Defining parameters
Level: | \( N \) | = | \( 3009 = 3 \cdot 17 \cdot 59 \) |
Weight: | \( k \) | = | \( 2 \) |
Nonzero newspaces: | \( 20 \) | ||
Sturm bound: | \(1336320\) | ||
Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(3009))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 337792 | 250387 | 87405 |
Cusp forms | 330369 | 246971 | 83398 |
Eisenstein series | 7423 | 3416 | 4007 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(3009))\)
We only show spaces with even 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.
"n/a" means that newforms for that character have not been added to the database yet
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(3009))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_1(3009)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(51))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(59))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(177))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1003))\)\(^{\oplus 2}\)