Defining parameters
Level: | \( N \) | = | \( 123 = 3 \cdot 41 \) |
Weight: | \( k \) | = | \( 2 \) |
Nonzero newspaces: | \( 8 \) | ||
Newform subspaces: | \( 13 \) | ||
Sturm bound: | \(2240\) | ||
Trace bound: | \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(123))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 640 | 459 | 181 |
Cusp forms | 481 | 379 | 102 |
Eisenstein series | 159 | 80 | 79 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(123))\)
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 \(S_{2}^{\mathrm{old}}(\Gamma_1(123))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_1(123)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(41))\)\(^{\oplus 2}\)