Defining parameters
Level: | \( N \) | \(=\) | \( 280 = 2^{3} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 280.q (of order \(3\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 7 \) |
Character field: | \(\Q(\zeta_{3})\) | ||
Newform subspaces: | \( 5 \) | ||
Sturm bound: | \(96\) | ||
Trace bound: | \(3\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(280, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 112 | 16 | 96 |
Cusp forms | 80 | 16 | 64 |
Eisenstein series | 32 | 0 | 32 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(280, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
280.2.q.a | $2$ | $2.236$ | \(\Q(\sqrt{-3}) \) | None | \(0\) | \(-1\) | \(1\) | \(-5\) | \(q+(-1+\zeta_{6})q^{3}+\zeta_{6}q^{5}+(-3+\zeta_{6})q^{7}+\cdots\) |
280.2.q.b | $2$ | $2.236$ | \(\Q(\sqrt{-3}) \) | None | \(0\) | \(1\) | \(1\) | \(1\) | \(q+(1-\zeta_{6})q^{3}+\zeta_{6}q^{5}+(-1+3\zeta_{6})q^{7}+\cdots\) |
280.2.q.c | $2$ | $2.236$ | \(\Q(\sqrt{-3}) \) | None | \(0\) | \(2\) | \(1\) | \(4\) | \(q+(2-2\zeta_{6})q^{3}+\zeta_{6}q^{5}+(3-2\zeta_{6})q^{7}+\cdots\) |
280.2.q.d | $4$ | $2.236$ | \(\Q(\sqrt{2}, \sqrt{-3})\) | None | \(0\) | \(2\) | \(-2\) | \(-2\) | \(q+(1+\beta _{1}+\beta _{2})q^{3}+\beta _{2}q^{5}+(-1+\beta _{1}+\cdots)q^{7}+\cdots\) |
280.2.q.e | $6$ | $2.236$ | 6.0.11337408.1 | None | \(0\) | \(0\) | \(-3\) | \(6\) | \(q-\beta _{5}q^{3}+(-1+\beta _{2})q^{5}+(1-\beta _{1}-\beta _{5})q^{7}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(280, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(280, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(140, [\chi])\)\(^{\oplus 2}\)