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Properties

Label 3775.1
Level 3775
Weight 1
Dimension 114
Nonzero newspaces 6
Newform subspaces 18
Sturm bound 1140000
Trace bound 1

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Defining parameters

Level: \( N \) = \( 3775 = 5^{2} \cdot 151 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 6 \)
Newform subspaces: \( 18 \)
Sturm bound: \(1140000\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(3775))\).

Total New Old
Modular forms 4357 3169 1188
Cusp forms 157 114 43
Eisenstein series 4200 3055 1145

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 78 0 4 32

Trace form

\( 114 q - q^{2} + 4 q^{4} + 4 q^{5} + 4 q^{8} + 8 q^{9} + 2 q^{10} - 2 q^{13} + q^{16} + 3 q^{17} + q^{18} + 5 q^{19} - 2 q^{20} - 10 q^{21} - 2 q^{22} + 2 q^{23} - 4 q^{25} - q^{29} - 3 q^{31} + 3 q^{32}+ \cdots + 10 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(3775))\)

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
3775.1.c \(\chi_{3775}(3774, \cdot)\) 3775.1.c.a 4 1
3775.1.c.b 4
3775.1.c.c 6
3775.1.d \(\chi_{3775}(301, \cdot)\) 3775.1.d.a 1 1
3775.1.d.b 2
3775.1.d.c 2
3775.1.d.d 3
3775.1.d.e 4
3775.1.d.f 4
3775.1.d.g 6
3775.1.g \(\chi_{3775}(907, \cdot)\) None 0 2
3775.1.n \(\chi_{3775}(1176, \cdot)\) 3775.1.n.a 2 2
3775.1.p \(\chi_{3775}(874, \cdot)\) None 0 2
3775.1.q \(\chi_{3775}(1049, \cdot)\) None 0 4
3775.1.s \(\chi_{3775}(1446, \cdot)\) None 0 4
3775.1.t \(\chi_{3775}(696, \cdot)\) None 0 4
3775.1.u \(\chi_{3775}(1056, \cdot)\) 3775.1.u.a 4 4
3775.1.u.b 8
3775.1.u.c 8
3775.1.u.d 24
3775.1.v \(\chi_{3775}(596, \cdot)\) None 0 4
3775.1.w \(\chi_{3775}(2106, \cdot)\) None 0 4
3775.1.y \(\chi_{3775}(1144, \cdot)\) None 0 4
3775.1.z \(\chi_{3775}(1804, \cdot)\) None 0 4
3775.1.ba \(\chi_{3775}(294, \cdot)\) None 0 4
3775.1.bb \(\chi_{3775}(754, \cdot)\) 3775.1.bb.a 4 4
3775.1.bb.b 24
3775.1.bg \(\chi_{3775}(394, \cdot)\) None 0 4
3775.1.bh \(\chi_{3775}(1351, \cdot)\) None 0 4
3775.1.bi \(\chi_{3775}(32, \cdot)\) 3775.1.bi.a 4 4
3775.1.bq \(\chi_{3775}(668, \cdot)\) None 0 8
3775.1.bt \(\chi_{3775}(1267, \cdot)\) None 0 8
3775.1.bu \(\chi_{3775}(152, \cdot)\) None 0 8
3775.1.bv \(\chi_{3775}(2122, \cdot)\) None 0 8
3775.1.bw \(\chi_{3775}(8, \cdot)\) None 0 8
3775.1.cb \(\chi_{3775}(517, \cdot)\) None 0 8
3775.1.ch \(\chi_{3775}(226, \cdot)\) None 0 8
3775.1.cj \(\chi_{3775}(119, \cdot)\) None 0 8
3775.1.ck \(\chi_{3775}(929, \cdot)\) None 0 8
3775.1.cl \(\chi_{3775}(739, \cdot)\) None 0 8
3775.1.cm \(\chi_{3775}(519, \cdot)\) None 0 8
3775.1.cr \(\chi_{3775}(264, \cdot)\) None 0 8
3775.1.cs \(\chi_{3775}(821, \cdot)\) None 0 8
3775.1.ct \(\chi_{3775}(1041, \cdot)\) None 0 8
3775.1.cu \(\chi_{3775}(46, \cdot)\) None 0 8
3775.1.cv \(\chi_{3775}(421, \cdot)\) None 0 8
3775.1.cw \(\chi_{3775}(566, \cdot)\) None 0 8
3775.1.cx \(\chi_{3775}(149, \cdot)\) None 0 8
3775.1.cz \(\chi_{3775}(329, \cdot)\) None 0 20
3775.1.db \(\chi_{3775}(216, \cdot)\) None 0 20
3775.1.dc \(\chi_{3775}(26, \cdot)\) None 0 20
3775.1.dd \(\chi_{3775}(211, \cdot)\) None 0 20
3775.1.de \(\chi_{3775}(631, \cdot)\) None 0 20
3775.1.dg \(\chi_{3775}(154, \cdot)\) None 0 20
3775.1.dh \(\chi_{3775}(24, \cdot)\) None 0 20
3775.1.dk \(\chi_{3775}(204, \cdot)\) None 0 20
3775.1.dl \(\chi_{3775}(79, \cdot)\) None 0 20
3775.1.dn \(\chi_{3775}(41, \cdot)\) None 0 20
3775.1.do \(\chi_{3775}(38, \cdot)\) None 0 16
3775.1.dt \(\chi_{3775}(153, \cdot)\) None 0 16
3775.1.du \(\chi_{3775}(2, \cdot)\) None 0 16
3775.1.dv \(\chi_{3775}(183, \cdot)\) None 0 16
3775.1.dw \(\chi_{3775}(227, \cdot)\) None 0 16
3775.1.dz \(\chi_{3775}(318, \cdot)\) None 0 16
3775.1.ef \(\chi_{3775}(98, \cdot)\) None 0 40
3775.1.ei \(\chi_{3775}(72, \cdot)\) None 0 40
3775.1.ej \(\chi_{3775}(68, \cdot)\) None 0 40
3775.1.ek \(\chi_{3775}(123, \cdot)\) None 0 40
3775.1.el \(\chi_{3775}(278, \cdot)\) None 0 40
3775.1.ep \(\chi_{3775}(56, \cdot)\) None 0 40
3775.1.eq \(\chi_{3775}(14, \cdot)\) None 0 40
3775.1.et \(\chi_{3775}(199, \cdot)\) None 0 40
3775.1.eu \(\chi_{3775}(89, \cdot)\) None 0 40
3775.1.ex \(\chi_{3775}(114, \cdot)\) None 0 40
3775.1.ey \(\chi_{3775}(96, \cdot)\) None 0 40
3775.1.ez \(\chi_{3775}(51, \cdot)\) None 0 40
3775.1.fa \(\chi_{3775}(6, \cdot)\) None 0 40
3775.1.fb \(\chi_{3775}(71, \cdot)\) None 0 40
3775.1.fd \(\chi_{3775}(54, \cdot)\) None 0 40
3775.1.fe \(\chi_{3775}(17, \cdot)\) None 0 80
3775.1.fj \(\chi_{3775}(22, \cdot)\) None 0 80
3775.1.fk \(\chi_{3775}(47, \cdot)\) None 0 80
3775.1.fl \(\chi_{3775}(18, \cdot)\) None 0 80
3775.1.fn \(\chi_{3775}(37, \cdot)\) None 0 80

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(3775))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(3775)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(151))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(755))\)\(^{\oplus 2}\)