Defining parameters
Level: | \( N \) | \(=\) | \( 8 = 2^{3} \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 8.d (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 8 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(7\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{7}(8, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 7 | 7 | 0 |
Cusp forms | 5 | 5 | 0 |
Eisenstein series | 2 | 2 | 0 |
Trace form
Decomposition of \(S_{7}^{\mathrm{new}}(8, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
8.7.d.a | $1$ | $1.840$ | \(\Q\) | \(\Q(\sqrt{-2}) \) | \(-8\) | \(46\) | \(0\) | \(0\) | \(q-8q^{2}+46q^{3}+2^{6}q^{4}-368q^{6}+\cdots\) |
8.7.d.b | $4$ | $1.840$ | 4.0.3803625.2 | None | \(2\) | \(-48\) | \(0\) | \(0\) | \(q+\beta _{1}q^{2}+(-13+2\beta _{1}+\beta _{2})q^{3}+(-12+\cdots)q^{4}+\cdots\) |