Defining parameters
Level: | \( N \) | = | \( 228 = 2^{2} \cdot 3 \cdot 19 \) |
Weight: | \( k \) | = | \( 3 \) |
Nonzero newspaces: | \( 12 \) | ||
Newform subspaces: | \( 27 \) | ||
Sturm bound: | \(8640\) | ||
Trace bound: | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(228))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 3060 | 1290 | 1770 |
Cusp forms | 2700 | 1218 | 1482 |
Eisenstein series | 360 | 72 | 288 |
Trace form
Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(228))\)
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 \(S_{3}^{\mathrm{old}}(\Gamma_1(228))\) into lower level spaces
\( S_{3}^{\mathrm{old}}(\Gamma_1(228)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(57))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(76))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(114))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(228))\)\(^{\oplus 1}\)