Defining parameters
Level: | \( N \) | \(=\) | \( 731 = 17 \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 731.d (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 17 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(132\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(731, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 68 | 64 | 4 |
Cusp forms | 64 | 64 | 0 |
Eisenstein series | 4 | 0 | 4 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(731, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
731.2.d.a | $2$ | $5.837$ | \(\Q(\sqrt{-2}) \) | None | \(2\) | \(0\) | \(0\) | \(0\) | \(q+q^{2}-q^{4}+\beta q^{5}-3q^{8}+3q^{9}+\beta q^{10}+\cdots\) |
731.2.d.b | $8$ | $5.837$ | \(\mathbb{Q}[x]/(x^{8} + \cdots)\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\beta _{1}q^{3}-2q^{4}-\beta _{3}q^{5}+(\beta _{1}-\beta _{7})q^{7}+\cdots\) |
731.2.d.c | $20$ | $5.837$ | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) | None | \(2\) | \(0\) | \(0\) | \(0\) | \(q+\beta _{6}q^{2}+\beta _{13}q^{3}+(2+\beta _{1})q^{4}+\beta _{10}q^{5}+\cdots\) |
731.2.d.d | $34$ | $5.837$ | None | \(-6\) | \(0\) | \(0\) | \(0\) |