Defining parameters
Level: | \( N \) | \(=\) | \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 546.bm (of order \(6\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 91 \) |
Character field: | \(\Q(\zeta_{6})\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(224\) | ||
Trace bound: | \(1\) | ||
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.bm.a | $16$ | $4.360$ | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) | None | \(0\) | \(8\) | \(0\) | \(-2\) | \(q+(\beta _{12}+\beta _{13})q^{2}+\beta _{3}q^{3}-q^{4}+(\beta _{2}+\cdots)q^{5}+\cdots\) |
546.2.bm.b | $20$ | $4.360$ | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) | None | \(0\) | \(-10\) | \(0\) | \(0\) | \(q+(-\beta _{10}+\beta _{11})q^{2}+\beta _{12}q^{3}-q^{4}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(546, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(546, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(91, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(182, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(273, [\chi])\)\(^{\oplus 2}\)