Properties

Label 3552.1
Level 3552
Weight 1
Dimension 52
Nonzero newspaces 3
Newform subspaces 8
Sturm bound 700416
Trace bound 1

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Defining parameters

Level: \( N \) = \( 3552 = 2^{5} \cdot 3 \cdot 37 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 3 \)
Newform subspaces: \( 8 \)
Sturm bound: \(700416\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(3552))\).

Total New Old
Modular forms 5200 752 4448
Cusp forms 592 52 540
Eisenstein series 4608 700 3908

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 44 0 8 0

Trace form

\( 52 q + 4 q^{7} - 8 q^{9} - 4 q^{13} + 4 q^{21} - 8 q^{25} - 4 q^{33} - 8 q^{37} - 32 q^{40} + 8 q^{49} - 32 q^{58} + 4 q^{63} + 4 q^{73} + 8 q^{81} + 4 q^{93} + 8 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(3552))\)

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
3552.1.b \(\chi_{3552}(1183, \cdot)\) None 0 1
3552.1.d \(\chi_{3552}(1999, \cdot)\) None 0 1
3552.1.g \(\chi_{3552}(2369, \cdot)\) None 0 1
3552.1.i \(\chi_{3552}(1553, \cdot)\) 3552.1.i.a 1 1
3552.1.i.b 1
3552.1.i.c 1
3552.1.i.d 1
3552.1.i.e 8
3552.1.k \(\chi_{3552}(223, \cdot)\) None 0 1
3552.1.m \(\chi_{3552}(2959, \cdot)\) None 0 1
3552.1.n \(\chi_{3552}(3329, \cdot)\) None 0 1
3552.1.p \(\chi_{3552}(593, \cdot)\) None 0 1
3552.1.s \(\chi_{3552}(2041, \cdot)\) None 0 2
3552.1.t \(\chi_{3552}(1079, \cdot)\) None 0 2
3552.1.w \(\chi_{3552}(191, \cdot)\) None 0 2
3552.1.y \(\chi_{3552}(1481, \cdot)\) None 0 2
3552.1.z \(\chi_{3552}(665, \cdot)\) None 0 2
3552.1.bc \(\chi_{3552}(623, \cdot)\) None 0 2
3552.1.bd \(\chi_{3552}(1153, \cdot)\) None 0 2
3552.1.bg \(\chi_{3552}(295, \cdot)\) None 0 2
3552.1.bh \(\chi_{3552}(1111, \cdot)\) None 0 2
3552.1.bj \(\chi_{3552}(1585, \cdot)\) None 0 2
3552.1.bl \(\chi_{3552}(265, \cdot)\) None 0 2
3552.1.bo \(\chi_{3552}(2855, \cdot)\) None 0 2
3552.1.bq \(\chi_{3552}(545, \cdot)\) None 0 2
3552.1.br \(\chi_{3552}(2801, \cdot)\) None 0 2
3552.1.bs \(\chi_{3552}(2431, \cdot)\) None 0 2
3552.1.bu \(\chi_{3552}(175, \cdot)\) None 0 2
3552.1.bw \(\chi_{3552}(1025, \cdot)\) 3552.1.bw.a 4 2
3552.1.bw.b 4
3552.1.by \(\chi_{3552}(2321, \cdot)\) None 0 2
3552.1.cb \(\chi_{3552}(1951, \cdot)\) None 0 2
3552.1.cd \(\chi_{3552}(655, \cdot)\) None 0 2
3552.1.ce \(\chi_{3552}(221, \cdot)\) 3552.1.ce.a 32 4
3552.1.cf \(\chi_{3552}(667, \cdot)\) None 0 4
3552.1.ci \(\chi_{3552}(1067, \cdot)\) None 0 4
3552.1.cj \(\chi_{3552}(1141, \cdot)\) None 0 4
3552.1.cm \(\chi_{3552}(253, \cdot)\) None 0 4
3552.1.cn \(\chi_{3552}(179, \cdot)\) None 0 4
3552.1.cs \(\chi_{3552}(149, \cdot)\) None 0 4
3552.1.ct \(\chi_{3552}(739, \cdot)\) None 0 4
3552.1.cv \(\chi_{3552}(695, \cdot)\) None 0 4
3552.1.cy \(\chi_{3552}(1657, \cdot)\) None 0 4
3552.1.da \(\chi_{3552}(97, \cdot)\) None 0 4
3552.1.db \(\chi_{3552}(343, \cdot)\) None 0 4
3552.1.de \(\chi_{3552}(1063, \cdot)\) None 0 4
3552.1.dg \(\chi_{3552}(1873, \cdot)\) None 0 4
3552.1.dh \(\chi_{3552}(2687, \cdot)\) None 0 4
