Defining parameters
Level: | \( N \) | \(=\) | \( 54 = 2 \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 54.c (of order \(3\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 9 \) |
Character field: | \(\Q(\zeta_{3})\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(36\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(54, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 66 | 6 | 60 |
Cusp forms | 42 | 6 | 36 |
Eisenstein series | 24 | 0 | 24 |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(54, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
54.4.c.a | $2$ | $3.186$ | \(\Q(\sqrt{-3}) \) | None | \(2\) | \(0\) | \(-9\) | \(31\) | \(q+(2-2\zeta_{6})q^{2}-4\zeta_{6}q^{4}-9\zeta_{6}q^{5}+\cdots\) |
54.4.c.b | $4$ | $3.186$ | \(\Q(\sqrt{-3}, \sqrt{-35})\) | None | \(-4\) | \(0\) | \(-9\) | \(-19\) | \(q+2\beta _{1}q^{2}+(-4-4\beta _{1})q^{4}+(-4-4\beta _{1}+\cdots)q^{5}+\cdots\) |
Decomposition of \(S_{4}^{\mathrm{old}}(54, [\chi])\) into lower level spaces
\( S_{4}^{\mathrm{old}}(54, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(27, [\chi])\)\(^{\oplus 2}\)