Defining parameters
Level: | \( N \) | \(=\) | \( 216 = 2^{3} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 216.f (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 24 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(72\) | ||
Trace bound: | \(4\) | ||
Distinguishing \(T_p\): | \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(216, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 42 | 16 | 26 |
Cusp forms | 30 | 16 | 14 |
Eisenstein series | 12 | 0 | 12 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(216, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
216.2.f.a | $8$ | $1.725$ | 8.0.\(\cdots\).3 | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\beta _{3}q^{2}+(-1-\beta _{1}-\beta _{4})q^{4}+\beta _{2}q^{5}+\cdots\) |
216.2.f.b | $8$ | $1.725$ | 8.0.170772624.1 | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\beta _{4}q^{2}-\beta _{3}q^{4}+\beta _{2}q^{5}+(\beta _{1}-\beta _{3}+\cdots)q^{7}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(216, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(216, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 3}\)