Defining parameters
Level: | \( N \) | \(=\) | \( 429 = 3 \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 429.e (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 429 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(112\) | ||
Trace bound: | \(4\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(429, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 60 | 60 | 0 |
Cusp forms | 52 | 52 | 0 |
Eisenstein series | 8 | 8 | 0 |
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.e.a | $8$ | $3.426$ | 8.0.\(\cdots\).21 | \(\Q(\sqrt{-39}) \) | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\beta _{3}q^{2}-\beta _{2}q^{3}+(-2-\beta _{2})q^{4}+(\beta _{1}+\cdots)q^{5}+\cdots\) |
429.2.e.b | $8$ | $3.426$ | 8.0.3317760000.2 | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\beta _{1}q^{2}+\beta _{2}q^{3}+q^{4}+\beta _{6}q^{5}-\beta _{4}q^{6}+\cdots\) |
429.2.e.c | $16$ | $3.426$ | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) | None | \(0\) | \(-4\) | \(0\) | \(0\) | \(q+\beta _{3}q^{2}-\beta _{5}q^{3}+(-1+\beta _{4}+\beta _{5}+\cdots)q^{4}+\cdots\) |
429.2.e.d | $20$ | $3.426$ | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) | \(\Q(\sqrt{-143}) \) | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\beta _{4}q^{2}+\beta _{1}q^{3}+(-2+\beta _{8})q^{4}+\beta _{7}q^{6}+\cdots\) |