3552.1.dj \(\chi_{3552}(233, \cdot)\) None 0 4
3552.1.dm \(\chi_{3552}(137, \cdot)\) None 0 4
3552.1.dn \(\chi_{3552}(911, \cdot)\) None 0 4
3552.1.dq \(\chi_{3552}(23, \cdot)\) None 0 4
3552.1.dr \(\chi_{3552}(985, \cdot)\) None 0 4
3552.1.dt \(\chi_{3552}(559, \cdot)\) None 0 6
3552.1.dv \(\chi_{3552}(881, \cdot)\) None 0 6
3552.1.dw \(\chi_{3552}(305, \cdot)\) None 0 6
3552.1.dz \(\chi_{3552}(271, \cdot)\) None 0 6
3552.1.ea \(\chi_{3552}(65, \cdot)\) None 0 6
3552.1.ed \(\chi_{3552}(511, \cdot)\) None 0 6
3552.1.ee \(\chi_{3552}(127, \cdot)\) None 0 6
3552.1.eh \(\chi_{3552}(641, \cdot)\) None 0 6
3552.1.ek \(\chi_{3552}(307, \cdot)\) None 0 8
3552.1.el \(\chi_{3552}(269, \cdot)\) None 0 8
3552.1.em \(\chi_{3552}(325, \cdot)\) None 0 8
3552.1.en \(\chi_{3552}(251, \cdot)\) None 0 8
3552.1.eq \(\chi_{3552}(1139, \cdot)\) None 0 8
3552.1.er \(\chi_{3552}(1213, \cdot)\) None 0 8
3552.1.eu \(\chi_{3552}(211, \cdot)\) None 0 8
3552.1.ev \(\chi_{3552}(101, \cdot)\) None 0 8
3552.1.ey \(\chi_{3552}(241, \cdot)\) None 0 12
3552.1.ez \(\chi_{3552}(143, \cdot)\) None 0 12
3552.1.fd \(\chi_{3552}(7, \cdot)\) None 0 12
3552.1.ff \(\chi_{3552}(329, \cdot)\) None 0 12
3552.1.fi \(\chi_{3552}(167, \cdot)\) None 0 12
3552.1.fj \(\chi_{3552}(217, \cdot)\) None 0 12
3552.1.fk \(\chi_{3552}(503, \cdot)\) None 0 12
3552.1.fl \(\chi_{3552}(313, \cdot)\) None 0 12
3552.1.fp \(\chi_{3552}(41, \cdot)\) None 0 12
3552.1.fr \(\chi_{3552}(151, \cdot)\) None 0 12
3552.1.fs \(\chi_{3552}(383, \cdot)\) None 0 12
3552.1.ft \(\chi_{3552}(385, \cdot)\) None 0 12
3552.1.fy \(\chi_{3552}(61, \cdot)\) None 0 24
3552.1.fz \(\chi_{3552}(59, \cdot)\) None 0 24
3552.1.ga \(\chi_{3552}(379, \cdot)\) None 0 24
3552.1.gb \(\chi_{3552}(77, \cdot)\) None 0 24
3552.1.ge \(\chi_{3552}(53, \cdot)\) None 0 24
3552.1.gf \(\chi_{3552}(67, \cdot)\) None 0 24
3552.1.gk \(\chi_{3552}(35, \cdot)\) None 0 24
3552.1.gl \(\chi_{3552}(13, \cdot)\) None 0 24

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(3552))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(3552)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 24}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 20}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 16}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 10}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(37))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(74))\)\(^{\oplus 10}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(96))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(111))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(148))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(222))\)\(^{\oplus 5}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(296))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(444))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(592))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(888))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(1184))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(1776))\)\(^{\oplus 2}\)