Defining parameters
Level: | \( N \) | = | \( 45 = 3^{2} \cdot 5 \) |
Weight: | \( k \) | = | \( 5 \) |
Nonzero newspaces: | \( 6 \) | ||
Newform subspaces: | \( 10 \) | ||
Sturm bound: | \(720\) | ||
Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{5}(\Gamma_1(45))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 320 | 222 | 98 |
Cusp forms | 256 | 194 | 62 |
Eisenstein series | 64 | 28 | 36 |
Trace form
Decomposition of \(S_{5}^{\mathrm{new}}(\Gamma_1(45))\)
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 \(S_{5}^{\mathrm{old}}(\Gamma_1(45))\) into lower level spaces
\( S_{5}^{\mathrm{old}}(\Gamma_1(45)) \cong \) \(S_{5}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 1}\)