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Properties

Label 1232.1
Level 1232
Weight 1
Dimension 44
Nonzero newspaces 5
Newform subspaces 9
Sturm bound 92160
Trace bound 11

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Defining parameters

Level: \( N \) = \( 1232 = 2^{4} \cdot 7 \cdot 11 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 5 \)
Newform subspaces: \( 9 \)
Sturm bound: \(92160\)
Trace bound: \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(1232))\).

Total New Old
Modular forms 1850 448 1402
Cusp forms 170 44 126
Eisenstein series 1680 404 1276

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

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

Trace form

\( 44 q + 4 q^{4} + q^{7} + 3 q^{9} + 3 q^{11} + 4 q^{14} - 4 q^{16} - 4 q^{18} - 2 q^{22} + 2 q^{23} + 3 q^{25} + 2 q^{29} + 7 q^{37} - 2 q^{43} - 2 q^{44} + 7 q^{49} + 4 q^{50} - q^{53} - 4 q^{56} + 4 q^{58}+ \cdots - 2 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(1232))\)

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
1232.1.b \(\chi_{1232}(881, \cdot)\) None 0 1
1232.1.d \(\chi_{1232}(505, \cdot)\) None 0 1
1232.1.g \(\chi_{1232}(615, \cdot)\) None 0 1
1232.1.i \(\chi_{1232}(463, \cdot)\) None 0 1
1232.1.k \(\chi_{1232}(1079, \cdot)\) None 0 1
1232.1.m \(\chi_{1232}(1231, \cdot)\) 1232.1.m.a 2 1
1232.1.m.b 2
1232.1.n \(\chi_{1232}(1121, \cdot)\) None 0 1
1232.1.p \(\chi_{1232}(265, \cdot)\) None 0 1
1232.1.t \(\chi_{1232}(155, \cdot)\) None 0 2
1232.1.u \(\chi_{1232}(307, \cdot)\) 1232.1.u.a 2 2
1232.1.u.b 2
1232.1.v \(\chi_{1232}(573, \cdot)\) None 0 2
1232.1.w \(\chi_{1232}(197, \cdot)\) None 0 2
1232.1.bb \(\chi_{1232}(65, \cdot)\) None 0 2
1232.1.bc \(\chi_{1232}(89, \cdot)\) None 0 2
1232.1.bd \(\chi_{1232}(23, \cdot)\) None 0 2
1232.1.bf \(\chi_{1232}(703, \cdot)\) None 0 2
1232.1.bh \(\chi_{1232}(87, \cdot)\) None 0 2
1232.1.bj \(\chi_{1232}(639, \cdot)\) None 0 2
1232.1.bm \(\chi_{1232}(353, \cdot)\) None 0 2
1232.1.bo \(\chi_{1232}(681, \cdot)\) None 0 2
1232.1.bp \(\chi_{1232}(377, \cdot)\) None 0 4
1232.1.br \(\chi_{1232}(337, \cdot)\) None 0 4
1232.1.bs \(\chi_{1232}(447, \cdot)\) None 0 4
1232.1.bu \(\chi_{1232}(71, \cdot)\) None 0 4
1232.1.bw \(\chi_{1232}(15, \cdot)\) None 0 4
1232.1.by \(\chi_{1232}(167, \cdot)\) None 0 4
1232.1.cb \(\chi_{1232}(57, \cdot)\) None 0 4
1232.1.cd \(\chi_{1232}(97, \cdot)\) 1232.1.cd.a 4 4
1232.1.ce \(\chi_{1232}(131, \cdot)\) None 0 4
1232.1.cf \(\chi_{1232}(67, \cdot)\) None 0 4
1232.1.ck \(\chi_{1232}(109, \cdot)\) None 0 4
1232.1.cl \(\chi_{1232}(45, \cdot)\) None 0 4
1232.1.cp \(\chi_{1232}(29, \cdot)\) None 0 8
1232.1.cq \(\chi_{1232}(69, \cdot)\) 1232.1.cq.a 8 8
1232.1.cq.b 8
1232.1.cr \(\chi_{1232}(83, \cdot)\) 1232.1.cr.a 8 8
1232.1.cr.b 8
1232.1.cs \(\chi_{1232}(267, \cdot)\) None 0 8
1232.1.cv \(\chi_{1232}(233, \cdot)\) None 0 8
1232.1.cx \(\chi_{1232}(257, \cdot)\) None 0 8
1232.1.da \(\chi_{1232}(191, \cdot)\) None 0 8
1232.1.dc \(\chi_{1232}(215, \cdot)\) None 0 8
1232.1.de \(\chi_{1232}(255, \cdot)\) None 0 8
1232.1.dg \(\chi_{1232}(135, \cdot)\) None 0 8
1232.1.dh \(\chi_{1232}(185, \cdot)\) None 0 8
1232.1.di \(\chi_{1232}(193, \cdot)\) None 0 8
1232.1.dk \(\chi_{1232}(5, \cdot)\) None 0 16
1232.1.dl \(\chi_{1232}(149, \cdot)\) None 0 16
1232.1.dq \(\chi_{1232}(163, \cdot)\) None 0 16
1232.1.dr \(\chi_{1232}(19, \cdot)\) None 0 16

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(1232))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(1232)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 20}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 16}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 10}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 10}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(44))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(56))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(77))\)\(^{\oplus 5}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(88))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(112))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(154))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(176))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(308))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(616))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(1232))\)\(^{\oplus 1}\)