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Properties

Label 93.2
Level 93
Weight 2
Dimension 209
Nonzero newspaces 8
Newform subspaces 18
Sturm bound 1280
Trace bound 1

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Defining parameters

Level: \( N \) = \( 93 = 3 \cdot 31 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 8 \)
Newform subspaces: \( 18 \)
Sturm bound: \(1280\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(93))\).

Total New Old
Modular forms 380 269 111
Cusp forms 261 209 52
Eisenstein series 119 60 59

Trace form

\( 209 q - 3 q^{2} - 16 q^{3} - 37 q^{4} - 6 q^{5} - 18 q^{6} - 38 q^{7} - 15 q^{8} - 16 q^{9} + O(q^{10}) \) \( 209 q - 3 q^{2} - 16 q^{3} - 37 q^{4} - 6 q^{5} - 18 q^{6} - 38 q^{7} - 15 q^{8} - 16 q^{9} - 48 q^{10} - 12 q^{11} - 22 q^{12} - 44 q^{13} - 24 q^{14} - 21 q^{15} - 61 q^{16} - 18 q^{17} - 18 q^{18} - 50 q^{19} - 42 q^{20} - 18 q^{21} - 6 q^{22} + 6 q^{23} + 30 q^{24} + 9 q^{25} + 18 q^{26} - 16 q^{27} + 74 q^{28} + 30 q^{29} + 42 q^{30} - q^{31} + 117 q^{32} + 3 q^{33} + 36 q^{34} + 12 q^{35} - 2 q^{36} + 22 q^{37} + 6 q^{39} - 12 q^{41} - 9 q^{42} - 64 q^{43} - 84 q^{44} - 21 q^{45} - 102 q^{46} - 48 q^{47} - q^{48} - 27 q^{49} + 57 q^{50} + 57 q^{51} + 22 q^{52} + 6 q^{53} + 147 q^{54} + 18 q^{55} + 150 q^{56} + 55 q^{57} + 90 q^{58} + 138 q^{60} + 118 q^{61} + 87 q^{62} + 82 q^{63} + 83 q^{64} + 96 q^{65} + 174 q^{66} - 38 q^{67} + 84 q^{68} + 51 q^{69} + 96 q^{70} + 48 q^{71} + 135 q^{72} - 44 q^{73} + 36 q^{74} + 29 q^{75} - 20 q^{76} - 36 q^{77} - 102 q^{78} - 110 q^{79} - 186 q^{80} - 76 q^{81} - 156 q^{82} - 84 q^{83} - 251 q^{84} - 138 q^{85} - 132 q^{86} - 105 q^{87} - 210 q^{88} - 90 q^{89} - 213 q^{90} - 142 q^{91} - 168 q^{92} - 166 q^{93} - 204 q^{94} - 120 q^{95} - 213 q^{96} - 128 q^{97} - 171 q^{98} - 102 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(93))\)

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
93.2.a \(\chi_{93}(1, \cdot)\) 93.2.a.a 2 1
93.2.a.b 3
93.2.c \(\chi_{93}(92, \cdot)\) 93.2.c.a 8 1
93.2.e \(\chi_{93}(25, \cdot)\) 93.2.e.a 4 2
93.2.e.b 6
93.2.f \(\chi_{93}(4, \cdot)\) 93.2.f.a 8 4
93.2.f.b 16
93.2.g \(\chi_{93}(26, \cdot)\) 93.2.g.a 2 2
93.2.g.b 2
93.2.g.c 2
93.2.g.d 4
93.2.g.e 4
93.2.g.f 4
93.2.k \(\chi_{93}(23, \cdot)\) 93.2.k.a 32 4
93.2.m \(\chi_{93}(7, \cdot)\) 93.2.m.a 16 8
93.2.m.b 24
93.2.p \(\chi_{93}(11, \cdot)\) 93.2.p.a 8 8
93.2.p.b 64

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(93))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(93)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(31))\)\(^{\oplus 2}\)