Defining parameters
Level: | \( N \) | \(=\) | \( 714 = 2 \cdot 3 \cdot 7 \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 714.f (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 21 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(288\) | ||
Trace bound: | \(17\) | ||
Distinguishing \(T_p\): | \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(714, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 152 | 40 | 112 |
Cusp forms | 136 | 40 | 96 |
Eisenstein series | 16 | 0 | 16 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(714, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
714.2.f.a | $20$ | $5.701$ | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) | None | \(0\) | \(0\) | \(0\) | \(4\) | \(q+\beta _{1}q^{2}+\beta _{9}q^{3}-q^{4}+\beta _{14}q^{5}+\beta _{6}q^{6}+\cdots\) |
714.2.f.b | $20$ | $5.701$ | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) | None | \(0\) | \(0\) | \(0\) | \(4\) | \(q-\beta _{1}q^{2}-\beta _{4}q^{3}-q^{4}-\beta _{14}q^{5}+\beta _{10}q^{6}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(714, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(714, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(357, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 2}\)