Defining parameters
Level: | \( N \) | \(=\) | \( 140 = 2^{2} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 140.c (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 140 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(48\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(140, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 28 | 28 | 0 |
Cusp forms | 20 | 20 | 0 |
Eisenstein series | 8 | 8 | 0 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(140, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
140.2.c.a | $4$ | $1.118$ | \(\Q(\sqrt{2}, \sqrt{-5})\) | \(\Q(\sqrt{-5}) \) | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\beta _{2}q^{2}+(-2\beta _{1}-\beta _{2})q^{3}+2q^{4}+\cdots\) |
140.2.c.b | $16$ | $1.118$ | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\beta _{3}q^{2}-\beta _{9}q^{3}+(-1+\beta _{6})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\) |