Defining parameters
Level: | \( N \) | = | \( 186 = 2 \cdot 3 \cdot 31 \) |
Weight: | \( k \) | = | \( 2 \) |
Nonzero newspaces: | \( 8 \) | ||
Newform subspaces: | \( 21 \) | ||
Sturm bound: | \(3840\) | ||
Trace bound: | \(4\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(186))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 1080 | 241 | 839 |
Cusp forms | 841 | 241 | 600 |
Eisenstein series | 239 | 0 | 239 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(186))\)
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 \(S_{2}^{\mathrm{old}}(\Gamma_1(186))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_1(186)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(31))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(62))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(93))\)\(^{\oplus 2}\)