Defining parameters
Level: | \( N \) | = | \( 504 = 2^{3} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | = | \( 1 \) |
Nonzero newspaces: | \( 7 \) | ||
Newform subspaces: | \( 10 \) | ||
Sturm bound: | \(13824\) | ||
Trace bound: | \(7\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(504))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 646 | 121 | 525 |
Cusp forms | 70 | 31 | 39 |
Eisenstein series | 576 | 90 | 486 |
The following table gives the dimensions of subspaces with specified projective image type.
\(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
---|---|---|---|---|
Dimension | 19 | 8 | 4 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(504))\)
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 \(S_{1}^{\mathrm{old}}(\Gamma_1(504))\) into lower level spaces
\( S_{1}^{\mathrm{old}}(\Gamma_1(504)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(56))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(63))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(84))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(168))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(252))\)\(^{\oplus 2}\)