Defining parameters
Level: | \( N \) | \(=\) | \( 825 = 3 \cdot 5^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 825.m (of order \(5\) and degree \(4\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 275 \) |
Character field: | \(\Q(\zeta_{5})\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(240\) | ||
Trace bound: | \(2\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(825, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 496 | 240 | 256 |
Cusp forms | 464 | 240 | 224 |
Eisenstein series | 32 | 0 | 32 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(825, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
825.2.m.a | $4$ | $6.588$ | \(\Q(\zeta_{10})\) | None | \(-2\) | \(1\) | \(-5\) | \(3\) | \(q+(-1+\zeta_{10}-\zeta_{10}^{2})q^{2}+\zeta_{10}q^{3}+\cdots\) |
825.2.m.b | $4$ | $6.588$ | \(\Q(\zeta_{10})\) | None | \(0\) | \(-1\) | \(5\) | \(6\) | \(q-\zeta_{10}q^{3}-2\zeta_{10}^{2}q^{4}+(2-\zeta_{10}+2\zeta_{10}^{2}+\cdots)q^{5}+\cdots\) |
825.2.m.c | $116$ | $6.588$ | None | \(-2\) | \(-29\) | \(-1\) | \(-13\) | ||
825.2.m.d | $116$ | $6.588$ | None | \(4\) | \(29\) | \(-3\) | \(-2\) |
Decomposition of \(S_{2}^{\mathrm{old}}(825, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(825, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(275, [\chi])\)\(^{\oplus 2}\)