Defining parameters
Level: | \( N \) | = | \( 1536 = 2^{9} \cdot 3 \) |
Weight: | \( k \) | = | \( 1 \) |
Nonzero newspaces: | \( 2 \) | ||
Newform subspaces: | \( 5 \) | ||
Sturm bound: | \(131072\) | ||
Trace bound: | \(9\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(1536))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 1616 | 240 | 1376 |
Cusp forms | 80 | 16 | 64 |
Eisenstein series | 1536 | 224 | 1312 |
The following table gives the dimensions of subspaces with specified projective image type.
\(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
---|---|---|---|---|
Dimension | 16 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(1536))\)
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 |
---|---|---|---|---|
1536.1.b | \(\chi_{1536}(1279, \cdot)\) | None | 0 | 1 |
1536.1.e | \(\chi_{1536}(1025, \cdot)\) | 1536.1.e.a | 4 | 1 |
1536.1.e.b | 4 | |||
1536.1.g | \(\chi_{1536}(511, \cdot)\) | None | 0 | 1 |
1536.1.h | \(\chi_{1536}(257, \cdot)\) | 1536.1.h.a | 2 | 1 |
1536.1.h.b | 2 | |||
1536.1.h.c | 4 | |||
1536.1.i | \(\chi_{1536}(641, \cdot)\) | None | 0 | 2 |
1536.1.l | \(\chi_{1536}(127, \cdot)\) | None | 0 | 2 |
1536.1.m | \(\chi_{1536}(319, \cdot)\) | None | 0 | 4 |
1536.1.p | \(\chi_{1536}(65, \cdot)\) | None | 0 | 4 |
1536.1.q | \(\chi_{1536}(161, \cdot)\) | None | 0 | 8 |
1536.1.t | \(\chi_{1536}(31, \cdot)\) | None | 0 | 8 |
1536.1.u | \(\chi_{1536}(79, \cdot)\) | None | 0 | 16 |
1536.1.x | \(\chi_{1536}(17, \cdot)\) | None | 0 | 16 |
1536.1.y | \(\chi_{1536}(41, \cdot)\) | None | 0 | 32 |
1536.1.bb | \(\chi_{1536}(7, \cdot)\) | None | 0 | 32 |
1536.1.bc | \(\chi_{1536}(19, \cdot)\) | None | 0 | 64 |
1536.1.bf | \(\chi_{1536}(5, \cdot)\) | None | 0 | 64 |
Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(1536))\) into lower level spaces
\( S_{1}^{\mathrm{old}}(\Gamma_1(1536)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(128))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(192))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(256))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(384))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(512))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(768))\)\(^{\oplus 2}\)