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 N = 1875=354 1875 = 3 \cdot 5^{4}
Weight: k k = 2 2
Nonzero newspaces: 12 12
Sturm bound: 500000500000
Trace bound: 44

Dimensions

The following table gives the dimensions of various subspaces of M2(Γ1(1875))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

85632q160q3320q4288q6320q7160q9400q10160q12320q13200q15544q16+20q17150q18280q19268q21240q22+40q23+150q99+O(q100) 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}+ \cdots - 150 q^{99}+O(q^{100}) Copy content Toggle raw display

Decomposition of S2new(Γ1(1875))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 Sknew(N,χ) S_k^{\mathrm{new}}(N, \chi) we list available newforms together with their dimension.

Label χ\chi Newforms Dimension χ\chi degree
1875.2.a χ1875(1,)\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 χ1875(1249,)\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 χ1875(182,)\chi_{1875}(182, \cdot) n/a 288 2
1875.2.g χ1875(376,)\chi_{1875}(376, \cdot) n/a 320 4
1875.2.i χ1875(124,)\chi_{1875}(124, \cdot) n/a 320 4
1875.2.l χ1875(68,)\chi_{1875}(68, \cdot) n/a 1184 8
1875.2.m χ1875(76,)\chi_{1875}(76, \cdot) n/a 1480 20
1875.2.o χ1875(49,)\chi_{1875}(49, \cdot) n/a 1520 20
1875.2.r χ1875(32,)\chi_{1875}(32, \cdot) n/a 5760 40
1875.2.s χ1875(16,)\chi_{1875}(16, \cdot) n/a 12600 100
1875.2.v χ1875(4,)\chi_{1875}(4, \cdot) n/a 12400 100
1875.2.x χ1875(2,)\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 S2old(Γ1(1875))S_{2}^{\mathrm{old}}(\Gamma_1(1875)) into lower level spaces