Defining parameters
Level: | \( N \) | \(=\) | \( 1560 = 2^{3} \cdot 3 \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1560.ec (of order \(6\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 13 \) |
Character field: | \(\Q(\zeta_{6})\) | ||
Newform subspaces: | \( 5 \) | ||
Sturm bound: | \(672\) | ||
Trace bound: | \(7\) | ||
Distinguishing \(T_p\): | \(7\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(1560, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 704 | 56 | 648 |
Cusp forms | 640 | 56 | 584 |
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.ec.a | $8$ | $12.457$ | \(\Q(\zeta_{24})\) | None | \(0\) | \(-4\) | \(0\) | \(0\) | \(q-\zeta_{24}^{4}q^{3}-\zeta_{24}^{6}q^{5}+(\zeta_{24}-\zeta_{24}^{5}+\cdots)q^{7}+\cdots\) |
1560.2.ec.b | $8$ | $12.457$ | 8.0.56070144.2 | None | \(0\) | \(4\) | \(0\) | \(-6\) | \(q+(1-\beta _{6})q^{3}+(-\beta _{4}+\beta _{5})q^{5}+(-2+\cdots)q^{7}+\cdots\) |
1560.2.ec.c | $8$ | $12.457$ | 8.0.\(\cdots\).1 | None | \(0\) | \(4\) | \(0\) | \(0\) | \(q+(1-\beta _{2})q^{3}+\beta _{4}q^{5}+(\beta _{3}+\beta _{4})q^{7}+\cdots\) |
1560.2.ec.d | $16$ | $12.457$ | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) | None | \(0\) | \(-8\) | \(0\) | \(0\) | \(q+(-1-\beta _{5})q^{3}+\beta _{12}q^{5}+(\beta _{1}-\beta _{9}+\cdots)q^{7}+\cdots\) |
1560.2.ec.e | $16$ | $12.457$ | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) | None | \(0\) | \(8\) | \(0\) | \(-6\) | \(q-\beta _{7}q^{3}+(-\beta _{8}+\beta _{9})q^{5}+(-\beta _{11}+\cdots)q^{7}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(1560, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(1560, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(13, [\chi])\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(52, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(65, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(78, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(104, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(130, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(156, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(195, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(260, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(312, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(390, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(520, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(780, [\chi])\)\(^{\oplus 2}\)