Defining parameters
Level: | \( N \) | \(=\) | \( 475 = 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 475.v (of order \(20\) and degree \(8\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 475 \) |
Character field: | \(\Q(\zeta_{20})\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(100\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(2\) |
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.v.a | $16$ | $3.793$ | 16.0.\(\cdots\).1 | \(\Q(\sqrt{-19}) \) | \(0\) | \(0\) | \(-2\) | \(-6\) | \(q+2\beta _{4}q^{4}+(1-\beta _{2}+\beta _{3}+\beta _{5}-\beta _{6}+\cdots)q^{5}+\cdots\) |
475.2.v.b | $368$ | $3.793$ | None | \(0\) | \(0\) | \(-16\) | \(-8\) |