Properties

Label 256.9
Level 256
Weight 9
Dimension 9164
Nonzero newspaces 6
Sturm bound 36864
Trace bound 9

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Defining parameters

Level: \( N \) = \( 256 = 2^{8} \)
Weight: \( k \) = \( 9 \)
Nonzero newspaces: \( 6 \)
Sturm bound: \(36864\)
Trace bound: \(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(\Gamma_1(256))\).

Total New Old
Modular forms 16560 9268 7292
Cusp forms 16208 9164 7044
Eisenstein series 352 104 248

Trace form

\( 9164 q - 32 q^{2} - 24 q^{3} - 32 q^{4} - 32 q^{5} - 32 q^{6} - 24 q^{7} - 32 q^{8} - 40 q^{9} - 32 q^{10} - 24 q^{11} - 32 q^{12} - 32 q^{13} - 32 q^{14} - 24 q^{15} - 32 q^{16} - 48 q^{17} - 32 q^{18}+ \cdots - 52512 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{9}^{\mathrm{new}}(\Gamma_1(256))\)

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 available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
256.9.c \(\chi_{256}(255, \cdot)\) 256.9.c.a 1 1
256.9.c.b 1
256.9.c.c 2
256.9.c.d 2
256.9.c.e 2
256.9.c.f 2
256.9.c.g 2
256.9.c.h 2
256.9.c.i 4
256.9.c.j 4
256.9.c.k 8
256.9.c.l 8
256.9.c.m 12
256.9.c.n 12
256.9.d \(\chi_{256}(127, \cdot)\) 256.9.d.a 2 1
256.9.d.b 4
256.9.d.c 4
256.9.d.d 4
256.9.d.e 4
256.9.d.f 4
256.9.d.g 4
256.9.d.h 4
256.9.d.i 16
256.9.d.j 16
256.9.f \(\chi_{256}(63, \cdot)\) n/a 128 2
256.9.h \(\chi_{256}(31, \cdot)\) n/a 248 4
256.9.j \(\chi_{256}(15, \cdot)\) n/a 504 8
256.9.l \(\chi_{256}(7, \cdot)\) None 0 16
256.9.n \(\chi_{256}(3, \cdot)\) n/a 8160 32

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{9}^{\mathrm{old}}(\Gamma_1(256))\) into lower level spaces

\( S_{9}^{\mathrm{old}}(\Gamma_1(256)) \cong \) \(S_{9}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 9}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 8}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 7}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 6}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 5}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 4}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(64))\)\(^{\oplus 3}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(128))\)\(^{\oplus 2}\)