Defining parameters
| Level: | \( N \) | \(=\) | \( 228 = 2^{2} \cdot 3 \cdot 19 \) |
| Weight: | \( k \) | \(=\) | \( 3 \) |
| Character orbit: | \([\chi]\) | \(=\) | 228.b (of order \(2\) and degree \(1\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 228 \) |
| Character field: | \(\Q\) | ||
| Newform subspaces: | \( 5 \) | ||
| Sturm bound: | \(120\) | ||
| Trace bound: | \(3\) | ||
| Distinguishing \(T_p\): | \(5\), \(11\), \(29\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(228, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 84 | 84 | 0 |
| Cusp forms | 76 | 76 | 0 |
| Eisenstein series | 8 | 8 | 0 |
Trace form
Decomposition of \(S_{3}^{\mathrm{new}}(228, [\chi])\) into newform subspaces
| Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
|---|---|---|---|---|---|---|---|---|---|
| $a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
| 228.3.b.a | $1$ | $6.213$ | \(\Q\) | \(\Q(\sqrt{-57}) \) | \(-2\) | \(-3\) | \(0\) | \(0\) | \(q-2q^{2}-3q^{3}+4q^{4}+6q^{6}-8q^{8}+\cdots\) |
| 228.3.b.b | $1$ | $6.213$ | \(\Q\) | \(\Q(\sqrt{-57}) \) | \(-2\) | \(3\) | \(0\) | \(0\) | \(q-2q^{2}+3q^{3}+4q^{4}-6q^{6}-8q^{8}+\cdots\) |
| 228.3.b.c | $1$ | $6.213$ | \(\Q\) | \(\Q(\sqrt{-57}) \) | \(2\) | \(-3\) | \(0\) | \(0\) | \(q+2q^{2}-3q^{3}+4q^{4}-6q^{6}+8q^{8}+\cdots\) |
| 228.3.b.d | $1$ | $6.213$ | \(\Q\) | \(\Q(\sqrt{-57}) \) | \(2\) | \(3\) | \(0\) | \(0\) | \(q+2q^{2}+3q^{3}+4q^{4}+6q^{6}+8q^{8}+\cdots\) |
| 228.3.b.e | $72$ | $6.213$ | None | \(0\) | \(0\) | \(0\) | \(0\) | ||