Defining parameters
Level: | \( N \) | \(=\) | \( 312 = 2^{3} \cdot 3 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 312.m (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 104 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 3 \) | ||
Sturm bound: | \(112\) | ||
Trace bound: | \(2\) | ||
Distinguishing \(T_p\): | \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(312, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 60 | 28 | 32 |
Cusp forms | 52 | 28 | 24 |
Eisenstein series | 8 | 0 | 8 |
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.m.a | $2$ | $2.491$ | \(\Q(\sqrt{-1}) \) | None | \(-2\) | \(0\) | \(-4\) | \(0\) | \(q+(-1+i)q^{2}-iq^{3}-2iq^{4}-2q^{5}+\cdots\) |
312.2.m.b | $2$ | $2.491$ | \(\Q(\sqrt{-1}) \) | None | \(2\) | \(0\) | \(4\) | \(0\) | \(q+(1+i)q^{2}+iq^{3}+2iq^{4}+2q^{5}+\cdots\) |
312.2.m.c | $24$ | $2.491$ | None | \(0\) | \(0\) | \(0\) | \(0\) |
Decomposition of \(S_{2}^{\mathrm{old}}(312, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(312, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(104, [\chi])\)\(^{\oplus 2}\)