Defining parameters
Level: | \( N \) | \(=\) | \( 297 = 3^{3} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 297.n (of order \(15\) and degree \(8\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 99 \) |
Character field: | \(\Q(\zeta_{15})\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(72\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(297, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 336 | 112 | 224 |
Cusp forms | 240 | 80 | 160 |
Eisenstein series | 96 | 32 | 64 |
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.n.a | $8$ | $2.372$ | \(\Q(\zeta_{15})\) | None | \(4\) | \(0\) | \(-6\) | \(-1\) | \(q+(-\zeta_{15}-\zeta_{15}^{2}-\zeta_{15}^{5}-\zeta_{15}^{6}+\cdots)q^{2}+\cdots\) |
297.2.n.b | $72$ | $2.372$ | None | \(1\) | \(0\) | \(8\) | \(-2\) |
Decomposition of \(S_{2}^{\mathrm{old}}(297, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(297, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(99, [\chi])\)\(^{\oplus 2}\)