Defining parameters
Level: | \( N \) | \(=\) | \( 156 = 2^{2} \cdot 3 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 156.w (of order \(12\) and degree \(4\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 52 \) |
Character field: | \(\Q(\zeta_{12})\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(56\) | ||
Trace bound: | \(2\) | ||
Distinguishing \(T_p\): | \(5\), \(7\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(156, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 128 | 56 | 72 |
Cusp forms | 96 | 56 | 40 |
Eisenstein series | 32 | 0 | 32 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(156, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
156.2.w.a | $4$ | $1.246$ | \(\Q(\zeta_{12})\) | None | \(2\) | \(0\) | \(-4\) | \(-6\) | \(q+(1+\zeta_{12}-\zeta_{12}^{2})q^{2}+(-\zeta_{12}+\zeta_{12}^{3})q^{3}+\cdots\) |
156.2.w.b | $4$ | $1.246$ | \(\Q(\zeta_{12})\) | None | \(4\) | \(0\) | \(-4\) | \(6\) | \(q+(1+\zeta_{12}^{3})q^{2}+(\zeta_{12}-\zeta_{12}^{3})q^{3}+\cdots\) |
156.2.w.c | $24$ | $1.246$ | None | \(-4\) | \(0\) | \(2\) | \(-2\) | ||
156.2.w.d | $24$ | $1.246$ | None | \(-2\) | \(0\) | \(2\) | \(2\) |
Decomposition of \(S_{2}^{\mathrm{old}}(156, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(156, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(52, [\chi])\)\(^{\oplus 2}\)