Properties

Label 480.2
Level 480
Weight 2
Dimension 2316
Nonzero newspaces 20
Newform subspaces 48
Sturm bound 24576
Trace bound 17

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Defining parameters

Level: \( N \) = \( 480 = 2^{5} \cdot 3 \cdot 5 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 20 \)
Newform subspaces: \( 48 \)
Sturm bound: \(24576\)
Trace bound: \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(480))\).

Total New Old
Modular forms 6656 2436 4220
Cusp forms 5633 2316 3317
Eisenstein series 1023 120 903

Trace form

\( 2316 q - 8 q^{3} - 16 q^{4} - 4 q^{5} - 24 q^{6} - 16 q^{7} - 20 q^{9} + O(q^{10}) \) \( 2316 q - 8 q^{3} - 16 q^{4} - 4 q^{5} - 24 q^{6} - 16 q^{7} - 20 q^{9} - 8 q^{10} + 24 q^{12} + 8 q^{13} + 64 q^{14} + 32 q^{16} + 32 q^{17} + 8 q^{18} + 8 q^{19} + 32 q^{20} + 8 q^{21} + 32 q^{22} + 48 q^{23} - 32 q^{24} - 28 q^{25} - 80 q^{26} + 64 q^{27} - 96 q^{28} + 8 q^{29} - 60 q^{30} + 88 q^{31} - 80 q^{32} + 8 q^{33} - 64 q^{34} + 96 q^{35} - 128 q^{36} + 24 q^{37} - 80 q^{38} + 56 q^{39} - 64 q^{40} + 48 q^{41} - 128 q^{42} + 48 q^{43} - 16 q^{44} - 32 q^{45} - 48 q^{46} - 112 q^{48} - 28 q^{49} - 24 q^{50} - 40 q^{51} - 112 q^{52} + 40 q^{53} - 112 q^{54} - 40 q^{55} - 112 q^{56} - 80 q^{57} - 160 q^{58} - 128 q^{59} - 136 q^{60} + 72 q^{61} - 96 q^{62} - 64 q^{63} - 256 q^{64} - 72 q^{65} - 200 q^{66} - 160 q^{67} - 208 q^{68} + 24 q^{69} - 336 q^{70} - 144 q^{71} - 128 q^{72} - 72 q^{73} - 288 q^{74} - 76 q^{75} - 304 q^{76} - 64 q^{77} - 184 q^{78} - 136 q^{79} - 264 q^{80} - 68 q^{81} - 176 q^{82} - 80 q^{83} - 48 q^{84} - 152 q^{85} - 128 q^{86} - 208 q^{87} - 192 q^{88} - 128 q^{89} - 120 q^{90} - 96 q^{91} - 128 q^{92} - 128 q^{93} - 64 q^{94} - 64 q^{95} + 128 q^{96} - 88 q^{97} + 64 q^{98} - 232 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(480))\)

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
480.2.a \(\chi_{480}(1, \cdot)\) 480.2.a.a 1 1
480.2.a.b 1
480.2.a.c 1
480.2.a.d 1
480.2.a.e 1
480.2.a.f 1
480.2.a.g 1
480.2.a.h 1
480.2.b \(\chi_{480}(431, \cdot)\) 480.2.b.a 8 1
480.2.b.b 8
480.2.d \(\chi_{480}(49, \cdot)\) 480.2.d.a 6 1
480.2.d.b 6
480.2.f \(\chi_{480}(289, \cdot)\) 480.2.f.a 2 1
480.2.f.b 2
480.2.f.c 2
480.2.f.d 2
480.2.f.e 4
480.2.h \(\chi_{480}(191, \cdot)\) 480.2.h.a 4 1
480.2.h.b 4
480.2.h.c 4
480.2.h.d 4
480.2.k \(\chi_{480}(241, \cdot)\) 480.2.k.a 2 1
480.2.k.b 6
480.2.m \(\chi_{480}(239, \cdot)\) 480.2.m.a 4 1
480.2.m.b 16
480.2.o \(\chi_{480}(479, \cdot)\) 480.2.o.a 24 1
480.2.s \(\chi_{480}(121, \cdot)\) None 0 2
480.2.t \(\chi_{480}(119, \cdot)\) None 0 2
480.2.v \(\chi_{480}(257, \cdot)\) 480.2.v.a 4 2
480.2.v.b 4
480.2.v.c 16
480.2.v.d 24
480.2.w \(\chi_{480}(127, \cdot)\) 480.2.w.a 4 2
480.2.w.b 4
480.2.w.c 8
480.2.w.d 8
480.2.y \(\chi_{480}(7, \cdot)\) None 0 2
480.2.bb \(\chi_{480}(233, \cdot)\) None 0 2
480.2.bc \(\chi_{480}(103, \cdot)\) None 0 2
480.2.bf \(\chi_{480}(137, \cdot)\) None 0 2
480.2.bh \(\chi_{480}(367, \cdot)\) 480.2.bh.a 24 2
480.2.bi \(\chi_{480}(17, \cdot)\) 480.2.bi.a 4 2
480.2.bi.b 4
480.2.bi.c 32
480.2.bk \(\chi_{480}(71, \cdot)\) None 0 2
480.2.bl \(\chi_{480}(169, \cdot)\) None 0 2
480.2.bo \(\chi_{480}(43, \cdot)\) 480.2.bo.a 192 4
480.2.br \(\chi_{480}(173, \cdot)\) 480.2.br.a 368 4
480.2.bs \(\chi_{480}(59, \cdot)\) 480.2.bs.a 16 4
480.2.bs.b 352
480.2.bv \(\chi_{480}(61, \cdot)\) 480.2.bv.a 56 4
480.2.bv.b 72
480.2.bx \(\chi_{480}(11, \cdot)\) 480.2.bx.a 256 4
480.2.by \(\chi_{480}(109, \cdot)\) 480.2.by.a 192 4
480.2.cb \(\chi_{480}(53, \cdot)\) 480.2.cb.a 368 4
480.2.cc \(\chi_{480}(163, \cdot)\) 480.2.cc.a 192 4

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(480))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(480)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(60))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(80))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(96))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(120))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(160))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(240))\)\(^{\oplus 2}\)