Defining parameters
Level: | \( N \) | \(=\) | \( 429 = 3 \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 429.bn (of order \(30\) and degree \(8\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 143 \) |
Character field: | \(\Q(\zeta_{30})\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(112\) | ||
Trace bound: | \(3\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(429, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 480 | 224 | 256 |
Cusp forms | 416 | 224 | 192 |
Eisenstein series | 64 | 0 | 64 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(429, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
429.2.bn.a | $112$ | $3.426$ | None | \(0\) | \(-14\) | \(0\) | \(0\) | ||
429.2.bn.b | $112$ | $3.426$ | None | \(0\) | \(14\) | \(0\) | \(0\) |
Decomposition of \(S_{2}^{\mathrm{old}}(429, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(429, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(143, [\chi])\)\(^{\oplus 2}\)