Defining parameters
Level: | \( N \) | \(=\) | \( 118 = 2 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 118.c (of order \(29\) and degree \(28\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 59 \) |
Character field: | \(\Q(\zeta_{29})\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(30\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(118, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 476 | 140 | 336 |
Cusp forms | 364 | 140 | 224 |
Eisenstein series | 112 | 0 | 112 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(118, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
118.2.c.a | $56$ | $0.942$ | None | \(2\) | \(-1\) | \(1\) | \(4\) | ||
118.2.c.b | $84$ | $0.942$ | None | \(-3\) | \(-5\) | \(-5\) | \(-8\) |
Decomposition of \(S_{2}^{\mathrm{old}}(118, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(118, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(59, [\chi])\)\(^{\oplus 2}\)