Defining parameters
Level: | \( N \) | \(=\) | \( 1064 = 2^{3} \cdot 7 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1064.s (of order \(3\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 133 \) |
Character field: | \(\Q(\zeta_{3})\) | ||
Newform subspaces: | \( 5 \) | ||
Sturm bound: | \(320\) | ||
Trace bound: | \(3\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(1064, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 336 | 80 | 256 |
Cusp forms | 304 | 80 | 224 |
Eisenstein series | 32 | 0 | 32 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(1064, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
1064.2.s.a | $2$ | $8.496$ | \(\Q(\sqrt{-3}) \) | None | \(0\) | \(-1\) | \(4\) | \(4\) | \(q-\zeta_{6}q^{3}+2q^{5}+(3-2\zeta_{6})q^{7}+(2-2\zeta_{6})q^{9}+\cdots\) |
1064.2.s.b | $2$ | $8.496$ | \(\Q(\sqrt{-3}) \) | None | \(0\) | \(1\) | \(4\) | \(4\) | \(q+\zeta_{6}q^{3}+2q^{5}+(1+2\zeta_{6})q^{7}+(2-2\zeta_{6})q^{9}+\cdots\) |
1064.2.s.c | $4$ | $8.496$ | \(\Q(\sqrt{-3}, \sqrt{17})\) | None | \(0\) | \(1\) | \(-6\) | \(-8\) | \(q+\beta _{1}q^{3}+(-1+\beta _{3})q^{5}+(-3+2\beta _{2}+\cdots)q^{7}+\cdots\) |
1064.2.s.d | $32$ | $8.496$ | None | \(0\) | \(-3\) | \(2\) | \(1\) | ||
1064.2.s.e | $40$ | $8.496$ | None | \(0\) | \(-2\) | \(-4\) | \(1\) |
Decomposition of \(S_{2}^{\mathrm{old}}(1064, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(1064, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(133, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(266, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(532, [\chi])\)\(^{\oplus 2}\)