Defining parameters
Level: | \( N \) | \(=\) | \( 20 = 2^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 20.d (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 20 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(21\) | ||
Trace bound: | \(2\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{7}(20, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 20 | 20 | 0 |
Cusp forms | 16 | 16 | 0 |
Eisenstein series | 4 | 4 | 0 |
Trace form
Decomposition of \(S_{7}^{\mathrm{new}}(20, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
20.7.d.a | $1$ | $4.601$ | \(\Q\) | \(\Q(\sqrt{-5}) \) | \(-8\) | \(-44\) | \(-125\) | \(524\) | \(q-8q^{2}-44q^{3}+2^{6}q^{4}-5^{3}q^{5}+352q^{6}+\cdots\) |
20.7.d.b | $1$ | $4.601$ | \(\Q\) | \(\Q(\sqrt{-5}) \) | \(8\) | \(44\) | \(-125\) | \(-524\) | \(q+8q^{2}+44q^{3}+2^{6}q^{4}-5^{3}q^{5}+352q^{6}+\cdots\) |
20.7.d.c | $2$ | $4.601$ | \(\Q(\sqrt{-1}) \) | \(\Q(\sqrt{-1}) \) | \(0\) | \(0\) | \(-234\) | \(0\) | \(q+2iq^{2}-2^{6}q^{4}+(-117+11i)q^{5}+\cdots\) |
20.7.d.d | $12$ | $4.601$ | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) | None | \(0\) | \(0\) | \(460\) | \(0\) | \(q-\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{3}+(6+\beta _{4}-\beta _{8}+\cdots)q^{4}+\cdots\) |