Defining parameters
Level: | \( N \) | \(=\) | \( 156 = 2^{2} \cdot 3 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 156.o (of order \(6\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 39 \) |
Character field: | \(\Q(\zeta_{6})\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(84\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(156, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 124 | 18 | 106 |
Cusp forms | 100 | 18 | 82 |
Eisenstein series | 24 | 0 | 24 |
Trace form
Decomposition of \(S_{3}^{\mathrm{new}}(156, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
156.3.o.a | $2$ | $4.251$ | \(\Q(\sqrt{-3}) \) | \(\Q(\sqrt{-3}) \) | \(0\) | \(3\) | \(0\) | \(-11\) | \(q+3\zeta_{6}q^{3}+(-11+11\zeta_{6})q^{7}+(-9+\cdots)q^{9}+\cdots\) |
156.3.o.b | $16$ | $4.251$ | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) | None | \(0\) | \(-3\) | \(0\) | \(2\) | \(q+\beta _{10}q^{3}-\beta _{11}q^{5}+(1+\beta _{1}+\beta _{3}+\cdots)q^{7}+\cdots\) |
Decomposition of \(S_{3}^{\mathrm{old}}(156, [\chi])\) into lower level spaces
\( S_{3}^{\mathrm{old}}(156, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(78, [\chi])\)\(^{\oplus 2}\)