Defining parameters
Level: | \( N \) | \(=\) | \( 1120 = 2^{5} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1120.bz (of order \(6\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 56 \) |
Character field: | \(\Q(\zeta_{6})\) | ||
Newform subspaces: | \( 6 \) | ||
Sturm bound: | \(384\) | ||
Trace bound: | \(7\) | ||
Distinguishing \(T_p\): | \(3\), \(13\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(1120, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 416 | 64 | 352 |
Cusp forms | 352 | 64 | 288 |
Eisenstein series | 64 | 0 | 64 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(1120, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
1120.2.bz.a | $4$ | $8.943$ | \(\Q(\zeta_{12})\) | None | \(0\) | \(6\) | \(-2\) | \(0\) | \(q+(2-\zeta_{12}^{2})q^{3}+(-1+\zeta_{12}^{2})q^{5}+\cdots\) |
1120.2.bz.b | $4$ | $8.943$ | \(\Q(\sqrt{-2}, \sqrt{-3})\) | None | \(0\) | \(6\) | \(-2\) | \(10\) | \(q+(2+\beta _{1}-\beta _{2}-\beta _{3})q^{3}+(-1+\beta _{2}+\cdots)q^{5}+\cdots\) |
1120.2.bz.c | $4$ | $8.943$ | \(\Q(\sqrt{-2}, \sqrt{-3})\) | None | \(0\) | \(6\) | \(2\) | \(-10\) | \(q+(2+\beta _{1}-\beta _{2}-\beta _{3})q^{3}+(1-\beta _{2})q^{5}+\cdots\) |
1120.2.bz.d | $4$ | $8.943$ | \(\Q(\zeta_{12})\) | None | \(0\) | \(6\) | \(2\) | \(0\) | \(q+(2-\zeta_{12}^{2})q^{3}+(1-\zeta_{12}^{2})q^{5}+(\zeta_{12}+\cdots)q^{7}+\cdots\) |
1120.2.bz.e | $24$ | $8.943$ | None | \(0\) | \(-12\) | \(-12\) | \(-10\) | ||
1120.2.bz.f | $24$ | $8.943$ | None | \(0\) | \(-12\) | \(12\) | \(10\) |
Decomposition of \(S_{2}^{\mathrm{old}}(1120, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(1120, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(224, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(280, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(560, [\chi])\)\(^{\oplus 2}\)