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Properties

Label 122.2
Level 122
Weight 2
Dimension 154
Nonzero newspaces 8
Newform subspaces 14
Sturm bound 1860
Trace bound 3

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Defining parameters

Level: \( N \) = \( 122 = 2 \cdot 61 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 8 \)
Newform subspaces: \( 14 \)
Sturm bound: \(1860\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(122))\).

Total New Old
Modular forms 525 154 371
Cusp forms 406 154 252
Eisenstein series 119 0 119

Trace form

\( 154 q - q^{2} - 4 q^{3} - q^{4} - 6 q^{5} - 4 q^{6} - 8 q^{7} - q^{8} - 13 q^{9} + O(q^{10}) \) \( 154 q - q^{2} - 4 q^{3} - q^{4} - 6 q^{5} - 4 q^{6} - 8 q^{7} - q^{8} - 13 q^{9} - 6 q^{10} - 12 q^{11} - 4 q^{12} - 14 q^{13} - 8 q^{14} - 24 q^{15} - q^{16} - 18 q^{17} - 13 q^{18} - 20 q^{19} - 6 q^{20} - 32 q^{21} - 12 q^{22} - 24 q^{23} - 4 q^{24} - 31 q^{25} - 14 q^{26} - 40 q^{27} - 8 q^{28} - 30 q^{29} - 24 q^{30} - 32 q^{31} - q^{32} - 48 q^{33} - 18 q^{34} - 48 q^{35} - 13 q^{36} - 38 q^{37} - 20 q^{38} - 56 q^{39} - 6 q^{40} - 42 q^{41} - 32 q^{42} - 44 q^{43} - 12 q^{44} - 78 q^{45} - 24 q^{46} + 12 q^{47} + 16 q^{48} + 83 q^{49} + 44 q^{50} + 48 q^{51} + 61 q^{52} + 6 q^{53} + 140 q^{54} + 168 q^{55} + 52 q^{56} + 160 q^{57} + 90 q^{58} + 60 q^{59} - 24 q^{60} + 199 q^{61} + 148 q^{62} + 156 q^{63} - q^{64} + 36 q^{65} + 72 q^{66} + 172 q^{67} + 42 q^{68} + 144 q^{69} + 132 q^{70} - 12 q^{71} + 62 q^{72} + 46 q^{73} + 37 q^{74} + 16 q^{75} - 36 q^{77} - 56 q^{78} - 80 q^{79} - 6 q^{80} - 121 q^{81} - 42 q^{82} - 84 q^{83} - 32 q^{84} - 108 q^{85} - 44 q^{86} - 120 q^{87} - 12 q^{88} - 90 q^{89} - 78 q^{90} - 112 q^{91} - 24 q^{92} - 128 q^{93} - 48 q^{94} - 120 q^{95} - 4 q^{96} - 98 q^{97} - 57 q^{98} - 156 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(122))\)

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
122.2.a \(\chi_{122}(1, \cdot)\) 122.2.a.a 1 1
122.2.a.b 2
122.2.a.c 3
122.2.b \(\chi_{122}(121, \cdot)\) 122.2.b.a 2 1
122.2.b.b 4
122.2.c \(\chi_{122}(13, \cdot)\) 122.2.c.a 4 2
122.2.c.b 6
122.2.e \(\chi_{122}(9, \cdot)\) 122.2.e.a 12 4
122.2.e.b 16
122.2.f \(\chi_{122}(75, \cdot)\) 122.2.f.a 8 2
122.2.g \(\chi_{122}(3, \cdot)\) 122.2.g.a 24 4
122.2.i \(\chi_{122}(15, \cdot)\) 122.2.i.a 16 8
122.2.i.b 24
122.2.k \(\chi_{122}(5, \cdot)\) 122.2.k.a 32 8

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(122))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(122)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(61))\)\(^{\oplus 2}\)