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Properties

Label 1020.2
Level 1020
Weight 2
Dimension 10828
Nonzero newspaces 36
Sturm bound 110592
Trace bound 33

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Defining parameters

Level: \( N \) = \( 1020 = 2^{2} \cdot 3 \cdot 5 \cdot 17 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 36 \)
Sturm bound: \(110592\)
Trace bound: \(33\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1020))\).

Total New Old
Modular forms 28928 11196 17732
Cusp forms 26369 10828 15541
Eisenstein series 2559 368 2191

Trace form

\( 10828 q - 4 q^{3} - 16 q^{4} - 4 q^{5} - 32 q^{6} + 8 q^{7} + 24 q^{8} - 12 q^{9} + O(q^{10}) \) \( 10828 q - 4 q^{3} - 16 q^{4} - 4 q^{5} - 32 q^{6} + 8 q^{7} + 24 q^{8} - 12 q^{9} - 8 q^{10} - 16 q^{11} - 8 q^{12} - 48 q^{13} + 4 q^{15} - 64 q^{16} - 12 q^{17} - 64 q^{18} - 32 q^{19} - 40 q^{20} - 120 q^{21} - 48 q^{22} - 32 q^{23} - 32 q^{24} - 44 q^{25} + 96 q^{26} - 28 q^{27} + 112 q^{28} + 56 q^{29} - 32 q^{30} + 80 q^{31} + 120 q^{32} + 40 q^{33} + 200 q^{34} + 32 q^{35} - 16 q^{36} + 64 q^{37} + 128 q^{38} + 96 q^{39} + 48 q^{40} + 88 q^{41} + 64 q^{42} + 120 q^{43} + 128 q^{44} - 4 q^{45} + 16 q^{46} - 24 q^{48} - 28 q^{49} + 32 q^{50} + 76 q^{51} + 16 q^{52} + 40 q^{53} + 16 q^{54} + 48 q^{55} - 32 q^{56} + 184 q^{57} - 144 q^{58} + 80 q^{59} + 72 q^{61} - 112 q^{62} + 128 q^{63} - 112 q^{64} + 176 q^{65} - 160 q^{66} + 72 q^{67} - 336 q^{68} + 96 q^{69} - 176 q^{70} + 128 q^{71} - 248 q^{72} + 432 q^{73} - 192 q^{74} + 140 q^{75} - 384 q^{76} + 224 q^{77} - 256 q^{78} + 144 q^{79} - 120 q^{80} + 28 q^{81} - 304 q^{82} + 160 q^{83} - 304 q^{84} + 160 q^{85} - 128 q^{86} - 40 q^{87} - 240 q^{88} + 56 q^{89} - 304 q^{90} + 144 q^{91} - 112 q^{92} - 144 q^{93} - 240 q^{94} + 192 q^{95} - 480 q^{96} + 128 q^{97} - 48 q^{98} - 160 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1020))\)

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
1020.2.a \(\chi_{1020}(1, \cdot)\) 1020.2.a.a 1 1
1020.2.a.b 1
1020.2.a.c 1
1020.2.a.d 1
1020.2.a.e 1
1020.2.a.f 1
1020.2.a.g 1
1020.2.a.h 1
1020.2.a.i 2
1020.2.a.j 2
1020.2.b \(\chi_{1020}(1019, \cdot)\) n/a 208 1
1020.2.e \(\chi_{1020}(781, \cdot)\) 1020.2.e.a 2 1
1020.2.e.b 2
1020.2.e.c 4
1020.2.e.d 4
1020.2.g \(\chi_{1020}(409, \cdot)\) 1020.2.g.a 2 1
1020.2.g.b 2
1020.2.g.c 2
1020.2.g.d 10
1020.2.h \(\chi_{1020}(851, \cdot)\) n/a 128 1
1020.2.k \(\chi_{1020}(169, \cdot)\) 1020.2.k.a 2 1
1020.2.k.b 2
1020.2.k.c 8
1020.2.k.d 8
1020.2.l \(\chi_{1020}(611, \cdot)\) n/a 144 1
1020.2.n \(\chi_{1020}(239, \cdot)\) n/a 192 1
1020.2.r \(\chi_{1020}(463, \cdot)\) n/a 216 2
1020.2.s \(\chi_{1020}(353, \cdot)\) 1020.2.s.a 72 2
1020.2.v \(\chi_{1020}(137, \cdot)\) 1020.2.v.a 64 2
1020.2.w \(\chi_{1020}(103, \cdot)\) n/a 192 2
1020.2.y \(\chi_{1020}(769, \cdot)\) 1020.2.y.a 40 2
1020.2.ba \(\chi_{1020}(599, \cdot)\) n/a 416 2
1020.2.bd \(\chi_{1020}(361, \cdot)\) 1020.2.bd.a 12 2
1020.2.bd.b 12
1020.2.bf \(\chi_{1020}(191, \cdot)\) n/a 288 2
1020.2.bg \(\chi_{1020}(713, \cdot)\) 1020.2.bg.a 16 2
1020.2.bg.b 56
1020.2.bj \(\chi_{1020}(67, \cdot)\) n/a 216 2
1020.2.bk \(\chi_{1020}(523, \cdot)\) n/a 216 2
1020.2.bn \(\chi_{1020}(293, \cdot)\) 1020.2.bn.a 72 2
1020.2.bo \(\chi_{1020}(491, \cdot)\) n/a 576 4
1020.2.bp \(\chi_{1020}(121, \cdot)\) 1020.2.bp.a 24 4
1020.2.bp.b 24
1020.2.bs \(\chi_{1020}(257, \cdot)\) n/a 144 4
1020.2.bt \(\chi_{1020}(127, \cdot)\) n/a 432 4
1020.2.by \(\chi_{1020}(43, \cdot)\) n/a 432 4
1020.2.bz \(\chi_{1020}(53, \cdot)\) n/a 144 4
1020.2.cc \(\chi_{1020}(49, \cdot)\) 1020.2.cc.a 64 4
1020.2.cd \(\chi_{1020}(59, \cdot)\) n/a 832 4
1020.2.cg \(\chi_{1020}(73, \cdot)\) n/a 144 8
1020.2.ch \(\chi_{1020}(227, \cdot)\) n/a 1664 8
1020.2.ci \(\chi_{1020}(79, \cdot)\) n/a 864 8
1020.2.ck \(\chi_{1020}(41, \cdot)\) n/a 192 8
1020.2.cn \(\chi_{1020}(31, \cdot)\) n/a 576 8
1020.2.cp \(\chi_{1020}(29, \cdot)\) n/a 288 8
1020.2.cq \(\chi_{1020}(37, \cdot)\) n/a 144 8
1020.2.cr \(\chi_{1020}(23, \cdot)\) n/a 1664 8

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1020))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1020)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(34))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(51))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(60))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(68))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(85))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(102))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(170))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(204))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(255))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(340))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(510))\)\(^{\oplus 2}\)