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Properties

Label 1500.2
Level 1500
Weight 2
Dimension 23936
Nonzero newspaces 18
Sturm bound 240000
Trace bound 16

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Defining parameters

Level: \( N \) = \( 1500 = 2^{2} \cdot 3 \cdot 5^{3} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 18 \)
Sturm bound: \(240000\)
Trace bound: \(16\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1500))\).

Total New Old
Modular forms 61800 24448 37352
Cusp forms 58201 23936 34265
Eisenstein series 3599 512 3087

Trace form

\( 23936 q + 2 q^{3} - 68 q^{4} - 62 q^{6} - 4 q^{7} - 12 q^{8} - 70 q^{9} + O(q^{10}) \) \( 23936 q + 2 q^{3} - 68 q^{4} - 62 q^{6} - 4 q^{7} - 12 q^{8} - 70 q^{9} - 80 q^{10} - 8 q^{11} - 34 q^{12} - 144 q^{13} - 108 q^{16} - 60 q^{17} - 14 q^{18} - 80 q^{19} - 160 q^{21} - 52 q^{22} - 80 q^{23} + 14 q^{24} - 220 q^{25} + 16 q^{26} + 14 q^{27} - 36 q^{28} - 68 q^{29} - 40 q^{30} - 56 q^{31} + 20 q^{32} - 88 q^{33} - 36 q^{34} - 20 q^{35} + 10 q^{36} - 100 q^{37} + 136 q^{38} + 80 q^{39} + 20 q^{40} + 76 q^{41} + 178 q^{42} + 148 q^{43} + 280 q^{44} + 108 q^{46} + 160 q^{47} + 210 q^{48} + 122 q^{49} + 180 q^{50} + 108 q^{51} + 260 q^{52} + 184 q^{53} + 174 q^{54} + 80 q^{55} + 176 q^{56} + 120 q^{57} + 164 q^{58} + 152 q^{59} + 60 q^{60} - 172 q^{61} + 144 q^{62} + 188 q^{63} + 4 q^{64} + 10 q^{65} - 22 q^{66} - 4 q^{67} - 16 q^{68} + 112 q^{69} - 80 q^{70} - 18 q^{72} - 72 q^{73} + 80 q^{75} - 244 q^{76} + 48 q^{77} + 46 q^{78} + 24 q^{79} - 2 q^{81} - 164 q^{82} + 80 q^{83} - 134 q^{84} - 10 q^{85} - 176 q^{86} + 200 q^{87} - 436 q^{88} + 560 q^{89} - 100 q^{90} + 184 q^{91} - 344 q^{92} + 224 q^{93} - 596 q^{94} + 80 q^{95} - 190 q^{96} + 728 q^{97} - 536 q^{98} + 8 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1500))\)

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
1500.2.a \(\chi_{1500}(1, \cdot)\) 1500.2.a.a 2 1
1500.2.a.b 2
1500.2.a.c 2
1500.2.a.d 2
1500.2.a.e 2
1500.2.a.f 2
1500.2.a.g 2
1500.2.a.h 2
1500.2.d \(\chi_{1500}(1249, \cdot)\) 1500.2.d.a 4 1
1500.2.d.b 4
1500.2.d.c 4
1500.2.d.d 4
1500.2.e \(\chi_{1500}(251, \cdot)\) n/a 192 1
1500.2.h \(\chi_{1500}(1499, \cdot)\) n/a 192 1
1500.2.i \(\chi_{1500}(557, \cdot)\) 1500.2.i.a 32 2
1500.2.i.b 32
1500.2.j \(\chi_{1500}(307, \cdot)\) n/a 192 2
1500.2.m \(\chi_{1500}(301, \cdot)\) 1500.2.m.a 8 4
1500.2.m.b 8
1500.2.m.c 24
1500.2.m.d 24
1500.2.n \(\chi_{1500}(551, \cdot)\) n/a 672 4
1500.2.o \(\chi_{1500}(49, \cdot)\) 1500.2.o.a 16 4
1500.2.o.b 16
1500.2.o.c 24
1500.2.r \(\chi_{1500}(299, \cdot)\) n/a 672 4
1500.2.w \(\chi_{1500}(7, \cdot)\) n/a 720 8
1500.2.x \(\chi_{1500}(257, \cdot)\) n/a 240 8
1500.2.y \(\chi_{1500}(61, \cdot)\) n/a 480 20
1500.2.bb \(\chi_{1500}(59, \cdot)\) n/a 5920 20
1500.2.bc \(\chi_{1500}(109, \cdot)\) n/a 520 20
1500.2.bf \(\chi_{1500}(11, \cdot)\) n/a 5920 20
1500.2.bh \(\chi_{1500}(67, \cdot)\) n/a 6000 40
1500.2.bi \(\chi_{1500}(17, \cdot)\) n/a 2000 40

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1500))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1500)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(60))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(75))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(100))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(125))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(150))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(250))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(300))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(375))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(500))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(750))\)\(^{\oplus 2}\)