Defining parameters
Level: | \( N \) | \(=\) | \( 731 = 17 \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 731.e (of order \(3\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 43 \) |
Character field: | \(\Q(\zeta_{3})\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(132\) | ||
Trace bound: | \(2\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(731, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 136 | 116 | 20 |
Cusp forms | 128 | 116 | 12 |
Eisenstein series | 8 | 0 | 8 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(731, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
731.2.e.a | $58$ | $5.837$ | None | \(-6\) | \(3\) | \(-1\) | \(7\) | ||
731.2.e.b | $58$ | $5.837$ | None | \(2\) | \(-5\) | \(-3\) | \(-13\) |
Decomposition of \(S_{2}^{\mathrm{old}}(731, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(731, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(43, [\chi])\)\(^{\oplus 2}\)