Properties

Label 462.2
Level 462
Weight 2
Dimension 1353
Nonzero newspaces 16
Newform subspaces 61
Sturm bound 23040
Trace bound 4

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Defining parameters

Level: \( N \) = \( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 16 \)
Newform subspaces: \( 61 \)
Sturm bound: \(23040\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(462))\).

Total New Old
Modular forms 6240 1353 4887
Cusp forms 5281 1353 3928
Eisenstein series 959 0 959

Trace form

\( 1353 q - 3 q^{2} + q^{3} + 5 q^{4} + 6 q^{5} + 19 q^{6} + 37 q^{7} - 3 q^{8} + 53 q^{9} + O(q^{10}) \) \( 1353 q - 3 q^{2} + q^{3} + 5 q^{4} + 6 q^{5} + 19 q^{6} + 37 q^{7} - 3 q^{8} + 53 q^{9} + 46 q^{10} + 41 q^{11} + 21 q^{12} + 30 q^{13} + 5 q^{14} + 42 q^{15} - 3 q^{16} + 50 q^{17} - 17 q^{18} + 32 q^{19} - 18 q^{20} - 15 q^{21} - 23 q^{22} - 8 q^{23} - 25 q^{24} + 35 q^{25} - 18 q^{26} - 59 q^{27} + 9 q^{28} - 2 q^{29} - 54 q^{30} + 24 q^{31} - 3 q^{32} - 89 q^{33} - 6 q^{34} + 26 q^{35} + 3 q^{36} - 2 q^{37} + 12 q^{38} - 6 q^{39} + 6 q^{40} + 10 q^{41} + 35 q^{42} + 148 q^{43} + 41 q^{44} + 6 q^{45} + 104 q^{46} + 88 q^{47} + q^{48} + 117 q^{49} + 83 q^{50} + 32 q^{51} + 22 q^{52} + 30 q^{53} - 19 q^{54} + 98 q^{55} + 9 q^{56} + 6 q^{57} + 46 q^{58} + 36 q^{59} - 2 q^{60} - 26 q^{61} - 48 q^{62} - 217 q^{63} + 5 q^{64} - 204 q^{65} - 143 q^{66} - 196 q^{67} - 70 q^{68} - 264 q^{69} - 370 q^{70} - 392 q^{71} - 59 q^{72} - 318 q^{73} - 202 q^{74} - 407 q^{75} - 108 q^{76} - 267 q^{77} - 154 q^{78} - 240 q^{79} - 74 q^{80} - 291 q^{81} - 202 q^{82} - 252 q^{83} - 83 q^{84} - 300 q^{85} - 252 q^{86} - 270 q^{87} - 91 q^{88} - 198 q^{89} - 254 q^{90} - 386 q^{91} - 24 q^{92} - 160 q^{93} - 200 q^{94} - 144 q^{95} - 15 q^{96} - 34 q^{97} - 51 q^{98} - 83 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(462))\)

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
462.2.a \(\chi_{462}(1, \cdot)\) 462.2.a.a 1 1
462.2.a.b 1
462.2.a.c 1
462.2.a.d 1
462.2.a.e 1
462.2.a.f 1
462.2.a.g 1
462.2.a.h 2
462.2.c \(\chi_{462}(197, \cdot)\) 462.2.c.a 12 1
462.2.c.b 12
462.2.e \(\chi_{462}(307, \cdot)\) 462.2.e.a 8 1
462.2.e.b 8
462.2.g \(\chi_{462}(419, \cdot)\) 462.2.g.a 4 1
462.2.g.b 4
462.2.g.c 4
462.2.g.d 4
462.2.g.e 8
462.2.i \(\chi_{462}(67, \cdot)\) 462.2.i.a 2 2
462.2.i.b 2
462.2.i.c 2
462.2.i.d 2
462.2.i.e 4
462.2.i.f 6
462.2.i.g 6
462.2.j \(\chi_{462}(169, \cdot)\) 462.2.j.a 4 4
462.2.j.b 4
462.2.j.c 4
462.2.j.d 4
462.2.j.e 8
462.2.j.f 8
462.2.j.g 8
462.2.j.h 8
462.2.k \(\chi_{462}(89, \cdot)\) 462.2.k.a 4 2
462.2.k.b 4
462.2.k.c 4
462.2.k.d 8
462.2.k.e 8
462.2.k.f 8
462.2.k.g 20
462.2.n \(\chi_{462}(65, \cdot)\) 462.2.n.a 4 2
462.2.n.b 4
462.2.n.c 4
462.2.n.d 4
462.2.n.e 24
462.2.n.f 24
462.2.p \(\chi_{462}(241, \cdot)\) 462.2.p.a 16 2
462.2.p.b 16
462.2.s \(\chi_{462}(125, \cdot)\) 462.2.s.a 128 4
462.2.u \(\chi_{462}(13, \cdot)\) 462.2.u.a 32 4
462.2.u.b 32
462.2.w \(\chi_{462}(29, \cdot)\) 462.2.w.a 48 4
462.2.w.b 48
462.2.y \(\chi_{462}(25, \cdot)\) 462.2.y.a 24 8
462.2.y.b 24
462.2.y.c 40
462.2.y.d 40
462.2.ba \(\chi_{462}(19, \cdot)\) 462.2.ba.a 64 8
462.2.ba.b 64
462.2.bc \(\chi_{462}(95, \cdot)\) 462.2.bc.a 128 8
462.2.bc.b 128
462.2.bf \(\chi_{462}(5, \cdot)\) 462.2.bf.a 256 8

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(462))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(462)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(66))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(77))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(154))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(231))\)\(^{\oplus 2}\)