Defining parameters
Level: | \( N \) | \(=\) | \( 550 = 2 \cdot 5^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 550.l (of order \(5\) and degree \(4\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 275 \) |
Character field: | \(\Q(\zeta_{5})\) | ||
Newform subspaces: | \( 5 \) | ||
Sturm bound: | \(180\) | ||
Trace bound: | \(3\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(550, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 376 | 120 | 256 |
Cusp forms | 344 | 120 | 224 |
Eisenstein series | 32 | 0 | 32 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(550, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
550.2.l.a | $4$ | $4.392$ | \(\Q(\zeta_{10})\) | None | \(1\) | \(2\) | \(5\) | \(-6\) | \(q+\zeta_{10}^{3}q^{2}+(1+\zeta_{10}^{2}-\zeta_{10}^{3})q^{3}+\cdots\) |
550.2.l.b | $4$ | $4.392$ | \(\Q(\zeta_{10})\) | None | \(1\) | \(4\) | \(5\) | \(-2\) | \(q+\zeta_{10}^{3}q^{2}+q^{3}-\zeta_{10}q^{4}+(2-2\zeta_{10}+\cdots)q^{5}+\cdots\) |
550.2.l.c | $4$ | $4.392$ | \(\Q(\zeta_{10})\) | None | \(1\) | \(6\) | \(-5\) | \(-1\) | \(q+\zeta_{10}^{3}q^{2}+(1-\zeta_{10}^{2}+\zeta_{10}^{3})q^{3}+\cdots\) |
550.2.l.d | $48$ | $4.392$ | None | \(12\) | \(-22\) | \(-1\) | \(11\) | ||
550.2.l.e | $60$ | $4.392$ | None | \(-15\) | \(6\) | \(0\) | \(2\) |
Decomposition of \(S_{2}^{\mathrm{old}}(550, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(550, [\chi]) \cong \)