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Properties

Label 1156.1
Level 1156
Weight 1
Dimension 85
Nonzero newspaces 7
Newform subspaces 10
Sturm bound 83232
Trace bound 2

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Defining parameters

Level: \( N \) = \( 1156 = 2^{2} \cdot 17^{2} \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 7 \)
Newform subspaces: \( 10 \)
Sturm bound: \(83232\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(1156))\).

Total New Old
Modular forms 1091 454 637
Cusp forms 91 85 6
Eisenstein series 1000 369 631

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 85 0 0 0

Trace form

\( 85 q + q^{2} + q^{4} + 2 q^{5} + q^{8} + q^{9} + O(q^{10}) \) \( 85 q + q^{2} + q^{4} + 2 q^{5} + q^{8} + q^{9} - 6 q^{10} + 2 q^{13} - 7 q^{16} - 7 q^{18} - 6 q^{20} - 5 q^{25} - 6 q^{26} - 6 q^{29} + q^{32} + q^{36} + 2 q^{37} + 2 q^{40} - 6 q^{41} - 6 q^{45} + q^{49} + 3 q^{50} - 14 q^{52} - 6 q^{53} + 2 q^{58} + 2 q^{61} + q^{64} - 4 q^{65} - 4 q^{68} - 7 q^{72} - 6 q^{73} - 6 q^{74} + 2 q^{80} + q^{81} - 6 q^{82} - 4 q^{85} + 2 q^{89} - 6 q^{90} + 2 q^{97} - 7 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(1156))\)

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
1156.1.c \(\chi_{1156}(579, \cdot)\) 1156.1.c.a 1 1
1156.1.c.b 2
1156.1.d \(\chi_{1156}(1155, \cdot)\) 1156.1.d.a 2 1
1156.1.f \(\chi_{1156}(251, \cdot)\) 1156.1.f.a 2 2
1156.1.f.b 2
1156.1.g \(\chi_{1156}(155, \cdot)\) 1156.1.g.a 4 4
1156.1.g.b 8
1156.1.j \(\chi_{1156}(65, \cdot)\) None 0 8
1156.1.l \(\chi_{1156}(67, \cdot)\) 1156.1.l.a 16 16
1156.1.m \(\chi_{1156}(35, \cdot)\) 1156.1.m.a 16 16
1156.1.o \(\chi_{1156}(47, \cdot)\) 1156.1.o.a 32 32
1156.1.r \(\chi_{1156}(15, \cdot)\) None 0 64
1156.1.s \(\chi_{1156}(5, \cdot)\) None 0 128

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(1156))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(1156)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 9}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(34))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(68))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(289))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(578))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(1156))\)\(^{\oplus 1}\)