Defining parameters
Level: | \( N \) | \(=\) | \( 650 = 2 \cdot 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 650.y (of order \(15\) and degree \(8\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 325 \) |
Character field: | \(\Q(\zeta_{15})\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(210\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(650, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 864 | 288 | 576 |
Cusp forms | 800 | 288 | 512 |
Eisenstein series | 64 | 0 | 64 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(650, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
650.2.y.a | $136$ | $5.190$ | None | \(-17\) | \(0\) | \(-2\) | \(16\) | ||
650.2.y.b | $152$ | $5.190$ | None | \(19\) | \(0\) | \(4\) | \(-16\) |
Decomposition of \(S_{2}^{\mathrm{old}}(650, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(650, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(325, [\chi])\)\(^{\oplus 2}\)