Defining parameters
Level: | \( N \) | \(=\) | \( 12 = 2^{2} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 11 \) |
Character orbit: | \([\chi]\) | \(=\) | 12.c (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 3 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(22\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{11}(12, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 23 | 3 | 20 |
Cusp forms | 17 | 3 | 14 |
Eisenstein series | 6 | 0 | 6 |
Trace form
Decomposition of \(S_{11}^{\mathrm{new}}(12, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
12.11.c.a | $1$ | $7.624$ | \(\Q\) | \(\Q(\sqrt{-3}) \) | \(0\) | \(-243\) | \(0\) | \(22082\) | \(q-3^{5}q^{3}+22082q^{7}+3^{10}q^{9}+702218q^{13}+\cdots\) |
12.11.c.b | $2$ | $7.624$ | \(\Q(\sqrt{-35}) \) | None | \(0\) | \(234\) | \(0\) | \(-20636\) | \(q+(117+\beta )q^{3}+6\beta q^{5}-10318q^{7}+\cdots\) |
Decomposition of \(S_{11}^{\mathrm{old}}(12, [\chi])\) into lower level spaces
\( S_{11}^{\mathrm{old}}(12, [\chi]) \cong \) \(S_{11}^{\mathrm{new}}(3, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(6, [\chi])\)\(^{\oplus 2}\)