Defining parameters
Level: | \( N \) | \(=\) | \( 425 = 5^{2} \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 425.u (of order \(16\) and degree \(8\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 17 \) |
Character field: | \(\Q(\zeta_{16})\) | ||
Newform subspaces: | \( 6 \) | ||
Sturm bound: | \(135\) | ||
Trace bound: | \(12\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(425, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 768 | 480 | 288 |
Cusp forms | 672 | 432 | 240 |
Eisenstein series | 96 | 48 | 48 |
Trace form
Decomposition of \(S_{3}^{\mathrm{new}}(425, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
425.3.u.a | $8$ | $11.580$ | \(\Q(\zeta_{16})\) | None | \(0\) | \(0\) | \(0\) | \(16\) | \(q+(\zeta_{16}^{2}-\zeta_{16}^{4}-\zeta_{16}^{7})q^{2}+(-2\zeta_{16}^{2}+\cdots)q^{3}+\cdots\) |
425.3.u.b | $8$ | $11.580$ | \(\Q(\zeta_{16})\) | None | \(8\) | \(8\) | \(0\) | \(-8\) | \(q+(1-\zeta_{16}-\zeta_{16}^{2}+\zeta_{16}^{4}+\zeta_{16}^{5}+\cdots)q^{2}+\cdots\) |
425.3.u.c | $96$ | $11.580$ | None | \(0\) | \(0\) | \(0\) | \(0\) | ||
425.3.u.d | $96$ | $11.580$ | None | \(0\) | \(0\) | \(0\) | \(0\) | ||
425.3.u.e | $96$ | $11.580$ | None | \(0\) | \(0\) | \(0\) | \(0\) | ||
425.3.u.f | $128$ | $11.580$ | None | \(0\) | \(0\) | \(0\) | \(0\) |
Decomposition of \(S_{3}^{\mathrm{old}}(425, [\chi])\) into lower level spaces
\( S_{3}^{\mathrm{old}}(425, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(17, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(85, [\chi])\)\(^{\oplus 2}\)