Defining parameters
Level: | \( N \) | \(=\) | \( 429 = 3 \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 429.n (of order \(5\) and degree \(4\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 11 \) |
Character field: | \(\Q(\zeta_{5})\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(112\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(429, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 240 | 96 | 144 |
Cusp forms | 208 | 96 | 112 |
Eisenstein series | 32 | 0 | 32 |
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.n.a | $12$ | $3.426$ | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) | None | \(3\) | \(-3\) | \(8\) | \(5\) | \(q-\beta _{6}q^{2}+\beta _{4}q^{3}+(-\beta _{1}+\beta _{2}+\beta _{4}+\cdots)q^{4}+\cdots\) |
429.2.n.b | $20$ | $3.426$ | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) | None | \(1\) | \(5\) | \(4\) | \(-3\) | \(q+\beta _{5}q^{2}-\beta _{9}q^{3}+(-\beta _{3}-\beta _{5}-\beta _{7}+\cdots)q^{4}+\cdots\) |
429.2.n.c | $28$ | $3.426$ | None | \(1\) | \(7\) | \(-4\) | \(1\) | ||
429.2.n.d | $36$ | $3.426$ | None | \(3\) | \(-9\) | \(0\) | \(1\) |
Decomposition of \(S_{2}^{\mathrm{old}}(429, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(429, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(33, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(143, [\chi])\)\(^{\oplus 2}\)