - 12 q^{44} - 43 q^{45} - 24 q^{46} - 20 q^{47} - 4 q^{48} - q^{49} - 31 q^{50} - 16 q^{51} - 14 q^{52} + 9 q^{53} - 40 q^{54} + 40 q^{55} - 8 q^{56} - 24 q^{57} - 29 q^{58} - 32 q^{59} - 24 q^{60} - 6 q^{61} - 32 q^{62} + 8 q^{63} - q^{64} - 21 q^{65} - 48 q^{66} - 12 q^{67} - 18 q^{68} - 40 q^{69} - 20 q^{70} + 40 q^{71} - 13 q^{72} + 17 q^{73} + 46 q^{74} + 16 q^{75} + 36 q^{76} + 44 q^{77} + 56 q^{78} - 24 q^{79} - 6 q^{80} + 103 q^{81} + 14 q^{82} + 28 q^{83} + 52 q^{84} + 60 q^{85} + 96 q^{86} + 24 q^{87} - 12 q^{88} + 50 q^{89} + 62 q^{90} + 56 q^{91} + 60 q^{92} - 16 q^{93} + 8 q^{94} + 104 q^{95} - 4 q^{96} - 35 q^{97} + 55 q^{98} + 40 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(58))\)

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
58.2.a \(\chi_{58}(1, \cdot)\) 58.2.a.a 1 1
58.2.a.b 1
58.2.b \(\chi_{58}(57, \cdot)\) 58.2.b.a 2 1
58.2.d \(\chi_{58}(7, \cdot)\) 58.2.d.a 6 6
58.2.d.b 12
58.2.e \(\chi_{58}(5, \cdot)\) 58.2.e.a 12 6

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(58))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(58)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(29))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(58))\)\(^{\oplus 1}\)