Defining parameters
Level: | \( N \) | \(=\) | \( 287 = 7 \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 287.h (of order \(5\) and degree \(4\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 41 \) |
Character field: | \(\Q(\zeta_{5})\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(56\) | ||
Trace bound: | \(2\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(287, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 120 | 88 | 32 |
Cusp forms | 104 | 88 | 16 |
Eisenstein series | 16 | 0 | 16 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(287, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
287.2.h.a | $4$ | $2.292$ | \(\Q(\zeta_{10})\) | None | \(0\) | \(0\) | \(-1\) | \(1\) | \(q+(-1-2\zeta_{10}^{2}+2\zeta_{10}^{3})q^{3}+2\zeta_{10}^{3}q^{4}+\cdots\) |
287.2.h.b | $4$ | $2.292$ | \(\Q(\zeta_{10})\) | None | \(1\) | \(6\) | \(-2\) | \(-1\) | \(q+(-1+2\zeta_{10}-2\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots\) |
287.2.h.c | $40$ | $2.292$ | None | \(-3\) | \(0\) | \(-4\) | \(-10\) | ||
287.2.h.d | $40$ | $2.292$ | None | \(-2\) | \(-10\) | \(-1\) | \(10\) |
Decomposition of \(S_{2}^{\mathrm{old}}(287, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(287, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(41, [\chi])\)\(^{\oplus 2}\)