Defining parameters
Level: | \( N \) | \(=\) | \( 12 = 2^{2} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 12.c (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 3 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 1 \) | ||
Sturm bound: | \(10\) | ||
Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{5}(12, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 11 | 1 | 10 |
Cusp forms | 5 | 1 | 4 |
Eisenstein series | 6 | 0 | 6 |
Trace form
Decomposition of \(S_{5}^{\mathrm{new}}(12, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
12.5.c.a | $1$ | $1.240$ | \(\Q\) | \(\Q(\sqrt{-3}) \) | \(0\) | \(9\) | \(0\) | \(-94\) | \(q+9q^{3}-94q^{7}+3^{4}q^{9}+146q^{13}+\cdots\) |
Decomposition of \(S_{5}^{\mathrm{old}}(12, [\chi])\) into lower level spaces
\( S_{5}^{\mathrm{old}}(12, [\chi]) \cong \) \(S_{5}^{\mathrm{new}}(6, [\chi])\)\(^{\oplus 2}\)