Defining parameters
Level: | \( N \) | \(=\) | \( 430 = 2 \cdot 5 \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 430.k (of order \(7\) and degree \(6\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 43 \) |
Character field: | \(\Q(\zeta_{7})\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(132\) | ||
Trace bound: | \(2\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(430, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 420 | 72 | 348 |
Cusp forms | 372 | 72 | 300 |
Eisenstein series | 48 | 0 | 48 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(430, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
430.2.k.a | $12$ | $3.434$ | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) | None | \(-2\) | \(-1\) | \(-2\) | \(4\) | \(q+(-1+\beta _{7}+\beta _{8}-\beta _{9}+\beta _{10}-\beta _{11})q^{2}+\cdots\) |
430.2.k.b | $18$ | $3.434$ | \(\mathbb{Q}[x]/(x^{18} - \cdots)\) | None | \(-3\) | \(2\) | \(3\) | \(6\) | \(q-\beta _{3}q^{2}+\beta _{5}q^{3}+\beta _{4}q^{4}-\beta _{10}q^{5}+\cdots\) |
430.2.k.c | $18$ | $3.434$ | \(\mathbb{Q}[x]/(x^{18} - \cdots)\) | None | \(3\) | \(5\) | \(-3\) | \(8\) | \(q-\beta _{12}q^{2}+\beta _{1}q^{3}+(-1+\beta _{3}-\beta _{7}+\cdots)q^{4}+\cdots\) |
430.2.k.d | $24$ | $3.434$ | None | \(4\) | \(2\) | \(4\) | \(-2\) |
Decomposition of \(S_{2}^{\mathrm{old}}(430, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(430, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(43, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(86, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(215, [\chi])\)\(^{\oplus 2}\)