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Properties

Label 393.2
Level 393
Weight 2
Dimension 4159
Nonzero newspaces 8
Newform subspaces 18
Sturm bound 22880
Trace bound 1

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Defining parameters

Level: \( N \) = \( 393 = 3 \cdot 131 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 8 \)
Newform subspaces: \( 18 \)
Sturm bound: \(22880\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(393))\).

Total New Old
Modular forms 5980 4419 1561
Cusp forms 5461 4159 1302
Eisenstein series 519 260 259

Trace form

\( 4159 q - 3 q^{2} - 66 q^{3} - 137 q^{4} - 6 q^{5} - 68 q^{6} - 138 q^{7} - 15 q^{8} - 66 q^{9} + O(q^{10}) \) \( 4159 q - 3 q^{2} - 66 q^{3} - 137 q^{4} - 6 q^{5} - 68 q^{6} - 138 q^{7} - 15 q^{8} - 66 q^{9} - 148 q^{10} - 12 q^{11} - 72 q^{12} - 144 q^{13} - 24 q^{14} - 71 q^{15} - 161 q^{16} - 18 q^{17} - 68 q^{18} - 150 q^{19} - 42 q^{20} - 73 q^{21} - 166 q^{22} - 24 q^{23} - 80 q^{24} - 161 q^{25} - 42 q^{26} - 66 q^{27} - 186 q^{28} - 30 q^{29} - 83 q^{30} - 162 q^{31} - 63 q^{32} - 77 q^{33} - 184 q^{34} - 48 q^{35} - 72 q^{36} - 168 q^{37} - 60 q^{38} - 79 q^{39} - 220 q^{40} - 42 q^{41} - 89 q^{42} - 174 q^{43} - 84 q^{44} - 71 q^{45} - 202 q^{46} - 48 q^{47} - 96 q^{48} - 187 q^{49} - 93 q^{50} - 83 q^{51} - 228 q^{52} - 54 q^{53} - 68 q^{54} - 202 q^{55} - 120 q^{56} - 85 q^{57} - 220 q^{58} - 60 q^{59} - 107 q^{60} - 192 q^{61} - 96 q^{62} - 73 q^{63} - 257 q^{64} - 84 q^{65} - 101 q^{66} - 198 q^{67} - 126 q^{68} - 89 q^{69} - 274 q^{70} - 72 q^{71} - 80 q^{72} - 204 q^{73} - 114 q^{74} - 96 q^{75} - 270 q^{76} - 96 q^{77} - 107 q^{78} - 210 q^{79} - 186 q^{80} - 66 q^{81} - 256 q^{82} - 84 q^{83} - 121 q^{84} - 238 q^{85} - 132 q^{86} - 95 q^{87} - 310 q^{88} - 90 q^{89} - 83 q^{90} - 242 q^{91} - 168 q^{92} - 97 q^{93} - 274 q^{94} - 120 q^{95} - 128 q^{96} - 228 q^{97} - 171 q^{98} - 77 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(393))\)

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
393.2.a \(\chi_{393}(1, \cdot)\) 393.2.a.a 2 1
393.2.a.b 4
393.2.a.c 4
393.2.a.d 5
393.2.a.e 6
393.2.d \(\chi_{393}(392, \cdot)\) 393.2.d.a 10 1
393.2.d.b 32
393.2.e \(\chi_{393}(58, \cdot)\) 393.2.e.a 8 4
393.2.e.b 36
393.2.e.c 44
393.2.f \(\chi_{393}(173, \cdot)\) 393.2.f.a 24 4
393.2.f.b 144
393.2.i \(\chi_{393}(52, \cdot)\) 393.2.i.a 132 12
393.2.i.b 132
393.2.j \(\chi_{393}(32, \cdot)\) 393.2.j.a 504 12
393.2.m \(\chi_{393}(4, \cdot)\) 393.2.m.a 528 48
393.2.m.b 528
393.2.p \(\chi_{393}(2, \cdot)\) 393.2.p.a 2016 48

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(393))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(393)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(131))\)\(^{\oplus 2}\)