Defining parameters
Level: | \( N \) | \(=\) | \( 228 = 2^{2} \cdot 3 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 228.o (of order \(6\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 57 \) |
Character field: | \(\Q(\zeta_{6})\) | ||
Newform subspaces: | \( 3 \) | ||
Sturm bound: | \(120\) | ||
Trace bound: | \(7\) | ||
Distinguishing \(T_p\): | \(5\), \(7\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(228, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 172 | 28 | 144 |
Cusp forms | 148 | 28 | 120 |
Eisenstein series | 24 | 0 | 24 |
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.o.a | $2$ | $6.213$ | \(\Q(\sqrt{-3}) \) | \(\Q(\sqrt{-3}) \) | \(0\) | \(3\) | \(0\) | \(-26\) | \(q+3\zeta_{6}q^{3}-13q^{7}+(-9+9\zeta_{6})q^{9}+\cdots\) |
228.3.o.b | $2$ | $6.213$ | \(\Q(\sqrt{-3}) \) | \(\Q(\sqrt{-3}) \) | \(0\) | \(3\) | \(0\) | \(22\) | \(q+3\zeta_{6}q^{3}+11q^{7}+(-9+9\zeta_{6})q^{9}+\cdots\) |
228.3.o.c | $24$ | $6.213$ | None | \(0\) | \(-8\) | \(0\) | \(8\) |
Decomposition of \(S_{3}^{\mathrm{old}}(228, [\chi])\) into lower level spaces
\( S_{3}^{\mathrm{old}}(228, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(57, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(114, [\chi])\)\(^{\oplus 2}\)