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

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

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 the 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

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