Properties

Label 128.1
Level 128
Weight 1
Dimension 1
Nonzero newspaces 1
Newform subspaces 1
Sturm bound 1024
Trace bound 0

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Defining parameters

Level: \( N \) = \( 128 = 2^{7} \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 1 \)
Sturm bound: \(1024\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(128))\).

Total New Old
Modular forms 81 25 56
Cusp forms 1 1 0
Eisenstein series 80 24 56

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 1 0 0 0

Trace form

\( q - q^{9} + O(q^{10}) \) \( q - q^{9} - 2q^{17} + q^{25} + 2q^{41} + q^{49} - 2q^{73} + q^{81} - 2q^{89} - 2q^{97} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(128))\)

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
128.1.c \(\chi_{128}(127, \cdot)\) None 0 1
128.1.d \(\chi_{128}(63, \cdot)\) 128.1.d.a 1 1
128.1.f \(\chi_{128}(31, \cdot)\) None 0 2
128.1.h \(\chi_{128}(15, \cdot)\) None 0 4
128.1.j \(\chi_{128}(7, \cdot)\) None 0 8
128.1.l \(\chi_{128}(3, \cdot)\) None 0 16