Defining parameters
Level: | \( N \) | \(=\) | \( 114 = 2 \cdot 3 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 114.e (of order \(3\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 19 \) |
Character field: | \(\Q(\zeta_{3})\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(40\) | ||
Trace bound: | \(2\) | ||
Distinguishing \(T_p\): | \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(114, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 48 | 4 | 44 |
Cusp forms | 32 | 4 | 28 |
Eisenstein series | 16 | 0 | 16 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(114, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
114.2.e.a | $2$ | $0.910$ | \(\Q(\sqrt{-3}) \) | None | \(-1\) | \(1\) | \(4\) | \(-6\) | \(q+(-1+\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\) |
114.2.e.b | $2$ | $0.910$ | \(\Q(\sqrt{-3}) \) | None | \(1\) | \(1\) | \(0\) | \(2\) | \(q+(1-\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(114, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(114, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(38, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(57, [\chi])\)\(^{\oplus 2}\)