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Properties

Label 1620.2
Level 1620
Weight 2
Dimension 29232
Nonzero newspaces 24
Sturm bound 279936
Trace bound 16

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Defining parameters

Level: \( N \) = \( 1620 = 2^{2} \cdot 3^{4} \cdot 5 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 24 \)
Sturm bound: \(279936\)
Trace bound: \(16\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1620))\).

Total New Old
Modular forms 72144 29904 42240
Cusp forms 67825 29232 38593
Eisenstein series 4319 672 3647

Trace form

\( 29232 q - 24 q^{2} - 40 q^{4} - 69 q^{5} - 108 q^{6} + 6 q^{7} - 30 q^{8} - 72 q^{9} + O(q^{10}) \) \( 29232 q - 24 q^{2} - 40 q^{4} - 69 q^{5} - 108 q^{6} + 6 q^{7} - 30 q^{8} - 72 q^{9} - 91 q^{10} + 6 q^{11} - 36 q^{12} - 86 q^{13} - 54 q^{14} - 144 q^{16} - 84 q^{17} - 36 q^{18} - 36 q^{19} - 57 q^{20} - 270 q^{21} - 56 q^{22} - 114 q^{23} - 36 q^{24} - 147 q^{25} - 42 q^{26} - 54 q^{27} - 50 q^{28} - 174 q^{29} - 54 q^{30} - 54 q^{31} + 36 q^{32} - 126 q^{33} + 24 q^{34} - 84 q^{35} - 108 q^{36} - 188 q^{37} + 24 q^{38} - 7 q^{40} - 174 q^{41} + 54 q^{42} + 6 q^{43} + 270 q^{44} - 54 q^{45} + 2 q^{46} + 138 q^{47} + 162 q^{48} - 42 q^{49} + 159 q^{50} + 126 q^{51} + 102 q^{52} + 192 q^{53} + 216 q^{54} + 66 q^{55} + 390 q^{56} + 36 q^{57} + 118 q^{58} + 234 q^{59} + 63 q^{60} - 126 q^{61} + 366 q^{62} + 108 q^{63} + 122 q^{64} + 75 q^{65} + 36 q^{66} + 18 q^{67} + 228 q^{68} + 108 q^{69} + 41 q^{70} + 120 q^{71} - 36 q^{72} - 62 q^{73} + 114 q^{74} + 44 q^{76} + 234 q^{77} - 90 q^{78} - 42 q^{79} + 132 q^{80} - 72 q^{81} - 12 q^{82} + 174 q^{83} + 18 q^{84} - 20 q^{85} + 96 q^{86} + 288 q^{87} - 56 q^{88} + 282 q^{89} - 117 q^{90} + 126 q^{91} - 210 q^{92} + 324 q^{93} - 86 q^{94} + 252 q^{95} - 342 q^{96} + 70 q^{97} - 486 q^{98} + 180 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1620))\)

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
1620.2.a \(\chi_{1620}(1, \cdot)\) 1620.2.a.a 1 1
1620.2.a.b 1
1620.2.a.c 1
1620.2.a.d 1
1620.2.a.e 1
1620.2.a.f 1
1620.2.a.g 2
1620.2.a.h 2
1620.2.a.i 3
1620.2.a.j 3
1620.2.d \(\chi_{1620}(649, \cdot)\) 1620.2.d.a 2 1
1620.2.d.b 2
1620.2.d.c 6
1620.2.d.d 6
1620.2.d.e 8
1620.2.e \(\chi_{1620}(971, \cdot)\) 1620.2.e.a 48 1
1620.2.e.b 48
1620.2.h \(\chi_{1620}(1619, \cdot)\) n/a 136 1
1620.2.i \(\chi_{1620}(541, \cdot)\) 1620.2.i.a 2 2
1620.2.i.b 2
1620.2.i.c 2
1620.2.i.d 2
1620.2.i.e 2
1620.2.i.f 2
1620.2.i.g 2
1620.2.i.h 2
1620.2.i.i 2
1620.2.i.j 2
1620.2.i.k 2
1620.2.i.l 2
1620.2.i.m 4
1620.2.i.n 4
1620.2.j \(\chi_{1620}(1133, \cdot)\) 1620.2.j.a 24 2
1620.2.j.b 24
1620.2.k \(\chi_{1620}(163, \cdot)\) n/a 272 2
1620.2.n \(\chi_{1620}(539, \cdot)\) n/a 280 2
1620.2.q \(\chi_{1620}(431, \cdot)\) n/a 192 2
1620.2.r \(\chi_{1620}(109, \cdot)\) 1620.2.r.a 4 2
1620.2.r.b 4
1620.2.r.c 4
1620.2.r.d 4
1620.2.r.e 4
1620.2.r.f 4
1620.2.r.g 8
1620.2.r.h 16
1620.2.u \(\chi_{1620}(181, \cdot)\) 1620.2.u.a 30 6
1620.2.u.b 42
1620.2.x \(\chi_{1620}(53, \cdot)\) 1620.2.x.a 8 4
1620.2.x.b 8
1620.2.x.c 16
1620.2.x.d 16
1620.2.x.e 24
1620.2.x.f 24
1620.2.y \(\chi_{1620}(703, \cdot)\) n/a 560 4
1620.2.bb \(\chi_{1620}(179, \cdot)\) n/a 624 6
1620.2.bd \(\chi_{1620}(289, \cdot)\) n/a 108 6
1620.2.be \(\chi_{1620}(71, \cdot)\) n/a 432 6
1620.2.bg \(\chi_{1620}(61, \cdot)\) n/a 648 18
1620.2.bi \(\chi_{1620}(127, \cdot)\) n/a 1248 12
1620.2.bk \(\chi_{1620}(17, \cdot)\) n/a 216 12
1620.2.bm \(\chi_{1620}(59, \cdot)\) n/a 5760 18
1620.2.bo \(\chi_{1620}(11, \cdot)\) n/a 3888 18
1620.2.br \(\chi_{1620}(49, \cdot)\) n/a 972 18
1620.2.bs \(\chi_{1620}(77, \cdot)\) n/a 1944 36
1620.2.bv \(\chi_{1620}(7, \cdot)\) n/a 11520 36

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1620))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1620)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(54))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(60))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(81))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(90))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(108))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(135))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(162))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(180))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(270))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(324))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(405))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(540))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(810))\)\(^{\oplus 2}\)