Properties

Label 118.2
Level 118
Weight 2
Dimension 144
Nonzero newspaces 2
Newform subspaces 6
Sturm bound 1740
Trace bound 1

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Defining parameters

Level: \( N \) = \( 118 = 2 \cdot 59 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 6 \)
Sturm bound: \(1740\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(118))\).

Total New Old
Modular forms 493 144 349
Cusp forms 378 144 234
Eisenstein series 115 0 115

Trace form

\( 144 q - q^{2} - 4 q^{3} - q^{4} - 6 q^{5} - 4 q^{6} - 8 q^{7} - q^{8} - 13 q^{9} + O(q^{10}) \) \( 144 q - q^{2} - 4 q^{3} - q^{4} - 6 q^{5} - 4 q^{6} - 8 q^{7} - q^{8} - 13 q^{9} - 6 q^{10} - 12 q^{11} - 4 q^{12} - 14 q^{13} - 8 q^{14} - 24 q^{15} - q^{16} - 18 q^{17} - 13 q^{18} - 20 q^{19} - 6 q^{20} - 32 q^{21} - 12 q^{22} - 24 q^{23} - 4 q^{24} - 31 q^{25} - 14 q^{26} - 40 q^{27} - 8 q^{28} - 30 q^{29} - 24 q^{30} - 32 q^{31} - q^{32} - 48 q^{33} - 18 q^{34} - 48 q^{35} - 13 q^{36} - 38 q^{37} - 20 q^{38} - 56 q^{39} - 6 q^{40} - 42 q^{41} - 32 q^{42} - 44 q^{43} - 12 q^{44} - 20 q^{45} + 34 q^{46} + 10 q^{47} - 4 q^{48} + 59 q^{49} + 85 q^{50} + 160 q^{51} + 44 q^{52} + 62 q^{53} + 163 q^{54} + 102 q^{55} - 8 q^{56} + 210 q^{57} + 28 q^{58} + 57 q^{59} + 150 q^{60} + 54 q^{61} + 26 q^{62} + 186 q^{63} - q^{64} + 90 q^{65} + 155 q^{66} + 48 q^{67} + 40 q^{68} + 136 q^{69} + 68 q^{70} + 44 q^{71} - 13 q^{72} - 16 q^{73} + 20 q^{74} - 66 q^{75} - 20 q^{76} - 96 q^{77} - 56 q^{78} - 80 q^{79} - 6 q^{80} - 121 q^{81} - 42 q^{82} - 84 q^{83} - 32 q^{84} - 108 q^{85} - 44 q^{86} - 120 q^{87} - 12 q^{88} - 90 q^{89} - 78 q^{90} - 112 q^{91} - 24 q^{92} - 128 q^{93} - 48 q^{94} - 120 q^{95} - 4 q^{96} - 98 q^{97} - 57 q^{98} - 69 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(118))\)

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
118.2.a \(\chi_{118}(1, \cdot)\) 118.2.a.a 1 1
118.2.a.b 1
118.2.a.c 1
118.2.a.d 1
118.2.c \(\chi_{118}(3, \cdot)\) 118.2.c.a 56 28
118.2.c.b 84

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(118))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(118)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(59))\)\(^{\oplus 2}\)