Defining parameters
Level: | \( N \) | \(=\) | \( 69 = 3 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 69.e (of order \(11\) and degree \(10\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 23 \) |
Character field: | \(\Q(\zeta_{11})\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(32\) | ||
Trace bound: | \(2\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(69, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 260 | 120 | 140 |
Cusp forms | 220 | 120 | 100 |
Eisenstein series | 40 | 0 | 40 |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(69, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
69.4.e.a | $60$ | $4.071$ | None | \(0\) | \(-18\) | \(22\) | \(24\) | ||
69.4.e.b | $60$ | $4.071$ | None | \(4\) | \(18\) | \(-6\) | \(-4\) |
Decomposition of \(S_{4}^{\mathrm{old}}(69, [\chi])\) into lower level spaces
\( S_{4}^{\mathrm{old}}(69, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(23, [\chi])\)\(^{\oplus 2}\)