Properties

Label 2760.1
Level 2760
Weight 1
Dimension 132
Nonzero newspaces 4
Newform subspaces 16
Sturm bound 405504
Trace bound 1

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Defining parameters

Level: \( N \) = \( 2760 = 2^{3} \cdot 3 \cdot 5 \cdot 23 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 16 \)
Sturm bound: \(405504\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(2760))\).

Total New Old
Modular forms 4832 636 4196
Cusp forms 608 132 476
Eisenstein series 4224 504 3720

The following table gives the dimensions of subspaces with specified projective image type.

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 124 0 8 0

Trace form

\( 132 q + 4 q^{3} + 4 q^{6} + O(q^{10}) \) \( 132 q + 4 q^{3} + 4 q^{6} - 4 q^{10} + 8 q^{13} - 4 q^{15} - 8 q^{16} - 4 q^{24} + 4 q^{27} - 4 q^{30} - 8 q^{31} - 8 q^{34} - 8 q^{36} + 36 q^{39} + 4 q^{40} - 4 q^{46} - 8 q^{49} - 4 q^{54} + 36 q^{55} + 4 q^{60} - 8 q^{66} - 4 q^{75} - 16 q^{79} + 8 q^{85} - 4 q^{87} + 4 q^{90} - 4 q^{93} - 8 q^{94} + 4 q^{96} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(2760))\)

We only show spaces with odd 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
2760.1.b \(\chi_{2760}(2759, \cdot)\) None 0 1
2760.1.d \(\chi_{2760}(1289, \cdot)\) None 0 1
2760.1.g \(\chi_{2760}(2161, \cdot)\) None 0 1
2760.1.i \(\chi_{2760}(2071, \cdot)\) None 0 1
2760.1.j \(\chi_{2760}(781, \cdot)\) None 0 1
2760.1.l \(\chi_{2760}(691, \cdot)\) None 0 1
2760.1.o \(\chi_{2760}(1379, \cdot)\) 2760.1.o.a 1 1
2760.1.o.b 1
2760.1.o.c 1
2760.1.o.d 1
2760.1.q \(\chi_{2760}(2669, \cdot)\) None 0 1
2760.1.s \(\chi_{2760}(1519, \cdot)\) None 0 1
2760.1.u \(\chi_{2760}(1609, \cdot)\) None 0 1
2760.1.v \(\chi_{2760}(1841, \cdot)\) None 0 1
2760.1.x \(\chi_{2760}(551, \cdot)\) None 0 1
2760.1.ba \(\chi_{2760}(461, \cdot)\) None 0 1
2760.1.bc \(\chi_{2760}(1931, \cdot)\) None 0 1
2760.1.bd \(\chi_{2760}(139, \cdot)\) None 0 1
2760.1.bf \(\chi_{2760}(229, \cdot)\) None 0 1
2760.1.bg \(\chi_{2760}(323, \cdot)\) None 0 2
2760.1.bh \(\chi_{2760}(413, \cdot)\) None 0 2
2760.1.bm \(\chi_{2760}(643, \cdot)\) None 0 2
2760.1.bn \(\chi_{2760}(277, \cdot)\) None 0 2
2760.1.bo \(\chi_{2760}(367, \cdot)\) None 0 2
2760.1.bp \(\chi_{2760}(553, \cdot)\) None 0 2
2760.1.bu \(\chi_{2760}(47, \cdot)\) None 0 2
2760.1.bv \(\chi_{2760}(137, \cdot)\) 2760.1.bv.a 4 2
2760.1.bv.b 4
2760.1.bx \(\chi_{2760}(109, \cdot)\) None 0 10
2760.1.bz \(\chi_{2760}(259, \cdot)\) None 0 10
2760.1.ca \(\chi_{2760}(11, \cdot)\) None 0 10
2760.1.cc \(\chi_{2760}(101, \cdot)\) None 0 10
2760.1.cf \(\chi_{2760}(191, \cdot)\) None 0 10
2760.1.ch \(\chi_{2760}(41, \cdot)\) None 0 10
2760.1.ci \(\chi_{2760}(649, \cdot)\) None 0 10
2760.1.ck \(\chi_{2760}(439, \cdot)\) None 0 10
2760.1.cm \(\chi_{2760}(29, \cdot)\) 2760.1.cm.a 10 10
2760.1.cm.b 10
2760.1.cm.c 10
2760.1.cm.d 10
2760.1.cm.e 20
2760.1.cm.f 20
2760.1.co \(\chi_{2760}(419, \cdot)\) 2760.1.co.a 10 10
2760.1.co.b 10
2760.1.co.c 10
2760.1.co.d 10
2760.1.cr \(\chi_{2760}(211, \cdot)\) None 0 10
2760.1.ct \(\chi_{2760}(61, \cdot)\) None 0 10
2760.1.cu \(\chi_{2760}(31, \cdot)\) None 0 10
2760.1.cw \(\chi_{2760}(241, \cdot)\) None 0 10
2760.1.cz \(\chi_{2760}(209, \cdot)\) None 0 10
2760.1.db \(\chi_{2760}(359, \cdot)\) None 0 10
2760.1.dc \(\chi_{2760}(17, \cdot)\) None 0 20
2760.1.dd \(\chi_{2760}(167, \cdot)\) None 0 20
2760.1.di \(\chi_{2760}(73, \cdot)\) None 0 20
2760.1.dj \(\chi_{2760}(7, \cdot)\) None 0 20
2760.1.dk \(\chi_{2760}(13, \cdot)\) None 0 20
2760.1.dl \(\chi_{2760}(43, \cdot)\) None 0 20
2760.1.dq \(\chi_{2760}(53, \cdot)\) None 0 20
2760.1.dr \(\chi_{2760}(347, \cdot)\) None 0 20

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(2760))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(2760)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 16}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(120))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(184))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(276))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(345))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(460))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(552))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(920))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(1380))\)\(^{\oplus 2}\)