Properties

Label 1776.1
Level 1776
Weight 1
Dimension 81
Nonzero newspaces 9
Newform subspaces 16
Sturm bound 175104
Trace bound 7

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Defining parameters

Level: \( N \) = \( 1776 = 2^{4} \cdot 3 \cdot 37 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 9 \)
Newform subspaces: \( 16 \)
Sturm bound: \(175104\)
Trace bound: \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(1776))\).

Total New Old
Modular forms 2320 395 1925
Cusp forms 304 81 223
Eisenstein series 2016 314 1702

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 73 0 8 0

Trace form

\( 81 q + 4 q^{3} - 8 q^{4} + O(q^{10}) \) \( 81 q + 4 q^{3} - 8 q^{4} - 8 q^{10} - 2 q^{13} + 8 q^{16} + 2 q^{19} - 3 q^{21} - q^{25} + q^{27} + 2 q^{31} + 5 q^{33} - 16 q^{34} - q^{37} + 2 q^{39} + 24 q^{40} + 2 q^{43} + 8 q^{46} - 16 q^{48} - 21 q^{49} - 2 q^{57} + 16 q^{58} - 2 q^{61} - 5 q^{63} - 8 q^{64} + 6 q^{67} - 8 q^{70} + 2 q^{75} + 8 q^{78} + 2 q^{79} - 24 q^{81} - 12 q^{85} - 8 q^{90} + 4 q^{91} - 2 q^{93} - 2 q^{97} - 3 q^{99} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(1776))\)

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
1776.1.b \(\chi_{1776}(1183, \cdot)\) None 0 1
1776.1.d \(\chi_{1776}(1111, \cdot)\) None 0 1
1776.1.g \(\chi_{1776}(593, \cdot)\) None 0 1
1776.1.i \(\chi_{1776}(665, \cdot)\) None 0 1
1776.1.k \(\chi_{1776}(223, \cdot)\) None 0 1
1776.1.m \(\chi_{1776}(295, \cdot)\) None 0 1
1776.1.n \(\chi_{1776}(1553, \cdot)\) 1776.1.n.a 1 1
1776.1.n.b 2
1776.1.n.c 2
1776.1.p \(\chi_{1776}(1481, \cdot)\) None 0 1
1776.1.s \(\chi_{1776}(253, \cdot)\) None 0 2
1776.1.t \(\chi_{1776}(1067, \cdot)\) None 0 2
1776.1.w \(\chi_{1776}(191, \cdot)\) 1776.1.w.a 2 2
1776.1.w.b 2
1776.1.y \(\chi_{1776}(149, \cdot)\) None 0 2
1776.1.z \(\chi_{1776}(221, \cdot)\) 1776.1.z.a 4 2
1776.1.z.b 4
1776.1.z.c 16
1776.1.bc \(\chi_{1776}(1079, \cdot)\) None 0 2
1776.1.bd \(\chi_{1776}(1153, \cdot)\) None 0 2
1776.1.bg \(\chi_{1776}(739, \cdot)\) None 0 2
1776.1.bh \(\chi_{1776}(667, \cdot)\) None 0 2
1776.1.bj \(\chi_{1776}(265, \cdot)\) None 0 2
1776.1.bl \(\chi_{1776}(1141, \cdot)\) None 0 2
1776.1.bo \(\chi_{1776}(179, \cdot)\) None 0 2
1776.1.bq \(\chi_{1776}(545, \cdot)\) 1776.1.bq.a 2 2
1776.1.br \(\chi_{1776}(137, \cdot)\) None 0 2
1776.1.bs \(\chi_{1776}(655, \cdot)\) None 0 2
1776.1.bu \(\chi_{1776}(1063, \cdot)\) None 0 2
1776.1.bw \(\chi_{1776}(1025, \cdot)\) 1776.1.bw.a 2 2
1776.1.by \(\chi_{1776}(233, \cdot)\) None 0 2
1776.1.cb \(\chi_{1776}(175, \cdot)\) None 0 2
1776.1.cd \(\chi_{1776}(343, \cdot)\) None 0 2
1776.1.cf \(\chi_{1776}(1139, \cdot)\) None 0 4
1776.1.ci \(\chi_{1776}(325, \cdot)\) None 0 4
1776.1.ck \(\chi_{1776}(97, \cdot)\) None 0 4
1776.1.cl \(\chi_{1776}(211, \cdot)\) None 0 4
1776.1.co \(\chi_{1776}(307, \cdot)\) None 0 4
1776.1.cq \(\chi_{1776}(985, \cdot)\) None 0 4
1776.1.cr \(\chi_{1776}(911, \cdot)\) 1776.1.cr.a 4 4
1776.1.cr.b 4
1776.1.ct \(\chi_{1776}(101, \cdot)\) None 0 4
1776.1.cw \(\chi_{1776}(269, \cdot)\) None 0 4
1776.1.cx \(\chi_{1776}(23, \cdot)\) None 0 4
1776.1.da \(\chi_{1776}(251, \cdot)\) None 0 4
1776.1.db \(\chi_{1776}(1213, \cdot)\) None 0 4
1776.1.dd \(\chi_{1776}(151, \cdot)\) None 0 6
1776.1.df \(\chi_{1776}(41, \cdot)\) None 0 6
1776.1.dg \(\chi_{1776}(329, \cdot)\) None 0 6
1776.1.dj \(\chi_{1776}(7, \cdot)\) None 0 6
1776.1.dk \(\chi_{1776}(65, \cdot)\) 1776.1.dk.a 6 6
1776.1.dn \(\chi_{1776}(511, \cdot)\) None 0 6
1776.1.do \(\chi_{1776}(127, \cdot)\) None 0 6
1776.1.dr \(\chi_{1776}(305, \cdot)\) 1776.1.dr.a 6 6
1776.1.ds \(\chi_{1776}(217, \cdot)\) None 0 12
1776.1.dt \(\chi_{1776}(167, \cdot)\) None 0 12
1776.1.dx \(\chi_{1776}(379, \cdot)\) None 0 12
1776.1.dz \(\chi_{1776}(53, \cdot)\) None 0 12
1776.1.ec \(\chi_{1776}(59, \cdot)\) None 0 12
1776.1.ed \(\chi_{1776}(13, \cdot)\) None 0 12
1776.1.ee \(\chi_{1776}(35, \cdot)\) None 0 12
1776.1.ef \(\chi_{1776}(61, \cdot)\) None 0 12
1776.1.ej \(\chi_{1776}(77, \cdot)\) None 0 12
1776.1.el \(\chi_{1776}(67, \cdot)\) None 0 12
1776.1.em \(\chi_{1776}(143, \cdot)\) 1776.1.em.a 12 12
1776.1.em.b 12
1776.1.en \(\chi_{1776}(241, \cdot)\) None 0 12

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(1776))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(1776)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(111))\)\(^{\oplus 5}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(148))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(296))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(444))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(592))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(888))\)\(^{\oplus 2}\)