Defining parameters
Level: | \( N \) | \(=\) | \( 320 = 2^{6} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 320.d (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 8 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(288\) | ||
Trace bound: | \(7\) | ||
Distinguishing \(T_p\): | \(3\), \(7\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{6}(320, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 252 | 40 | 212 |
Cusp forms | 228 | 40 | 188 |
Eisenstein series | 24 | 0 | 24 |
Trace form
Decomposition of \(S_{6}^{\mathrm{new}}(320, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
320.6.d.a | $8$ | $51.323$ | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) | None | \(0\) | \(0\) | \(0\) | \(-320\) | \(q-\beta _{4}q^{3}+5^{2}\beta _{1}q^{5}+(-40-3\beta _{2}+\cdots)q^{7}+\cdots\) |
320.6.d.b | $8$ | $51.323$ | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) | None | \(0\) | \(0\) | \(0\) | \(320\) | \(q-\beta _{4}q^{3}-5^{2}\beta _{1}q^{5}+(40+3\beta _{2}+\beta _{6}+\cdots)q^{7}+\cdots\) |
320.6.d.c | $12$ | $51.323$ | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) | None | \(0\) | \(0\) | \(0\) | \(-268\) | \(q+(3\beta _{1}-\beta _{4})q^{3}-5^{2}\beta _{1}q^{5}+(-22+\cdots)q^{7}+\cdots\) |
320.6.d.d | $12$ | $51.323$ | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) | None | \(0\) | \(0\) | \(0\) | \(268\) | \(q+(3\beta _{1}-\beta _{4})q^{3}+5^{2}\beta _{1}q^{5}+(22-\beta _{2}+\cdots)q^{7}+\cdots\) |
Decomposition of \(S_{6}^{\mathrm{old}}(320, [\chi])\) into lower level spaces
\( S_{6}^{\mathrm{old}}(320, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 2}\)