Defining parameters
Level: | \( N \) | \(=\) | \( 182 = 2 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 182.m (of order \(6\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 13 \) |
Character field: | \(\Q(\zeta_{6})\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(56\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(182, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 64 | 16 | 48 |
Cusp forms | 48 | 16 | 32 |
Eisenstein series | 16 | 0 | 16 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(182, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
182.2.m.a | $4$ | $1.453$ | \(\Q(\zeta_{12})\) | None | \(0\) | \(2\) | \(0\) | \(0\) | \(q+\zeta_{12}q^{2}+(1-\zeta_{12}-\zeta_{12}^{2}+2\zeta_{12}^{3})q^{3}+\cdots\) |
182.2.m.b | $12$ | $1.453$ | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) | None | \(0\) | \(-2\) | \(0\) | \(0\) | \(q-\beta _{5}q^{2}+(\beta _{2}+\beta _{10})q^{3}+(1-\beta _{7})q^{4}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(182, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(182, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(13, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(91, [\chi])\)\(^{\oplus 2}\)