Defining parameters
Level: | \( N \) | \(=\) | \( 476 = 2^{2} \cdot 7 \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 476.s (of order \(6\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 7 \) |
Character field: | \(\Q(\zeta_{6})\) | ||
Newform subspaces: | \( 1 \) | ||
Sturm bound: | \(216\) | ||
Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(476, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 300 | 44 | 256 |
Cusp forms | 276 | 44 | 232 |
Eisenstein series | 24 | 0 | 24 |
Trace form
Decomposition of \(S_{3}^{\mathrm{new}}(476, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
476.3.s.a | $44$ | $12.970$ | None | \(0\) | \(-6\) | \(0\) | \(22\) |
Decomposition of \(S_{3}^{\mathrm{old}}(476, [\chi])\) into lower level spaces
\( S_{3}^{\mathrm{old}}(476, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(14, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(119, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(238, [\chi])\)\(^{\oplus 2}\)