Defining parameters
Level: | \( N \) | \(=\) | \( 475 = 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 475.l (of order \(9\) and degree \(6\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 19 \) |
Character field: | \(\Q(\zeta_{9})\) | ||
Newform subspaces: | \( 6 \) | ||
Sturm bound: | \(100\) | ||
Trace bound: | \(3\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(475, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 336 | 210 | 126 |
Cusp forms | 264 | 174 | 90 |
Eisenstein series | 72 | 36 | 36 |
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.l.a | $6$ | $3.793$ | \(\Q(\zeta_{18})\) | None | \(6\) | \(3\) | \(0\) | \(0\) | \(q+(1+\zeta_{18}-\zeta_{18}^{4}-\zeta_{18}^{5})q^{2}+(1+\cdots)q^{3}+\cdots\) |
475.2.l.b | $18$ | $3.793$ | \(\mathbb{Q}[x]/(x^{18} + \cdots)\) | None | \(-3\) | \(3\) | \(0\) | \(0\) | \(q+\beta _{14}q^{2}+(\beta _{4}-\beta _{6}+\beta _{7}+\beta _{15})q^{3}+\cdots\) |
475.2.l.c | $18$ | $3.793$ | \(\mathbb{Q}[x]/(x^{18} - \cdots)\) | None | \(3\) | \(3\) | \(0\) | \(0\) | \(q+(\beta _{4}-\beta _{15})q^{2}+(-\beta _{5}-\beta _{6}-\beta _{8}+\cdots)q^{3}+\cdots\) |
475.2.l.d | $42$ | $3.793$ | None | \(0\) | \(-3\) | \(0\) | \(0\) | ||
475.2.l.e | $42$ | $3.793$ | None | \(0\) | \(3\) | \(0\) | \(0\) | ||
475.2.l.f | $48$ | $3.793$ | None | \(0\) | \(0\) | \(0\) | \(0\) |
Decomposition of \(S_{2}^{\mathrm{old}}(475, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(475, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(19, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(95, [\chi])\)\(^{\oplus 2}\)