Defining parameters
Level: | \( N \) | = | \( 1020 = 2^{2} \cdot 3 \cdot 5 \cdot 17 \) |
Weight: | \( k \) | = | \( 1 \) |
Nonzero newspaces: | \( 2 \) | ||
Newform subspaces: | \( 3 \) | ||
Sturm bound: | \(55296\) | ||
Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(1020))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 1434 | 212 | 1222 |
Cusp forms | 154 | 36 | 118 |
Eisenstein series | 1280 | 176 | 1104 |
The following table gives the dimensions of subspaces with specified projective image type.
\(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
---|---|---|---|---|
Dimension | 36 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(1020))\)
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.
Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(1020))\) into lower level spaces
\( S_{1}^{\mathrm{old}}(\Gamma_1(1020)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(68))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(204))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(255))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(340))\)\(^{\oplus 2}\)