Defining parameters
Level: | \( N \) | \(=\) | \( 475 = 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 475.x (of order \(30\) and degree \(8\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 475 \) |
Character field: | \(\Q(\zeta_{30})\) | ||
Newform subspaces: | \( 1 \) | ||
Sturm bound: | \(100\) | ||
Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(475, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 416 | 416 | 0 |
Cusp forms | 384 | 384 | 0 |
Eisenstein series | 32 | 32 | 0 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(475, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
475.2.x.a | $384$ | $3.793$ | None | \(-5\) | \(-5\) | \(-5\) | \(0\) |