Defining parameters
Level: | \( N \) | \(=\) | \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 546.k (of order \(3\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 91 \) |
Character field: | \(\Q(\zeta_{3})\) | ||
Newform subspaces: | \( 5 \) | ||
Sturm bound: | \(224\) | ||
Trace bound: | \(3\) | ||
Distinguishing \(T_p\): | \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(546, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 240 | 36 | 204 |
Cusp forms | 208 | 36 | 172 |
Eisenstein series | 32 | 0 | 32 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(546, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
546.2.k.a | $2$ | $4.360$ | \(\Q(\sqrt{-3}) \) | None | \(-1\) | \(-2\) | \(0\) | \(-5\) | \(q-\zeta_{6}q^{2}-q^{3}+(-1+\zeta_{6})q^{4}+\zeta_{6}q^{6}+\cdots\) |
546.2.k.b | $8$ | $4.360$ | 8.0.447703281.1 | None | \(-4\) | \(-8\) | \(2\) | \(3\) | \(q+\beta _{3}q^{2}-q^{3}+(-1-\beta _{3})q^{4}+(1-2\beta _{1}+\cdots)q^{5}+\cdots\) |
546.2.k.c | $8$ | $4.360$ | 8.0.447703281.1 | None | \(-4\) | \(8\) | \(2\) | \(-3\) | \(q-\beta _{2}q^{2}+q^{3}+(-1+\beta _{2})q^{4}+(1-\beta _{2}+\cdots)q^{5}+\cdots\) |
546.2.k.d | $8$ | $4.360$ | 8.0.6498455769.2 | None | \(4\) | \(8\) | \(-2\) | \(3\) | \(q+(1-\beta _{4})q^{2}+q^{3}-\beta _{4}q^{4}+\beta _{2}q^{5}+\cdots\) |
546.2.k.e | $10$ | $4.360$ | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) | None | \(5\) | \(-10\) | \(-2\) | \(4\) | \(q+(1+\beta _{5})q^{2}-q^{3}+\beta _{5}q^{4}+(\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(546, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(546, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(91, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(182, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(273, [\chi])\)\(^{\oplus 2}\)