Defining parameters
Level: | \( N \) | \(=\) | \( 58 = 2 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 58.e (of order \(14\) and degree \(6\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 29 \) |
Character field: | \(\Q(\zeta_{14})\) | ||
Newform subspaces: | \( 1 \) | ||
Sturm bound: | \(15\) | ||
Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(58, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 60 | 12 | 48 |
Cusp forms | 36 | 12 | 24 |
Eisenstein series | 24 | 0 | 24 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(58, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
58.2.e.a | $12$ | $0.463$ | \(\Q(\zeta_{28})\) | None | \(0\) | \(0\) | \(-2\) | \(4\) | \(q-\zeta_{28}^{9}q^{2}+(-\zeta_{28}-\zeta_{28}^{3}-\zeta_{28}^{5}+\cdots)q^{3}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(58, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(58, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(29, [\chi])\)\(^{\oplus 2}\)