Defining parameters
Level: | \( N \) | \(=\) | \( 312 = 2^{3} \cdot 3 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 312.bf (of order \(6\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 13 \) |
Character field: | \(\Q(\zeta_{6})\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(112\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(312, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 128 | 12 | 116 |
Cusp forms | 96 | 12 | 84 |
Eisenstein series | 32 | 0 | 32 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(312, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
312.2.bf.a | $4$ | $2.491$ | \(\Q(\zeta_{12})\) | None | \(0\) | \(2\) | \(0\) | \(6\) | \(q+(1-\zeta_{12}^{2})q^{3}+(1-2\zeta_{12}^{2})q^{5}+(2+\cdots)q^{7}+\cdots\) |
312.2.bf.b | $8$ | $2.491$ | 8.0.649638144.4 | None | \(0\) | \(-4\) | \(0\) | \(0\) | \(q+\beta _{2}q^{3}+(-\beta _{2}-\beta _{6})q^{5}+(1+\beta _{1}+\cdots)q^{7}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(312, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(312, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(13, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(52, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(78, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(104, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(156, [\chi])\)\(^{\oplus 2}\)