Defining parameters
Level: | \( N \) | = | \( 84 = 2^{2} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | = | \( 8 \) |
Nonzero newspaces: | \( 8 \) | ||
Newform subspaces: | \( 16 \) | ||
Sturm bound: | \(3072\) | ||
Trace bound: | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_1(84))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 1404 | 564 | 840 |
Cusp forms | 1284 | 548 | 736 |
Eisenstein series | 120 | 16 | 104 |
Trace form
Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_1(84))\)
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 \(S_{8}^{\mathrm{old}}(\Gamma_1(84))\) into lower level spaces
\( S_{8}^{\mathrm{old}}(\Gamma_1(84)) \cong \) \(S_{8}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 8}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 6}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 6}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 3}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(84))\)\(^{\oplus 1}\)