Defining parameters
Level: | \( N \) | \(=\) | \( 286 = 2 \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 286.b (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 13 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(84\) | ||
Trace bound: | \(10\) | ||
Distinguishing \(T_p\): | \(3\), \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(286, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 46 | 10 | 36 |
Cusp forms | 38 | 10 | 28 |
Eisenstein series | 8 | 0 | 8 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(286, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
286.2.b.a | $2$ | $2.284$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+iq^{2}-q^{4}+3iq^{5}+iq^{7}-iq^{8}+\cdots\) |
286.2.b.b | $2$ | $2.284$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+iq^{2}-q^{4}-2iq^{5}-4iq^{7}-iq^{8}+\cdots\) |
286.2.b.c | $2$ | $2.284$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(6\) | \(0\) | \(0\) | \(q+iq^{2}+3q^{3}-q^{4}+iq^{5}+3iq^{6}+\cdots\) |
286.2.b.d | $4$ | $2.284$ | \(\Q(i, \sqrt{17})\) | None | \(0\) | \(-2\) | \(0\) | \(0\) | \(q+\beta _{2}q^{2}+(-1+\beta _{3})q^{3}-q^{4}+\beta _{2}q^{5}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(286, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(286, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(26, [\chi])\)\(^{\oplus 2}\)