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Properties

Label 158.2
Level 158
Weight 2
Dimension 259
Nonzero newspaces 4
Newform subspaces 14
Sturm bound 3120
Trace bound 1

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Defining parameters

Level: \( N \) = \( 158 = 2 \cdot 79 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 14 \)
Sturm bound: \(3120\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(158))\).

Total New Old
Modular forms 858 259 599
Cusp forms 703 259 444
Eisenstein series 155 0 155

Trace form

\( 259 q - q^{2} - 4 q^{3} - q^{4} - 6 q^{5} - 4 q^{6} - 8 q^{7} - q^{8} - 13 q^{9} + O(q^{10}) \) \( 259 q - q^{2} - 4 q^{3} - q^{4} - 6 q^{5} - 4 q^{6} - 8 q^{7} - q^{8} - 13 q^{9} - 6 q^{10} - 12 q^{11} - 4 q^{12} - 14 q^{13} - 8 q^{14} - 24 q^{15} - q^{16} - 18 q^{17} - 13 q^{18} - 20 q^{19} - 6 q^{20} - 32 q^{21} - 12 q^{22} - 24 q^{23} - 4 q^{24} - 31 q^{25} - 14 q^{26} - 40 q^{27} - 8 q^{28} - 30 q^{29} - 24 q^{30} - 32 q^{31} - q^{32} - 48 q^{33} - 18 q^{34} - 48 q^{35} - 13 q^{36} - 38 q^{37} - 20 q^{38} - 56 q^{39} - 6 q^{40} - 42 q^{41} - 32 q^{42} - 44 q^{43} - 12 q^{44} - 78 q^{45} - 24 q^{46} - 48 q^{47} - 4 q^{48} - 57 q^{49} - 31 q^{50} - 72 q^{51} - 14 q^{52} - 54 q^{53} - 40 q^{54} - 72 q^{55} - 8 q^{56} - 80 q^{57} - 30 q^{58} - 60 q^{59} - 24 q^{60} - 62 q^{61} - 32 q^{62} - q^{64} + 72 q^{65} + 108 q^{66} + 114 q^{67} + 60 q^{68} + 216 q^{69} + 264 q^{70} + 84 q^{71} - 13 q^{72} + 82 q^{73} + 118 q^{74} + 188 q^{75} + 162 q^{76} + 138 q^{77} + 100 q^{78} + 389 q^{79} - 6 q^{80} + 347 q^{81} + 114 q^{82} + 150 q^{83} + 150 q^{84} + 204 q^{85} + 112 q^{86} + 36 q^{87} - 12 q^{88} + 66 q^{89} + 234 q^{90} + 200 q^{91} + 54 q^{92} + 54 q^{93} + 108 q^{94} + 36 q^{95} - 4 q^{96} + 6 q^{97} - 57 q^{98} - 156 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(158))\)

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
158.2.a \(\chi_{158}(1, \cdot)\) 158.2.a.a 1 1
158.2.a.b 1
158.2.a.c 1
158.2.a.d 1
158.2.a.e 1
158.2.a.f 2
158.2.c \(\chi_{158}(23, \cdot)\) 158.2.c.a 2 2
158.2.c.b 2
158.2.c.c 4
158.2.c.d 4
158.2.e \(\chi_{158}(21, \cdot)\) 158.2.e.a 48 12
158.2.e.b 48
158.2.g \(\chi_{158}(5, \cdot)\) 158.2.g.a 72 24
158.2.g.b 72

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(158))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(158)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(79))\)\(^{\oplus 2}\)