Defining parameters
Level: | \( N \) | \(=\) | \( 222 = 2 \cdot 3 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 222.e (of order \(3\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 37 \) |
Character field: | \(\Q(\zeta_{3})\) | ||
Newform subspaces: | \( 3 \) | ||
Sturm bound: | \(76\) | ||
Trace bound: | \(2\) | ||
Distinguishing \(T_p\): | \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(222, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 84 | 8 | 76 |
Cusp forms | 68 | 8 | 60 |
Eisenstein series | 16 | 0 | 16 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(222, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
222.2.e.a | $2$ | $1.773$ | \(\Q(\sqrt{-3}) \) | None | \(-1\) | \(1\) | \(0\) | \(3\) | \(q+(-1+\zeta_{6})q^{2}+\zeta_{6}q^{3}-\zeta_{6}q^{4}-q^{6}+\cdots\) |
222.2.e.b | $2$ | $1.773$ | \(\Q(\sqrt{-3}) \) | None | \(1\) | \(-1\) | \(-1\) | \(-2\) | \(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{3}-\zeta_{6}q^{4}-\zeta_{6}q^{5}+\cdots\) |
222.2.e.c | $4$ | $1.773$ | \(\Q(\sqrt{-3}, \sqrt{-11})\) | None | \(2\) | \(2\) | \(-1\) | \(-3\) | \(q+(1-\beta _{1})q^{2}+\beta _{1}q^{3}-\beta _{1}q^{4}-\beta _{3}q^{5}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(222, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(222, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(37, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(74, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(111, [\chi])\)\(^{\oplus 2}\)