Defining parameters
Level: | \( N \) | \(=\) | \( 297 = 3^{3} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 297.e (of order \(3\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 9 \) |
Character field: | \(\Q(\zeta_{3})\) | ||
Newform subspaces: | \( 5 \) | ||
Sturm bound: | \(72\) | ||
Trace bound: | \(2\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(297, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 84 | 20 | 64 |
Cusp forms | 60 | 20 | 40 |
Eisenstein series | 24 | 0 | 24 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(297, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
297.2.e.a | $2$ | $2.372$ | \(\Q(\sqrt{-3}) \) | None | \(-2\) | \(0\) | \(-2\) | \(-4\) | \(q+(-2+2\zeta_{6})q^{2}-2\zeta_{6}q^{4}-2\zeta_{6}q^{5}+\cdots\) |
297.2.e.b | $2$ | $2.372$ | \(\Q(\sqrt{-3}) \) | None | \(0\) | \(0\) | \(-3\) | \(4\) | \(q+2\zeta_{6}q^{4}-3\zeta_{6}q^{5}+(4-4\zeta_{6})q^{7}+\cdots\) |
297.2.e.c | $2$ | $2.372$ | \(\Q(\sqrt{-3}) \) | None | \(1\) | \(0\) | \(1\) | \(-4\) | \(q+(1-\zeta_{6})q^{2}+\zeta_{6}q^{4}+\zeta_{6}q^{5}+(-4+\cdots)q^{7}+\cdots\) |
297.2.e.d | $6$ | $2.372$ | \(\Q(\zeta_{18})\) | None | \(0\) | \(0\) | \(3\) | \(3\) | \(q+(-\beta_{5}+\beta_{4}+\cdots-\beta_{2})q^{2}+\cdots+\beta_{5} q^{4}+\cdots\) |
297.2.e.e | $8$ | $2.372$ | 8.0.508277025.1 | None | \(1\) | \(0\) | \(4\) | \(-1\) | \(q+(\beta _{2}+\beta _{6})q^{2}+(\beta _{3}+3\beta _{5})q^{4}+(\beta _{3}+\cdots)q^{5}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(297, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(297, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(99, [\chi])\)\(^{\oplus 2}\)