Defining parameters
Level: | \( N \) | = | \( 84 = 2^{2} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | = | \( 2 \) |
Nonzero newspaces: | \( 8 \) | ||
Newform subspaces: | \( 13 \) | ||
Sturm bound: | \(768\) | ||
Trace bound: | \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(84))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 252 | 88 | 164 |
Cusp forms | 133 | 72 | 61 |
Eisenstein series | 119 | 16 | 103 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(84))\)
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 available newforms together with their dimension.
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(84))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_1(84)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 2}\)