Properties

Label 256.1
Level 256
Weight 1
Dimension 1
Nonzero newspaces 1
Newform subspaces 1
Sturm bound 4096
Trace bound 0

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Defining parameters

Level: \( N \) = \( 256 = 2^{8} \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 1 \)
Sturm bound: \(4096\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(256))\).

Total New Old
Modular forms 179 53 126
Cusp forms 3 1 2
Eisenstein series 176 52 124

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 \(S_{1}^{\mathrm{new}}(\Gamma_1(256))\)

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
256.1.c \(\chi_{256}(255, \cdot)\) 256.1.c.a 1 1
256.1.d \(\chi_{256}(127, \cdot)\) None 0 1
256.1.f \(\chi_{256}(63, \cdot)\) None 0 2
256.1.h \(\chi_{256}(31, \cdot)\) None 0 4
256.1.j \(\chi_{256}(15, \cdot)\) None 0 8
256.1.l \(\chi_{256}(7, \cdot)\) None 0 16
256.1.n \(\chi_{256}(3, \cdot)\) None 0 32

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(256))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(256)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(128))\)\(^{\oplus 2}\)