Properties

Label 1875.2
Level 1875
Weight 2
Dimension 85632
Nonzero newspaces 12
Sturm bound 500000
Trace bound 4

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Defining parameters

Level: \( N \) = \( 1875 = 3 \cdot 5^{4} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 12 \)
Sturm bound: \(500000\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1875))\).

Total New Old
Modular forms 127200 87168 40032
Cusp forms 122801 85632 37169
Eisenstein series 4399 1536 2863

Trace form

\( 85632 q - 160 q^{3} - 320 q^{4} - 288 q^{6} - 320 q^{7} - 160 q^{9} + O(q^{10}) \) \( 85632 q - 160 q^{3} - 320 q^{4} - 288 q^{6} - 320 q^{7} - 160 q^{9} - 400 q^{10} - 160 q^{12} - 320 q^{13} - 200 q^{15} - 544 q^{16} + 20 q^{17} - 150 q^{18} - 280 q^{19} - 268 q^{21} - 240 q^{22} + 40 q^{23} - 90 q^{24} - 400 q^{25} + 40 q^{26} - 160 q^{27} - 200 q^{28} + 40 q^{29} - 200 q^{30} - 536 q^{31} + 70 q^{32} - 140 q^{33} - 270 q^{34} - 256 q^{36} - 310 q^{37} + 60 q^{38} - 120 q^{39} - 400 q^{40} + 40 q^{41} - 60 q^{42} - 240 q^{43} + 140 q^{44} - 200 q^{45} - 456 q^{46} + 80 q^{47} - 50 q^{48} - 210 q^{49} - 358 q^{51} - 100 q^{52} + 90 q^{53} - 30 q^{54} - 400 q^{55} + 120 q^{56} - 80 q^{57} - 180 q^{58} + 80 q^{59} - 200 q^{60} - 536 q^{61} + 100 q^{62} - 170 q^{63} - 260 q^{64} - 300 q^{66} - 320 q^{67} - 230 q^{69} - 400 q^{70} - 300 q^{72} - 320 q^{73} - 200 q^{75} - 772 q^{76} - 230 q^{78} - 320 q^{79} - 328 q^{81} - 240 q^{82} + 80 q^{83} - 200 q^{84} - 400 q^{85} + 120 q^{86} - 130 q^{87} - 80 q^{88} + 150 q^{89} - 200 q^{90} - 416 q^{91} + 200 q^{92} - 50 q^{93} - 484 q^{96} - 40 q^{97} + 280 q^{98} - 150 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1875))\)

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
1875.2.a \(\chi_{1875}(1, \cdot)\) 1875.2.a.a 2 1
1875.2.a.b 2
1875.2.a.c 2
1875.2.a.d 2
1875.2.a.e 4
1875.2.a.f 4
1875.2.a.g 4
1875.2.a.h 4
1875.2.a.i 6
1875.2.a.j 6
1875.2.a.k 6
1875.2.a.l 6
1875.2.a.m 8
1875.2.a.n 8
1875.2.a.o 8
1875.2.a.p 8
1875.2.b \(\chi_{1875}(1249, \cdot)\) 1875.2.b.a 4 1
1875.2.b.b 4
1875.2.b.c 8
1875.2.b.d 8
1875.2.b.e 12
1875.2.b.f 12
1875.2.b.g 16
1875.2.b.h 16
1875.2.e \(\chi_{1875}(182, \cdot)\) n/a 288 2
1875.2.g \(\chi_{1875}(376, \cdot)\) n/a 320 4
1875.2.i \(\chi_{1875}(124, \cdot)\) n/a 320 4
1875.2.l \(\chi_{1875}(68, \cdot)\) n/a 1184 8
1875.2.m \(\chi_{1875}(76, \cdot)\) n/a 1480 20
1875.2.o \(\chi_{1875}(49, \cdot)\) n/a 1520 20
1875.2.r \(\chi_{1875}(32, \cdot)\) n/a 5760 40
1875.2.s \(\chi_{1875}(16, \cdot)\) n/a 12600 100
1875.2.v \(\chi_{1875}(4, \cdot)\) n/a 12400 100
1875.2.x \(\chi_{1875}(2, \cdot)\) n/a 49600 200

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1875))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1875)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(75))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(125))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(375))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(625))\)\(^{\oplus 2}\)