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Properties

Label 178.2
Level 178
Weight 2
Dimension 329
Nonzero newspaces 6
Newform subspaces 17
Sturm bound 3960
Trace bound 2

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Defining parameters

Level: \( N \) = \( 178 = 2 \cdot 89 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 6 \)
Newform subspaces: \( 17 \)
Sturm bound: \(3960\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(178))\).

Total New Old
Modular forms 1078 329 749
Cusp forms 903 329 574
Eisenstein series 175 0 175

Trace form

\( 329 q - q^{2} - 4 q^{3} - q^{4} - 6 q^{5} - 4 q^{6} - 8 q^{7} - q^{8} - 13 q^{9} + O(q^{10}) \) \( 329 q - q^{2} - 4 q^{3} - q^{4} - 6 q^{5} - 4 q^{6} - 8 q^{7} - q^{8} - 13 q^{9} - 6 q^{10} - 12 q^{11} - 4 q^{12} - 14 q^{13} - 8 q^{14} - 24 q^{15} - q^{16} - 18 q^{17} - 13 q^{18} - 20 q^{19} - 6 q^{20} - 32 q^{21} - 12 q^{22} - 24 q^{23} - 4 q^{24} - 31 q^{25} - 14 q^{26} - 40 q^{27} - 8 q^{28} - 30 q^{29} - 24 q^{30} - 32 q^{31} - q^{32} - 48 q^{33} - 18 q^{34} - 48 q^{35} - 13 q^{36} - 38 q^{37} - 20 q^{38} - 56 q^{39} - 6 q^{40} - 42 q^{41} - 32 q^{42} - 44 q^{43} - 12 q^{44} - 78 q^{45} - 24 q^{46} - 48 q^{47} - 4 q^{48} - 57 q^{49} - 31 q^{50} - 72 q^{51} - 14 q^{52} - 54 q^{53} - 40 q^{54} - 72 q^{55} - 8 q^{56} - 80 q^{57} - 30 q^{58} - 60 q^{59} - 24 q^{60} - 62 q^{61} - 32 q^{62} - 104 q^{63} - q^{64} - 84 q^{65} - 48 q^{66} - 68 q^{67} - 18 q^{68} - 96 q^{69} - 48 q^{70} - 72 q^{71} + 31 q^{72} + 14 q^{73} + 72 q^{74} + 316 q^{75} + 68 q^{76} + 80 q^{77} + 208 q^{78} + 96 q^{79} + 16 q^{80} + 319 q^{81} + 134 q^{82} + 180 q^{83} + 56 q^{84} + 156 q^{85} + 132 q^{86} + 320 q^{87} + 76 q^{88} + 263 q^{89} + 450 q^{90} + 240 q^{91} + 64 q^{92} + 312 q^{93} + 128 q^{94} + 144 q^{95} + 84 q^{96} + 166 q^{97} + 119 q^{98} + 284 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(178))\)

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
178.2.a \(\chi_{178}(1, \cdot)\) 178.2.a.a 1 1
178.2.a.b 1
178.2.a.c 2
178.2.a.d 3
178.2.b \(\chi_{178}(177, \cdot)\) 178.2.b.a 2 1
178.2.b.b 2
178.2.b.c 4
178.2.c \(\chi_{178}(55, \cdot)\) 178.2.c.a 2 2
178.2.c.b 2
178.2.c.c 4
178.2.c.d 6
178.2.e \(\chi_{178}(39, \cdot)\) 178.2.e.a 30 10
178.2.e.b 50
178.2.f \(\chi_{178}(11, \cdot)\) 178.2.f.a 40 10
178.2.f.b 40
178.2.g \(\chi_{178}(5, \cdot)\) 178.2.g.a 60 20
178.2.g.b 80

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(178))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(178)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(89))\)\(^{\oplus 2}\)