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Properties

Label 1075.1
Level 1075
Weight 1
Dimension 10
Nonzero newspaces 2
Newform subspaces 4
Sturm bound 92400
Trace bound 1

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Defining parameters

Level: \( N \) = \( 1075 = 5^{2} \cdot 43 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 4 \)
Sturm bound: \(92400\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(1075))\).

Total New Old
Modular forms 1198 851 347
Cusp forms 22 10 12
Eisenstein series 1176 841 335

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 10 0 0 0

Trace form

\( 10 q - 4 q^{4} - 4 q^{6} - 4 q^{9} + O(q^{10}) \) \( 10 q - 4 q^{4} - 4 q^{6} - 4 q^{9} - 6 q^{11} + 4 q^{14} + 6 q^{16} - 4 q^{21} + 8 q^{24} - 6 q^{31} + 2 q^{36} - 6 q^{41} + 6 q^{44} - 4 q^{49} - 6 q^{54} + 6 q^{56} + 2 q^{59} + 6 q^{66} - 10 q^{74} + 2 q^{79} + 6 q^{81} - 2 q^{84} - 2 q^{86} + 2 q^{96} + 6 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(1075))\)

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
1075.1.c \(\chi_{1075}(601, \cdot)\) 1075.1.c.a 1 1
1075.1.c.b 1
1075.1.c.c 6
1075.1.d \(\chi_{1075}(1074, \cdot)\) 1075.1.d.a 2 1
1075.1.f \(\chi_{1075}(732, \cdot)\) None 0 2
1075.1.i \(\chi_{1075}(351, \cdot)\) None 0 2
1075.1.k \(\chi_{1075}(424, \cdot)\) None 0 2
1075.1.m \(\chi_{1075}(214, \cdot)\) None 0 4
1075.1.n \(\chi_{1075}(171, \cdot)\) None 0 4
1075.1.q \(\chi_{1075}(307, \cdot)\) None 0 4
1075.1.r \(\chi_{1075}(174, \cdot)\) None 0 6
1075.1.s \(\chi_{1075}(51, \cdot)\) None 0 6
1075.1.w \(\chi_{1075}(87, \cdot)\) None 0 8
1075.1.z \(\chi_{1075}(107, \cdot)\) None 0 12
1075.1.ba \(\chi_{1075}(179, \cdot)\) None 0 8
1075.1.bc \(\chi_{1075}(136, \cdot)\) None 0 8
1075.1.be \(\chi_{1075}(149, \cdot)\) None 0 12
1075.1.bg \(\chi_{1075}(26, \cdot)\) None 0 12
1075.1.bh \(\chi_{1075}(92, \cdot)\) None 0 16
1075.1.bk \(\chi_{1075}(131, \cdot)\) None 0 24
1075.1.bl \(\chi_{1075}(39, \cdot)\) None 0 24
1075.1.bm \(\chi_{1075}(57, \cdot)\) None 0 24
1075.1.bp \(\chi_{1075}(47, \cdot)\) None 0 48
1075.1.br \(\chi_{1075}(46, \cdot)\) None 0 48
1075.1.bt \(\chi_{1075}(19, \cdot)\) None 0 48
1075.1.bv \(\chi_{1075}(13, \cdot)\) None 0 96

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(1075))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(1075)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(43))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(215))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(1075))\)\(^{\oplus 1}\)