Defining parameters
Level: | \( N \) | \(=\) | \( 115 = 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 115.g (of order \(11\) and degree \(10\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 23 \) |
Character field: | \(\Q(\zeta_{11})\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(48\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(115, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 380 | 240 | 140 |
Cusp forms | 340 | 240 | 100 |
Eisenstein series | 40 | 0 | 40 |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(115, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
115.4.g.a | $110$ | $6.785$ | None | \(-2\) | \(6\) | \(-55\) | \(-10\) | ||
115.4.g.b | $130$ | $6.785$ | None | \(6\) | \(-6\) | \(65\) | \(38\) |
Decomposition of \(S_{4}^{\mathrm{old}}(115, [\chi])\) into lower level spaces
\( S_{4}^{\mathrm{old}}(115, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(23, [\chi])\)\(^{\oplus 2}\)