Defining parameters
Level: | \( N \) | = | \( 69 = 3 \cdot 23 \) |
Weight: | \( k \) | = | \( 2 \) |
Nonzero newspaces: | \( 4 \) | ||
Newform subspaces: | \( 7 \) | ||
Sturm bound: | \(704\) | ||
Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(69))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 220 | 153 | 67 |
Cusp forms | 133 | 109 | 24 |
Eisenstein series | 87 | 44 | 43 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(69))\)
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 \(S_{2}^{\mathrm{old}}(\Gamma_1(69))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_1(69)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 2}\)