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Properties

Label 2400.1
Level 2400
Weight 1
Dimension 58
Nonzero newspaces 8
Newform subspaces 11
Sturm bound 307200
Trace bound 19

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Defining parameters

Level: \( N \) = \( 2400 = 2^{5} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 8 \)
Newform subspaces: \( 11 \)
Sturm bound: \(307200\)
Trace bound: \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(2400))\).

Total New Old
Modular forms 4020 468 3552
Cusp forms 436 58 378
Eisenstein series 3584 410 3174

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 58 0 0 0

Trace form

\( 58 q + 4 q^{7} + 2 q^{9} + O(q^{10}) \) \( 58 q + 4 q^{7} + 2 q^{9} + 4 q^{15} + 4 q^{21} + 8 q^{24} + 4 q^{31} - 4 q^{33} - 6 q^{49} + 4 q^{51} - 8 q^{54} + 4 q^{55} + 8 q^{61} + 4 q^{63} + 12 q^{69} - 4 q^{73} - 8 q^{76} + 12 q^{79} - 6 q^{81} + 4 q^{87} - 8 q^{94} + 16 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(2400))\)

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 available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
2400.1.c \(\chi_{2400}(449, \cdot)\) None 0 1
2400.1.e \(\chi_{2400}(1951, \cdot)\) None 0 1
2400.1.g \(\chi_{2400}(751, \cdot)\) None 0 1
2400.1.i \(\chi_{2400}(1649, \cdot)\) None 0 1
2400.1.j \(\chi_{2400}(799, \cdot)\) None 0 1
2400.1.l \(\chi_{2400}(1601, \cdot)\) 2400.1.l.a 4 1
2400.1.n \(\chi_{2400}(401, \cdot)\) 2400.1.n.a 1 1
2400.1.n.b 1
2400.1.p \(\chi_{2400}(1999, \cdot)\) None 0 1
2400.1.q \(\chi_{2400}(199, \cdot)\) None 0 2
2400.1.r \(\chi_{2400}(1001, \cdot)\) None 0 2
2400.1.u \(\chi_{2400}(143, \cdot)\) 2400.1.u.a 4 2
2400.1.u.b 8
2400.1.x \(\chi_{2400}(1393, \cdot)\) None 0 2
2400.1.z \(\chi_{2400}(1607, \cdot)\) None 0 2
2400.1.ba \(\chi_{2400}(1657, \cdot)\) None 0 2
2400.1.bd \(\chi_{2400}(407, \cdot)\) None 0 2
2400.1.be \(\chi_{2400}(457, \cdot)\) None 0 2
2400.1.bg \(\chi_{2400}(193, \cdot)\) None 0 2
2400.1.bj \(\chi_{2400}(1343, \cdot)\) None 0 2
2400.1.bm \(\chi_{2400}(1049, \cdot)\) None 0 2
2400.1.bn \(\chi_{2400}(151, \cdot)\) None 0 2
2400.1.bq \(\chi_{2400}(493, \cdot)\) None 0 4
2400.1.br \(\chi_{2400}(443, \cdot)\) 2400.1.br.a 8 4
2400.1.bu \(\chi_{2400}(451, \cdot)\) None 0 4
2400.1.bv \(\chi_{2400}(149, \cdot)\) None 0 4
2400.1.bx \(\chi_{2400}(499, \cdot)\) None 0 4
2400.1.ca \(\chi_{2400}(101, \cdot)\) 2400.1.ca.a 8 4
2400.1.cb \(\chi_{2400}(107, \cdot)\) 2400.1.cb.a 8 4
2400.1.ce \(\chi_{2400}(157, \cdot)\) None 0 4
2400.1.cf \(\chi_{2400}(209, \cdot)\) 2400.1.cf.a 8 4
2400.1.ch \(\chi_{2400}(271, \cdot)\) None 0 4
2400.1.cj \(\chi_{2400}(31, \cdot)\) None 0 4
2400.1.cl \(\chi_{2400}(929, \cdot)\) None 0 4
2400.1.cn \(\chi_{2400}(79, \cdot)\) None 0 4
2400.1.cp \(\chi_{2400}(881, \cdot)\) 2400.1.cp.a 4 4
2400.1.cp.b 4
2400.1.cr \(\chi_{2400}(161, \cdot)\) None 0 4
2400.1.ct \(\chi_{2400}(319, \cdot)\) None 0 4
2400.1.cw \(\chi_{2400}(41, \cdot)\) None 0 8
2400.1.cx \(\chi_{2400}(439, \cdot)\) None 0 8
2400.1.cy \(\chi_{2400}(287, \cdot)\) None 0 8
2400.1.db \(\chi_{2400}(97, \cdot)\) None 0 8
2400.1.dd \(\chi_{2400}(313, \cdot)\) None 0 8
2400.1.de \(\chi_{2400}(263, \cdot)\) None 0 8
2400.1.dh \(\chi_{2400}(73, \cdot)\) None 0 8
2400.1.di \(\chi_{2400}(23, \cdot)\) None 0 8
2400.1.dk \(\chi_{2400}(337, \cdot)\) None 0 8
2400.1.dn \(\chi_{2400}(47, \cdot)\) None 0 8
2400.1.do \(\chi_{2400}(391, \cdot)\) None 0 8
2400.1.dp \(\chi_{2400}(89, \cdot)\) None 0 8
2400.1.dt \(\chi_{2400}(203, \cdot)\) None 0 16
2400.1.du \(\chi_{2400}(13, \cdot)\) None 0 16
2400.1.dw \(\chi_{2400}(221, \cdot)\) None 0 16
2400.1.dz \(\chi_{2400}(19, \cdot)\) None 0 16
2400.1.eb \(\chi_{2400}(29, \cdot)\) None 0 16
2400.1.ec \(\chi_{2400}(91, \cdot)\) None 0 16
2400.1.ee \(\chi_{2400}(133, \cdot)\) None 0 16
2400.1.eh \(\chi_{2400}(83, \cdot)\) None 0 16

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(2400))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(2400)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 36}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 30}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 18}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 24}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 24}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 15}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 18}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 20}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 16}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 9}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 10}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 10}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(60))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(75))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(80))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(96))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(100))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(120))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(150))\)\(^{\oplus 5}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(160))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(200))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(240))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(300))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(400))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(480))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(600))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(800))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(1200))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(2400))\)\(^{\oplus 1}\)