Properties

Label 1404.1
Level 1404
Weight 1
Dimension 36
Nonzero newspaces 10
Newform subspaces 13
Sturm bound 108864
Trace bound 23

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Defining parameters

Level: \( N \) = \( 1404 = 2^{2} \cdot 3^{3} \cdot 13 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 10 \)
Newform subspaces: \( 13 \)
Sturm bound: \(108864\)
Trace bound: \(23\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(1404))\).

Total New Old
Modular forms 1995 388 1607
Cusp forms 195 36 159
Eisenstein series 1800 352 1448

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 28 8 0 0

Trace form

\( 36 q - 4 q^{4} - 4 q^{5} + 2 q^{7} + O(q^{10}) \) \( 36 q - 4 q^{4} - 4 q^{5} + 2 q^{7} - 4 q^{10} + 6 q^{13} - 4 q^{14} - 4 q^{16} + 4 q^{17} + 2 q^{19} - 2 q^{20} + 2 q^{22} + 3 q^{23} - 5 q^{25} + 2 q^{37} - 4 q^{38} + 4 q^{40} + 2 q^{41} + q^{43} - 10 q^{46} - 3 q^{49} - 2 q^{52} + 16 q^{53} - 2 q^{56} + 7 q^{61} + 4 q^{62} - 4 q^{64} + 2 q^{65} + 2 q^{67} + 2 q^{68} - 4 q^{70} + 2 q^{73} + q^{79} - 4 q^{80} + 4 q^{82} - 2 q^{85} + 4 q^{86} - 10 q^{88} - 4 q^{89} - q^{91} - 12 q^{94} - 14 q^{97} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(1404))\)

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
1404.1.d \(\chi_{1404}(53, \cdot)\) None 0 1
1404.1.e \(\chi_{1404}(1351, \cdot)\) 1404.1.e.a 2 1
1404.1.e.b 2
1404.1.e.c 4
1404.1.f \(\chi_{1404}(703, \cdot)\) None 0 1
1404.1.g \(\chi_{1404}(701, \cdot)\) 1404.1.g.a 2 1
1404.1.m \(\chi_{1404}(109, \cdot)\) 1404.1.m.a 4 2
1404.1.o \(\chi_{1404}(863, \cdot)\) None 0 2
1404.1.q \(\chi_{1404}(595, \cdot)\) 1404.1.q.a 2 2
1404.1.q.b 2
1404.1.r \(\chi_{1404}(269, \cdot)\) 1404.1.r.a 2 2
1404.1.u \(\chi_{1404}(881, \cdot)\) None 0 2
1404.1.v \(\chi_{1404}(451, \cdot)\) 1404.1.v.a 4 2
1404.1.y \(\chi_{1404}(991, \cdot)\) 1404.1.y.a 4 2
1404.1.z \(\chi_{1404}(233, \cdot)\) 1404.1.z.a 2 2
1404.1.ba \(\chi_{1404}(235, \cdot)\) None 0 2
1404.1.bb \(\chi_{1404}(17, \cdot)\) None 0 2
1404.1.bf \(\chi_{1404}(1205, \cdot)\) None 0 2
1404.1.bg \(\chi_{1404}(415, \cdot)\) None 0 2
1404.1.bh \(\chi_{1404}(521, \cdot)\) None 0 2
1404.1.bi \(\chi_{1404}(127, \cdot)\) None 0 2
1404.1.bn \(\chi_{1404}(667, \cdot)\) None 0 2
1404.1.bo \(\chi_{1404}(341, \cdot)\) None 0 2
1404.1.bq \(\chi_{1404}(485, \cdot)\) 1404.1.bq.a 2 2
1404.1.br \(\chi_{1404}(55, \cdot)\) None 0 2
1404.1.bw \(\chi_{1404}(73, \cdot)\) None 0 4
1404.1.bx \(\chi_{1404}(683, \cdot)\) None 0 4
1404.1.ca \(\chi_{1404}(215, \cdot)\) None 0 4
1404.1.cb \(\chi_{1404}(71, \cdot)\) None 0 4
1404.1.cd \(\chi_{1404}(37, \cdot)\) None 0 4
1404.1.cg \(\chi_{1404}(865, \cdot)\) 1404.1.cg.a 4 4
1404.1.ch \(\chi_{1404}(253, \cdot)\) None 0 4
1404.1.ck \(\chi_{1404}(359, \cdot)\) None 0 4
1404.1.cm \(\chi_{1404}(29, \cdot)\) None 0 6
1404.1.co \(\chi_{1404}(101, \cdot)\) None 0 6
1404.1.cp \(\chi_{1404}(211, \cdot)\) None 0 6
1404.1.cr \(\chi_{1404}(103, \cdot)\) None 0 6
1404.1.ct \(\chi_{1404}(79, \cdot)\) None 0 6
1404.1.cu \(\chi_{1404}(43, \cdot)\) None 0 6
1404.1.cv \(\chi_{1404}(173, \cdot)\) None 0 6
1404.1.cy \(\chi_{1404}(209, \cdot)\) None 0 6
1404.1.da \(\chi_{1404}(77, \cdot)\) None 0 6
1404.1.db \(\chi_{1404}(185, \cdot)\) None 0 6
1404.1.dd \(\chi_{1404}(355, \cdot)\) None 0 6
1404.1.df \(\chi_{1404}(139, \cdot)\) None 0 6
1404.1.dg \(\chi_{1404}(85, \cdot)\) None 0 12
1404.1.dj \(\chi_{1404}(47, \cdot)\) None 0 12
1404.1.dl \(\chi_{1404}(167, \cdot)\) None 0 12
1404.1.dn \(\chi_{1404}(229, \cdot)\) None 0 12
1404.1.dp \(\chi_{1404}(97, \cdot)\) None 0 12
1404.1.dq \(\chi_{1404}(11, \cdot)\) None 0 12

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(1404))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(1404)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(39))\)\(^{\oplus 9}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(52))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(108))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(117))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(156))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(351))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(468))\)\(^{\oplus 2}\)