Defining parameters
Level: | \( N \) | \(=\) | \( 156 = 2^{2} \cdot 3 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 156.i (of order \(3\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 13 \) |
Character field: | \(\Q(\zeta_{3})\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(112\) | ||
Trace bound: | \(3\) | ||
Distinguishing \(T_p\): | \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(156, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 180 | 16 | 164 |
Cusp forms | 156 | 16 | 140 |
Eisenstein series | 24 | 0 | 24 |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(156, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
156.4.i.a | $8$ | $9.204$ | \(\mathbb{Q}[x]/(x^{8} + \cdots)\) | None | \(0\) | \(-12\) | \(14\) | \(-11\) | \(q+(-3-3\beta _{2})q^{3}+(2+\beta _{5})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots\) |
156.4.i.b | $8$ | $9.204$ | \(\mathbb{Q}[x]/(x^{8} + \cdots)\) | None | \(0\) | \(12\) | \(6\) | \(15\) | \(q+3\beta _{1}q^{3}+(1+\beta _{4}+\beta _{5})q^{5}+(4-4\beta _{1}+\cdots)q^{7}+\cdots\) |
Decomposition of \(S_{4}^{\mathrm{old}}(156, [\chi])\) into lower level spaces
\( S_{4}^{\mathrm{old}}(156, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(13, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(26, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(52, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(78, [\chi])\)\(^{\oplus 2}\)