Properties

Label 1760.2
Level 1760
Weight 2
Dimension 46188
Nonzero newspaces 40
Sturm bound 368640
Trace bound 41

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Defining parameters

Level: \( N \) = \( 1760 = 2^{5} \cdot 5 \cdot 11 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 40 \)
Sturm bound: \(368640\)
Trace bound: \(41\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1760))\).

Total New Old
Modular forms 94720 47268 47452
Cusp forms 89601 46188 43413
Eisenstein series 5119 1080 4039

Trace form

\( 46188 q - 64 q^{2} - 52 q^{3} - 64 q^{4} - 100 q^{5} - 192 q^{6} - 52 q^{7} - 64 q^{8} - 100 q^{9} - 80 q^{10} - 164 q^{11} - 80 q^{12} - 40 q^{13} - 66 q^{15} - 112 q^{16} - 16 q^{17} + 16 q^{18} - 44 q^{19}+ \cdots + 252 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1760))\)

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
1760.2.a \(\chi_{1760}(1, \cdot)\) 1760.2.a.a 1 1
1760.2.a.b 1
1760.2.a.c 1
1760.2.a.d 1
1760.2.a.e 1
1760.2.a.f 1
1760.2.a.g 1
1760.2.a.h 1
1760.2.a.i 1
1760.2.a.j 1
1760.2.a.k 1
1760.2.a.l 1
1760.2.a.m 1
1760.2.a.n 1
1760.2.a.o 2
1760.2.a.p 2
1760.2.a.q 3
1760.2.a.r 3
1760.2.a.s 3
1760.2.a.t 3
1760.2.a.u 5
1760.2.a.v 5
1760.2.b \(\chi_{1760}(1409, \cdot)\) 1760.2.b.a 2 1
1760.2.b.b 2
1760.2.b.c 14
1760.2.b.d 14
1760.2.b.e 14
1760.2.b.f 14
1760.2.c \(\chi_{1760}(879, \cdot)\) 1760.2.c.a 4 1
1760.2.c.b 8
1760.2.c.c 56
1760.2.f \(\chi_{1760}(351, \cdot)\) 1760.2.f.a 4 1
1760.2.f.b 4
1760.2.f.c 16
1760.2.f.d 24
1760.2.g \(\chi_{1760}(881, \cdot)\) 1760.2.g.a 4 1
1760.2.g.b 12
1760.2.g.c 24
1760.2.l \(\chi_{1760}(529, \cdot)\) 1760.2.l.a 2 1
1760.2.l.b 2
1760.2.l.c 56
1760.2.m \(\chi_{1760}(1759, \cdot)\) 1760.2.m.a 72 1
1760.2.p \(\chi_{1760}(1231, \cdot)\) 1760.2.p.a 48 1
1760.2.s \(\chi_{1760}(727, \cdot)\) None 0 2
1760.2.t \(\chi_{1760}(857, \cdot)\) None 0 2
1760.2.v \(\chi_{1760}(791, \cdot)\) None 0 2
1760.2.w \(\chi_{1760}(441, \cdot)\) None 0 2
1760.2.z \(\chi_{1760}(463, \cdot)\) n/a 120 2
1760.2.bb \(\chi_{1760}(593, \cdot)\) n/a 136 2
1760.2.bd \(\chi_{1760}(417, \cdot)\) n/a 144 2
1760.2.bf \(\chi_{1760}(287, \cdot)\) n/a 120 2
1760.2.bh \(\chi_{1760}(89, \cdot)\) None 0 2
1760.2.bi \(\chi_{1760}(439, \cdot)\) None 0 2
1760.2.bk \(\chi_{1760}(23, \cdot)\) None 0 2
1760.2.bl \(\chi_{1760}(153, \cdot)\) None 0 2
1760.2.bo \(\chi_{1760}(641, \cdot)\) n/a 192 4
1760.2.bp \(\chi_{1760}(67, \cdot)\) n/a 960 4
1760.2.bs \(\chi_{1760}(373, \cdot)\) n/a 1136 4
1760.2.bt \(\chi_{1760}(219, \cdot)\) n/a 1136 4
1760.2.bv \(\chi_{1760}(221, \cdot)\) n/a 640 4
1760.2.by \(\chi_{1760}(131, \cdot)\) n/a 768 4
1760.2.ca \(\chi_{1760}(309, \cdot)\) n/a 960 4
1760.2.cc \(\chi_{1760}(197, \cdot)\) n/a 1136 4
1760.2.cd \(\chi_{1760}(243, \cdot)\) n/a 960 4
1760.2.cf \(\chi_{1760}(271, \cdot)\) n/a 192 4
1760.2.ci \(\chi_{1760}(479, \cdot)\) n/a 288 4
1760.2.cj \(\chi_{1760}(49, \cdot)\) n/a 272 4
1760.2.co \(\chi_{1760}(81, \cdot)\) n/a 192 4
1760.2.cp \(\chi_{1760}(831, \cdot)\) n/a 192 4
1760.2.cs \(\chi_{1760}(79, \cdot)\) n/a 272 4
1760.2.ct \(\chi_{1760}(289, \cdot)\) n/a 288 4
1760.2.cw \(\chi_{1760}(457, \cdot)\) None 0 8
1760.2.cx \(\chi_{1760}(487, \cdot)\) None 0 8
1760.2.cy \(\chi_{1760}(39, \cdot)\) None 0 8
1760.2.db \(\chi_{1760}(9, \cdot)\) None 0 8
1760.2.dc \(\chi_{1760}(193, \cdot)\) n/a 576 8
1760.2.de \(\chi_{1760}(223, \cdot)\) n/a 576 8
1760.2.dg \(\chi_{1760}(47, \cdot)\) n/a 544 8
1760.2.di \(\chi_{1760}(17, \cdot)\) n/a 544 8
1760.2.dk \(\chi_{1760}(201, \cdot)\) None 0 8
1760.2.dn \(\chi_{1760}(151, \cdot)\) None 0 8
1760.2.do \(\chi_{1760}(57, \cdot)\) None 0 8
1760.2.dp \(\chi_{1760}(103, \cdot)\) None 0 8
1760.2.ds \(\chi_{1760}(13, \cdot)\) n/a 4544 16
1760.2.dv \(\chi_{1760}(3, \cdot)\) n/a 4544 16
1760.2.dw \(\chi_{1760}(69, \cdot)\) n/a 4544 16
1760.2.dy \(\chi_{1760}(51, \cdot)\) n/a 3072 16
1760.2.eb \(\chi_{1760}(141, \cdot)\) n/a 3072 16
1760.2.ed \(\chi_{1760}(19, \cdot)\) n/a 4544 16
1760.2.ef \(\chi_{1760}(147, \cdot)\) n/a 4544 16
1760.2.eg \(\chi_{1760}(237, \cdot)\) n/a 4544 16

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1760))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1760)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(44))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(55))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(80))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(88))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(110))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(160))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(176))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(220))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(352))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(440))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(880))\)\(^{\oplus 2}\)