Properties

Label 175.1
Level 175
Weight 1
Dimension 4
Nonzero newspaces 2
Newform subspaces 3
Sturm bound 2400
Trace bound 9

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Defining parameters

Level: \( N \) = \( 175 = 5^{2} \cdot 7 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 3 \)
Sturm bound: \(2400\)
Trace bound: \(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(175))\).

Total New Old
Modular forms 172 107 65
Cusp forms 4 4 0
Eisenstein series 168 103 65

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 4 0 0 0

Trace form

\( 4q + O(q^{10}) \) \( 4q - 4q^{11} - 4q^{16} + 4q^{46} + 4q^{56} - 4q^{71} + 4q^{81} + 4q^{86} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(175))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
175.1.c \(\chi_{175}(174, \cdot)\) 175.1.c.a 2 1
175.1.d \(\chi_{175}(76, \cdot)\) 175.1.d.a 1 1
175.1.d.b 1
175.1.g \(\chi_{175}(43, \cdot)\) None 0 2
175.1.i \(\chi_{175}(26, \cdot)\) None 0 2
175.1.j \(\chi_{175}(24, \cdot)\) None 0 2
175.1.l \(\chi_{175}(6, \cdot)\) None 0 4
175.1.m \(\chi_{175}(34, \cdot)\) None 0 4
175.1.p \(\chi_{175}(18, \cdot)\) None 0 4
175.1.r \(\chi_{175}(8, \cdot)\) None 0 8
175.1.u \(\chi_{175}(19, \cdot)\) None 0 8
175.1.v \(\chi_{175}(31, \cdot)\) None 0 8
175.1.w \(\chi_{175}(2, \cdot)\) None 0 16