Defining parameters
Level: | \( N \) | = | \( 80 = 2^{4} \cdot 5 \) |
Weight: | \( k \) | = | \( 5 \) |
Nonzero newspaces: | \( 7 \) | ||
Newform subspaces: | \( 16 \) | ||
Sturm bound: | \(1920\) | ||
Trace bound: | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{5}(\Gamma_1(80))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 824 | 410 | 414 |
Cusp forms | 712 | 382 | 330 |
Eisenstein series | 112 | 28 | 84 |
Trace form
Decomposition of \(S_{5}^{\mathrm{new}}(\Gamma_1(80))\)
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 available newforms together with their dimension.
Decomposition of \(S_{5}^{\mathrm{old}}(\Gamma_1(80))\) into lower level spaces
\( S_{5}^{\mathrm{old}}(\Gamma_1(80)) \cong \) \(S_{5}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 10}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 8}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 5}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 2}\)