Properties

Label 460.2
Level 460
Weight 2
Dimension 3250
Nonzero newspaces 12
Newform subspaces 22
Sturm bound 25344
Trace bound 1

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Defining parameters

Level: \( N \) = \( 460 = 2^{2} \cdot 5 \cdot 23 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 12 \)
Newform subspaces: \( 22 \)
Sturm bound: \(25344\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(460))\).

Total New Old
Modular forms 6776 3498 3278
Cusp forms 5897 3250 2647
Eisenstein series 879 248 631

Trace form

\( 3250 q - 18 q^{2} + 4 q^{3} - 22 q^{4} - 56 q^{5} - 66 q^{6} - 4 q^{7} - 30 q^{8} - 46 q^{9} + O(q^{10}) \) \( 3250 q - 18 q^{2} + 4 q^{3} - 22 q^{4} - 56 q^{5} - 66 q^{6} - 4 q^{7} - 30 q^{8} - 46 q^{9} - 45 q^{10} - 22 q^{12} - 44 q^{13} - 22 q^{14} + 7 q^{15} - 50 q^{16} - 22 q^{17} - 10 q^{18} + 30 q^{19} - 25 q^{20} - 58 q^{21} - 44 q^{22} + 38 q^{23} - 44 q^{24} - 58 q^{25} - 74 q^{26} + 58 q^{27} - 22 q^{28} - 34 q^{29} - 33 q^{30} + 30 q^{31} - 38 q^{32} - 22 q^{33} - 66 q^{34} - 18 q^{35} - 200 q^{36} - 108 q^{37} - 132 q^{38} - 80 q^{39} - 113 q^{40} - 156 q^{41} - 242 q^{42} - 68 q^{43} - 176 q^{44} - 164 q^{45} - 242 q^{46} - 76 q^{47} - 198 q^{48} - 170 q^{49} - 27 q^{50} - 112 q^{51} - 234 q^{52} - 112 q^{53} - 198 q^{54} - 22 q^{55} - 176 q^{56} - 82 q^{57} - 148 q^{58} + 20 q^{59} - 55 q^{60} - 96 q^{61} - 22 q^{62} + 106 q^{63} - 22 q^{64} + 11 q^{65} + 40 q^{67} - 20 q^{68} + 78 q^{69} - 66 q^{70} + 134 q^{71} - 64 q^{72} + 40 q^{73} + 59 q^{75} + 44 q^{76} - 110 q^{77} + 198 q^{78} + 28 q^{79} + 34 q^{80} - 250 q^{81} + 78 q^{82} + 10 q^{83} + 286 q^{84} - 174 q^{85} + 154 q^{86} - 108 q^{87} + 154 q^{88} - 164 q^{89} + 142 q^{90} - 96 q^{91} + 176 q^{92} - 632 q^{93} + 132 q^{94} - 85 q^{95} + 352 q^{96} - 298 q^{97} + 126 q^{98} - 242 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(460))\)

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
460.2.a \(\chi_{460}(1, \cdot)\) 460.2.a.a 1 1
460.2.a.b 1
460.2.a.c 1
460.2.a.d 1
460.2.a.e 2
460.2.c \(\chi_{460}(369, \cdot)\) 460.2.c.a 12 1
460.2.e \(\chi_{460}(91, \cdot)\) 460.2.e.a 16 1
460.2.e.b 32
460.2.g \(\chi_{460}(459, \cdot)\) 460.2.g.a 4 1
460.2.g.b 8
460.2.g.c 56
460.2.i \(\chi_{460}(137, \cdot)\) 460.2.i.a 8 2
460.2.i.b 16
460.2.j \(\chi_{460}(47, \cdot)\) 460.2.j.a 132 2
460.2.m \(\chi_{460}(41, \cdot)\) 460.2.m.a 30 10
460.2.m.b 50
460.2.o \(\chi_{460}(19, \cdot)\) 460.2.o.a 40 10
460.2.o.b 640
460.2.q \(\chi_{460}(11, \cdot)\) 460.2.q.a 480 10
460.2.s \(\chi_{460}(9, \cdot)\) 460.2.s.a 120 10
460.2.w \(\chi_{460}(3, \cdot)\) 460.2.w.a 1360 20
460.2.x \(\chi_{460}(17, \cdot)\) 460.2.x.a 240 20

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(460))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(460)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(46))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(92))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(115))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(230))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(460))\)\(^{\oplus 1}\)