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Properties

Label 1488.1
Level 1488
Weight 1
Dimension 56
Nonzero newspaces 8
Newform subspaces 13
Sturm bound 122880
Trace bound 6

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Defining parameters

Level: \( N \) = \( 1488 = 2^{4} \cdot 3 \cdot 31 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 8 \)
Newform subspaces: \( 13 \)
Sturm bound: \(122880\)
Trace bound: \(6\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(1488))\).

Total New Old
Modular forms 1926 316 1610
Cusp forms 246 56 190
Eisenstein series 1680 260 1420

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 44 0 12 0

Trace form

\( 56 q + 3 q^{3} - 4 q^{6} + 2 q^{7} - 3 q^{9} - 4 q^{13} - 8 q^{16} + 4 q^{19} - 2 q^{21} + q^{25} - 3 q^{27} - 4 q^{28} + 9 q^{31} + 8 q^{33} - 4 q^{36} - 8 q^{37} - 2 q^{39} + 8 q^{43} - 8 q^{46} - q^{49}+ \cdots + 2 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(1488))\)

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
1488.1.b \(\chi_{1488}(1487, \cdot)\) 1488.1.b.a 1 1
1488.1.b.b 1
1488.1.d \(\chi_{1488}(1303, \cdot)\) None 0 1
1488.1.g \(\chi_{1488}(497, \cdot)\) None 0 1
1488.1.i \(\chi_{1488}(1177, \cdot)\) None 0 1
1488.1.k \(\chi_{1488}(559, \cdot)\) None 0 1
1488.1.m \(\chi_{1488}(743, \cdot)\) None 0 1
1488.1.n \(\chi_{1488}(433, \cdot)\) None 0 1
1488.1.p \(\chi_{1488}(1241, \cdot)\) None 0 1
1488.1.r \(\chi_{1488}(61, \cdot)\) None 0 2
1488.1.s \(\chi_{1488}(125, \cdot)\) None 0 2
1488.1.x \(\chi_{1488}(187, \cdot)\) None 0 2
1488.1.y \(\chi_{1488}(371, \cdot)\) None 0 2
1488.1.ba \(\chi_{1488}(377, \cdot)\) None 0 2
1488.1.bc \(\chi_{1488}(1153, \cdot)\) None 0 2
1488.1.bd \(\chi_{1488}(119, \cdot)\) None 0 2
1488.1.bf \(\chi_{1488}(1183, \cdot)\) None 0 2
1488.1.bh \(\chi_{1488}(409, \cdot)\) None 0 2
1488.1.bj \(\chi_{1488}(1121, \cdot)\) 1488.1.bj.a 2 2
1488.1.bj.b 4
1488.1.bm \(\chi_{1488}(439, \cdot)\) None 0 2
1488.1.bo \(\chi_{1488}(719, \cdot)\) 1488.1.bo.a 2 2
1488.1.bo.b 2
1488.1.bp \(\chi_{1488}(457, \cdot)\) None 0 4
1488.1.br \(\chi_{1488}(593, \cdot)\) 1488.1.br.a 4 4
1488.1.bu \(\chi_{1488}(295, \cdot)\) None 0 4
1488.1.bw \(\chi_{1488}(767, \cdot)\) 1488.1.bw.a 4 4
1488.1.bw.b 4
1488.1.bx \(\chi_{1488}(233, \cdot)\) None 0 4
1488.1.bz \(\chi_{1488}(337, \cdot)\) None 0 4
1488.1.ca \(\chi_{1488}(23, \cdot)\) None 0 4
1488.1.cc \(\chi_{1488}(655, \cdot)\) None 0 4
1488.1.ce \(\chi_{1488}(347, \cdot)\) None 0 4
1488.1.cf \(\chi_{1488}(67, \cdot)\) None 0 4
1488.1.ck \(\chi_{1488}(5, \cdot)\) 1488.1.ck.a 8 4
1488.1.cl \(\chi_{1488}(37, \cdot)\) None 0 4
1488.1.cn \(\chi_{1488}(275, \cdot)\) None 0 8
1488.1.co \(\chi_{1488}(163, \cdot)\) None 0 8
1488.1.ct \(\chi_{1488}(101, \cdot)\) None 0 8
1488.1.cu \(\chi_{1488}(85, \cdot)\) None 0 8
1488.1.cw \(\chi_{1488}(175, \cdot)\) None 0 8
1488.1.cy \(\chi_{1488}(167, \cdot)\) None 0 8
1488.1.cz \(\chi_{1488}(145, \cdot)\) None 0 8
1488.1.db \(\chi_{1488}(41, \cdot)\) None 0 8
1488.1.dc \(\chi_{1488}(239, \cdot)\) 1488.1.dc.a 8 8
1488.1.dc.b 8
1488.1.de \(\chi_{1488}(7, \cdot)\) None 0 8
1488.1.dh \(\chi_{1488}(113, \cdot)\) 1488.1.dh.a 8 8
1488.1.dj \(\chi_{1488}(73, \cdot)\) None 0 8
1488.1.dk \(\chi_{1488}(13, \cdot)\) None 0 16
1488.1.dl \(\chi_{1488}(173, \cdot)\) None 0 16
1488.1.dq \(\chi_{1488}(19, \cdot)\) None 0 16
1488.1.dr \(\chi_{1488}(11, \cdot)\) None 0 16

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(1488))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(1488)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 20}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 16}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 10}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(31))\)\(^{\oplus 10}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(62))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(93))\)\(^{\oplus 5}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(124))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(186))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(248))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(372))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(496))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(744))\)\(^{\oplus 2}\)