Defining parameters
Level: | \( N \) | \(=\) | \( 74 = 2 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 74.e (of order \(6\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 37 \) |
Character field: | \(\Q(\zeta_{6})\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(19\) | ||
Trace bound: | \(5\) | ||
Distinguishing \(T_p\): | \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(74, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 24 | 8 | 16 |
Cusp forms | 16 | 8 | 8 |
Eisenstein series | 8 | 0 | 8 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(74, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
74.2.e.a | $4$ | $0.591$ | \(\Q(\zeta_{12})\) | None | \(0\) | \(-2\) | \(-6\) | \(-8\) | \(q+\zeta_{12}q^{2}+(\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{3}+\cdots\) |
74.2.e.b | $4$ | $0.591$ | \(\Q(\zeta_{12})\) | None | \(0\) | \(-2\) | \(6\) | \(4\) | \(q+\zeta_{12}q^{2}+(-\zeta_{12}-\zeta_{12}^{2}-\zeta_{12}^{3})q^{3}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(74, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(74, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(37, [\chi])\)\(^{\oplus 2}\)