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Properties

Label 1288.1
Level 1288
Weight 1
Dimension 82
Nonzero newspaces 3
Newform subspaces 9
Sturm bound 101376
Trace bound 1

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Defining parameters

Level: \( N \) = \( 1288 = 2^{3} \cdot 7 \cdot 23 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 3 \)
Newform subspaces: \( 9 \)
Sturm bound: \(101376\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(1288))\).

Total New Old
Modular forms 1774 502 1272
Cusp forms 190 82 108
Eisenstein series 1584 420 1164

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 82 0 0 0

Trace form

\( 82 q + 2 q^{2} - 6 q^{4} + 2 q^{7} + 2 q^{8} - 2 q^{9} + O(q^{10}) \) \( 82 q + 2 q^{2} - 6 q^{4} + 2 q^{7} + 2 q^{8} - 2 q^{9} - 6 q^{14} - 8 q^{15} - 6 q^{16} + 34 q^{18} - 6 q^{23} - 2 q^{25} + 2 q^{28} + 36 q^{30} + 2 q^{32} - 2 q^{36} - 8 q^{39} + 2 q^{46} - 6 q^{49} - 10 q^{50} - 6 q^{56} - 8 q^{57} - 8 q^{60} - 10 q^{63} - 6 q^{64} - 8 q^{65} + 4 q^{71} - 10 q^{72} - 22 q^{74} - 8 q^{78} + 4 q^{79} + 30 q^{81} - 22 q^{88} - 6 q^{92} - 8 q^{95} - 20 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(1288))\)

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
1288.1.c \(\chi_{1288}(643, \cdot)\) 1288.1.c.a 1 1
1288.1.c.b 1
1288.1.d \(\chi_{1288}(1105, \cdot)\) None 0 1
1288.1.g \(\chi_{1288}(967, \cdot)\) None 0 1
1288.1.h \(\chi_{1288}(1149, \cdot)\) None 0 1
1288.1.k \(\chi_{1288}(505, \cdot)\) None 0 1
1288.1.l \(\chi_{1288}(323, \cdot)\) None 0 1
1288.1.o \(\chi_{1288}(461, \cdot)\) None 0 1
1288.1.p \(\chi_{1288}(1287, \cdot)\) None 0 1
1288.1.r \(\chi_{1288}(367, \cdot)\) None 0 2
1288.1.t \(\chi_{1288}(829, \cdot)\) None 0 2
1288.1.u \(\chi_{1288}(1059, \cdot)\) None 0 2
1288.1.x \(\chi_{1288}(137, \cdot)\) None 0 2
1288.1.y \(\chi_{1288}(597, \cdot)\) None 0 2
1288.1.bb \(\chi_{1288}(415, \cdot)\) None 0 2
1288.1.bc \(\chi_{1288}(185, \cdot)\) None 0 2
1288.1.bf \(\chi_{1288}(1011, \cdot)\) None 0 2
1288.1.bh \(\chi_{1288}(111, \cdot)\) None 0 10
1288.1.bi \(\chi_{1288}(13, \cdot)\) 1288.1.bi.a 10 10
1288.1.bi.b 10
1288.1.bi.c 10
1288.1.bi.d 10
1288.1.bi.e 20
1288.1.bl \(\chi_{1288}(211, \cdot)\) None 0 10
1288.1.bm \(\chi_{1288}(57, \cdot)\) None 0 10
1288.1.bp \(\chi_{1288}(309, \cdot)\) None 0 10
1288.1.bq \(\chi_{1288}(71, \cdot)\) None 0 10
1288.1.bt \(\chi_{1288}(41, \cdot)\) None 0 10
1288.1.bu \(\chi_{1288}(83, \cdot)\) 1288.1.bu.a 10 10
1288.1.bu.b 10
1288.1.bx \(\chi_{1288}(19, \cdot)\) None 0 20
1288.1.ca \(\chi_{1288}(73, \cdot)\) None 0 20
1288.1.cb \(\chi_{1288}(39, \cdot)\) None 0 20
1288.1.ce \(\chi_{1288}(37, \cdot)\) None 0 20
1288.1.cf \(\chi_{1288}(65, \cdot)\) None 0 20
1288.1.ci \(\chi_{1288}(123, \cdot)\) None 0 20
1288.1.cj \(\chi_{1288}(101, \cdot)\) None 0 20
1288.1.cl \(\chi_{1288}(103, \cdot)\) None 0 20

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(1288))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(1288)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(56))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(161))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(184))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(644))\)\(^{\oplus 2}\)