Properties

Label 95.1
Level 95
Weight 1
Dimension 3
Nonzero newspaces 1
Newform subspaces 2
Sturm bound 720
Trace bound 0

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Defining parameters

Level: \( N \) = \( 95 = 5 \cdot 19 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 2 \)
Sturm bound: \(720\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(95))\).

Total New Old
Modular forms 75 53 22
Cusp forms 3 3 0
Eisenstein series 72 50 22

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 3 0 0 0

Trace form

\( 3q + q^{4} - q^{5} - 4q^{6} + q^{9} + O(q^{10}) \) \( 3q + q^{4} - q^{5} - 4q^{6} + q^{9} - 2q^{11} - q^{16} - q^{19} - 3q^{20} + 3q^{25} + 4q^{26} + 4q^{30} + 3q^{36} - 4q^{39} + 2q^{44} - 3q^{45} + 3q^{49} - 2q^{55} - 2q^{61} - 3q^{64} - 4q^{74} - 3q^{76} + 3q^{80} - q^{81} + 3q^{95} + 4q^{96} + 2q^{99} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(95))\)

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
95.1.c \(\chi_{95}(56, \cdot)\) None 0 1
95.1.d \(\chi_{95}(94, \cdot)\) 95.1.d.a 1 1
95.1.d.b 2
95.1.f \(\chi_{95}(58, \cdot)\) None 0 2
95.1.h \(\chi_{95}(69, \cdot)\) None 0 2
95.1.j \(\chi_{95}(31, \cdot)\) None 0 2
95.1.m \(\chi_{95}(7, \cdot)\) None 0 4
95.1.n \(\chi_{95}(21, \cdot)\) None 0 6
95.1.o \(\chi_{95}(14, \cdot)\) None 0 6
95.1.q \(\chi_{95}(17, \cdot)\) None 0 12