Defining parameters
Level: | \( N \) | \(=\) | \( 1560 = 2^{3} \cdot 3 \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1560.dr (of order \(6\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 65 \) |
Character field: | \(\Q(\zeta_{6})\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(672\) | ||
Trace bound: | \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(1560, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 704 | 88 | 616 |
Cusp forms | 640 | 88 | 552 |
Eisenstein series | 64 | 0 | 64 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(1560, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
1560.2.dr.a | $44$ | $12.457$ | None | \(0\) | \(0\) | \(-2\) | \(2\) | ||
1560.2.dr.b | $44$ | $12.457$ | None | \(0\) | \(0\) | \(2\) | \(-2\) |
Decomposition of \(S_{2}^{\mathrm{old}}(1560, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(1560, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(65, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(130, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(195, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(260, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(390, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(520, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(780, [\chi])\)\(^{\oplus 2}\)