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Properties

Label 402.2
Level 402
Weight 2
Dimension 1123
Nonzero newspaces 8
Newform subspaces 27
Sturm bound 17952
Trace bound 4

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Defining parameters

Level: \( N \) = \( 402 = 2 \cdot 3 \cdot 67 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 8 \)
Newform subspaces: \( 27 \)
Sturm bound: \(17952\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(402))\).

Total New Old
Modular forms 4752 1123 3629
Cusp forms 4225 1123 3102
Eisenstein series 527 0 527

Trace form

\( 1123 q + q^{2} + q^{3} + q^{4} + 6 q^{5} + q^{6} + 8 q^{7} + q^{8} + q^{9} + O(q^{10}) \) \( 1123 q + q^{2} + q^{3} + q^{4} + 6 q^{5} + q^{6} + 8 q^{7} + q^{8} + q^{9} + 6 q^{10} + 12 q^{11} + q^{12} + 14 q^{13} + 8 q^{14} + 6 q^{15} + q^{16} + 18 q^{17} + q^{18} + 20 q^{19} + 6 q^{20} + 8 q^{21} + 12 q^{22} + 24 q^{23} + q^{24} + 31 q^{25} + 14 q^{26} + q^{27} + 8 q^{28} + 30 q^{29} + 6 q^{30} + 32 q^{31} + q^{32} + 12 q^{33} + 18 q^{34} + 48 q^{35} + q^{36} + 38 q^{37} + 20 q^{38} + 14 q^{39} + 6 q^{40} + 42 q^{41} + 8 q^{42} + 44 q^{43} + 12 q^{44} + 6 q^{45} + 24 q^{46} + 48 q^{47} + q^{48} + 57 q^{49} + 31 q^{50} + 18 q^{51} - 30 q^{52} - 78 q^{53} + q^{54} - 324 q^{55} + 8 q^{56} - 134 q^{57} - 234 q^{58} - 204 q^{59} - 126 q^{60} - 466 q^{61} - 100 q^{62} - 14 q^{63} + q^{64} - 444 q^{65} - 252 q^{66} - 197 q^{67} - 114 q^{68} - 108 q^{69} - 480 q^{70} - 456 q^{71} + q^{72} - 498 q^{73} - 94 q^{74} - 233 q^{75} - 244 q^{76} - 168 q^{77} - 118 q^{78} - 228 q^{79} + 6 q^{80} + q^{81} - 156 q^{82} - 48 q^{83} - 14 q^{84} + 108 q^{85} + 44 q^{86} + 30 q^{87} + 12 q^{88} + 90 q^{89} + 6 q^{90} + 112 q^{91} + 24 q^{92} + 32 q^{93} + 48 q^{94} + 120 q^{95} + q^{96} + 98 q^{97} + 57 q^{98} + 12 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(402))\)

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
402.2.a \(\chi_{402}(1, \cdot)\) 402.2.a.a 1 1
402.2.a.b 1
402.2.a.c 1
402.2.a.d 1
402.2.a.e 2
402.2.a.f 2
402.2.a.g 3
402.2.d \(\chi_{402}(401, \cdot)\) 402.2.d.a 12 1
402.2.d.b 12
402.2.e \(\chi_{402}(37, \cdot)\) 402.2.e.a 6 2
402.2.e.b 6
402.2.e.c 6
402.2.e.d 6
402.2.h \(\chi_{402}(239, \cdot)\) 402.2.h.a 22 2
402.2.h.b 22
402.2.i \(\chi_{402}(25, \cdot)\) 402.2.i.a 20 10
402.2.i.b 20
402.2.i.c 30
402.2.i.d 30
402.2.j \(\chi_{402}(5, \cdot)\) 402.2.j.a 120 10
402.2.j.b 120
402.2.m \(\chi_{402}(19, \cdot)\) 402.2.m.a 60 20
402.2.m.b 60
402.2.m.c 60
402.2.m.d 60
402.2.n \(\chi_{402}(11, \cdot)\) 402.2.n.a 220 20
402.2.n.b 220

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(402))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(402)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(67))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(134))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(201))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(402))\)\(^{\oplus 1}\)