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Properties

Label 1088.1
Level 1088
Weight 1
Dimension 37
Nonzero newspaces 6
Newform subspaces 9
Sturm bound 73728
Trace bound 25

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Defining parameters

Level: \( N \) = \( 1088 = 2^{6} \cdot 17 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 6 \)
Newform subspaces: \( 9 \)
Sturm bound: \(73728\)
Trace bound: \(25\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(1088))\).

Total New Old
Modular forms 1280 367 913
Cusp forms 128 37 91
Eisenstein series 1152 330 822

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 37 0 0 0

Trace form

\( 37 q + 2 q^{5} + q^{9} + O(q^{10}) \) \( 37 q + 2 q^{5} + q^{9} + 2 q^{13} - 3 q^{17} + 4 q^{21} - q^{25} + 2 q^{29} - 4 q^{33} + 2 q^{37} + 2 q^{41} + 2 q^{45} + q^{49} + 6 q^{53} - 16 q^{57} + 2 q^{61} - 4 q^{65} - 4 q^{69} + 2 q^{73} - 4 q^{77} - 23 q^{81} + 2 q^{85} - 10 q^{89} - 4 q^{93} - 6 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(1088))\)

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
1088.1.d \(\chi_{1088}(511, \cdot)\) None 0 1
1088.1.e \(\chi_{1088}(543, \cdot)\) None 0 1
1088.1.f \(\chi_{1088}(1055, \cdot)\) None 0 1
1088.1.g \(\chi_{1088}(1087, \cdot)\) 1088.1.g.a 1 1
1088.1.g.b 2
1088.1.i \(\chi_{1088}(591, \cdot)\) None 0 2
1088.1.k \(\chi_{1088}(271, \cdot)\) None 0 2
1088.1.n \(\chi_{1088}(735, \cdot)\) 1088.1.n.a 2 2
1088.1.n.b 2
1088.1.p \(\chi_{1088}(191, \cdot)\) 1088.1.p.a 2 2
1088.1.q \(\chi_{1088}(239, \cdot)\) None 0 2
1088.1.t \(\chi_{1088}(47, \cdot)\) None 0 2
1088.1.u \(\chi_{1088}(151, \cdot)\) None 0 4
1088.1.w \(\chi_{1088}(359, \cdot)\) None 0 4
1088.1.y \(\chi_{1088}(55, \cdot)\) None 0 4
1088.1.ba \(\chi_{1088}(127, \cdot)\) 1088.1.ba.a 4 4
1088.1.bf \(\chi_{1088}(15, \cdot)\) None 0 4
1088.1.bh \(\chi_{1088}(399, \cdot)\) None 0 4
1088.1.bi \(\chi_{1088}(103, \cdot)\) None 0 4
1088.1.bj \(\chi_{1088}(135, \cdot)\) None 0 4
1088.1.bl \(\chi_{1088}(223, \cdot)\) None 0 4
1088.1.bm \(\chi_{1088}(183, \cdot)\) None 0 4
1088.1.bo \(\chi_{1088}(247, \cdot)\) None 0 4
1088.1.br \(\chi_{1088}(87, \cdot)\) None 0 4
1088.1.bt \(\chi_{1088}(5, \cdot)\) None 0 8
1088.1.bu \(\chi_{1088}(141, \cdot)\) None 0 8
1088.1.bw \(\chi_{1088}(19, \cdot)\) None 0 8
1088.1.bz \(\chi_{1088}(45, \cdot)\) None 0 8
1088.1.cb \(\chi_{1088}(37, \cdot)\) None 0 8
1088.1.cc \(\chi_{1088}(113, \cdot)\) None 0 8
1088.1.ch \(\chi_{1088}(57, \cdot)\) None 0 8
1088.1.ci \(\chi_{1088}(245, \cdot)\) None 0 8
1088.1.ck \(\chi_{1088}(29, \cdot)\) None 0 8
1088.1.cm \(\chi_{1088}(67, \cdot)\) None 0 8
1088.1.co \(\chi_{1088}(97, \cdot)\) 1088.1.co.a 8 8
1088.1.co.b 8
1088.1.cq \(\chi_{1088}(265, \cdot)\) None 0 8
1088.1.ct \(\chi_{1088}(251, \cdot)\) None 0 8
1088.1.cu \(\chi_{1088}(115, \cdot)\) None 0 8
1088.1.cw \(\chi_{1088}(41, \cdot)\) None 0 8
1088.1.cz \(\chi_{1088}(65, \cdot)\) 1088.1.cz.a 8 8
1088.1.db \(\chi_{1088}(35, \cdot)\) None 0 8
1088.1.dd \(\chi_{1088}(73, \cdot)\) None 0 8
1088.1.de \(\chi_{1088}(155, \cdot)\) None 0 8
1088.1.df \(\chi_{1088}(219, \cdot)\) None 0 8
1088.1.dg \(\chi_{1088}(241, \cdot)\) None 0 8
1088.1.di \(\chi_{1088}(43, \cdot)\) None 0 8
1088.1.dk \(\chi_{1088}(197, \cdot)\) None 0 8
1088.1.dn \(\chi_{1088}(109, \cdot)\) None 0 8

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(1088))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(1088)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 14}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 10}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 7}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(34))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(64))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(68))\)\(^{\oplus 5}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(136))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(272))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(544))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(1088))\)\(^{\oplus 1}\)