Defining parameters
Level: | \( N \) | \(=\) | \( 5 \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 5.c (of order \(4\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 5 \) |
Character field: | \(\Q(i)\) | ||
Newform subspaces: | \( 1 \) | ||
Sturm bound: | \(3\) | ||
Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{7}(5, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 8 | 8 | 0 |
Cusp forms | 4 | 4 | 0 |
Eisenstein series | 4 | 4 | 0 |
Trace form
Decomposition of \(S_{7}^{\mathrm{new}}(5, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
5.7.c.a | $4$ | $1.150$ | \(\Q(i, \sqrt{201})\) | None | \(-10\) | \(30\) | \(-70\) | \(550\) | \(q+(-2+2\beta _{1}+\beta _{3})q^{2}+(7+8\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots\) |