Defining parameters
Level: | \( N \) | \(=\) | \( 338 = 2 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 338.e (of order \(6\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 13 \) |
Character field: | \(\Q(\zeta_{6})\) | ||
Newform subspaces: | \( 5 \) | ||
Sturm bound: | \(91\) | ||
Trace bound: | \(3\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(338, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 120 | 28 | 92 |
Cusp forms | 64 | 28 | 36 |
Eisenstein series | 56 | 0 | 56 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(338, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
338.2.e.a | $4$ | $2.699$ | \(\Q(\zeta_{12})\) | None | \(0\) | \(-2\) | \(0\) | \(0\) | \(q+\zeta_{12}q^{2}+(-1+\zeta_{12}^{2})q^{3}+\zeta_{12}^{2}q^{4}+\cdots\) |
338.2.e.b | $4$ | $2.699$ | \(\Q(\zeta_{12})\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+\zeta_{12}^{3}q^{5}+(4\zeta_{12}+\cdots)q^{7}+\cdots\) |
338.2.e.c | $4$ | $2.699$ | \(\Q(\zeta_{12})\) | None | \(0\) | \(2\) | \(0\) | \(0\) | \(q+\zeta_{12}q^{2}+(1-\zeta_{12}^{2})q^{3}+\zeta_{12}^{2}q^{4}+\cdots\) |
338.2.e.d | $4$ | $2.699$ | \(\Q(\zeta_{12})\) | None | \(0\) | \(6\) | \(0\) | \(0\) | \(q+\zeta_{12}q^{2}+(3-3\zeta_{12}^{2})q^{3}+\zeta_{12}^{2}q^{4}+\cdots\) |
338.2.e.e | $12$ | $2.699$ | 12.0.\(\cdots\).1 | None | \(0\) | \(-6\) | \(0\) | \(0\) | \(q+\beta _{6}q^{2}+(\beta _{4}+2\beta _{9})q^{3}+\beta _{7}q^{4}+(2\beta _{2}+\cdots)q^{5}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(338, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(338, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(13, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(26, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(169, [\chi])\)\(^{\oplus 2}\)