Defining parameters
Level: | \( N \) | = | \( 3072 = 2^{10} \cdot 3 \) |
Weight: | \( k \) | = | \( 1 \) |
Nonzero newspaces: | \( 4 \) | ||
Newform subspaces: | \( 15 \) | ||
Sturm bound: | \(524288\) | ||
Trace bound: | \(9\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(3072))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 3544 | 544 | 3000 |
Cusp forms | 216 | 64 | 152 |
Eisenstein series | 3328 | 480 | 2848 |
The following table gives the dimensions of subspaces with specified projective image type.
\(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
---|---|---|---|---|
Dimension | 64 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(3072))\)
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.
Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(3072))\) into lower level spaces
\( S_{1}^{\mathrm{old}}(\Gamma_1(3072)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(128))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(192))\)\(^{\oplus 5}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(256))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(384))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(512))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(768))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(1024))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(1536))\)\(^{\oplus 2}\)