Defining parameters
Level: | \( N \) | = | \( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | = | \( 2 \) |
Nonzero newspaces: | \( 12 \) | ||
Newform subspaces: | \( 32 \) | ||
Sturm bound: | \(4608\) | ||
Trace bound: | \(4\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(210))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 1344 | 249 | 1095 |
Cusp forms | 961 | 249 | 712 |
Eisenstein series | 383 | 0 | 383 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(210))\)
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.
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(210))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_1(210)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(70))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(105))\)\(^{\oplus 2}\)