Defining parameters
Level: | \( N \) | \(=\) | \( 80 = 2^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 20 \) |
Character orbit: | \([\chi]\) | \(=\) | 80.c (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 5 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(240\) | ||
Trace bound: | \(5\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{20}(80, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 234 | 58 | 176 |
Cusp forms | 222 | 56 | 166 |
Eisenstein series | 12 | 2 | 10 |
Trace form
Decomposition of \(S_{20}^{\mathrm{new}}(80, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
80.20.c.a | $8$ | $183.053$ | \(\mathbb{Q}[x]/(x^{8} + \cdots)\) | None | \(0\) | \(0\) | \(147000\) | \(0\) | \(q+\beta _{2}q^{3}+(18375-\beta _{1}-3^{3}\beta _{2}+\beta _{3}+\cdots)q^{5}+\cdots\) |
80.20.c.b | $10$ | $183.053$ | \(\mathbb{Q}[x]/(x^{10} + \cdots)\) | None | \(0\) | \(0\) | \(-897466\) | \(0\) | \(q+\beta _{1}q^{3}+(-89747+8\beta _{1}+\beta _{2})q^{5}+\cdots\) |
80.20.c.c | $10$ | $183.053$ | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) | None | \(0\) | \(0\) | \(2902670\) | \(0\) | \(q+\beta _{1}q^{3}+(290267+11\beta _{1}+2\beta _{2}+\cdots)q^{5}+\cdots\) |
80.20.c.d | $28$ | $183.053$ | None | \(0\) | \(0\) | \(-3935164\) | \(0\) |
Decomposition of \(S_{20}^{\mathrm{old}}(80, [\chi])\) into lower level spaces
\( S_{20}^{\mathrm{old}}(80, [\chi]) \simeq \) \(S_{20}^{\mathrm{new}}(5, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{20}^{\mathrm{new}}(10, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{20}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{20}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 2}\)