Defining parameters
Level: | \( N \) | \(=\) | \( 1344 = 2^{6} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1344.s (of order \(4\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 48 \) |
Character field: | \(\Q(i)\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(512\) | ||
Trace bound: | \(3\) | ||
Distinguishing \(T_p\): | \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(1344, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 544 | 96 | 448 |
Cusp forms | 480 | 96 | 384 |
Eisenstein series | 64 | 0 | 64 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(1344, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
1344.2.s.a | $4$ | $10.732$ | \(\Q(\zeta_{8})\) | None | \(0\) | \(0\) | \(4\) | \(4\) | \(q+(-\zeta_{8}-\zeta_{8}^{3})q^{3}+(1+\zeta_{8}+\zeta_{8}^{2}+\cdots)q^{5}+\cdots\) |
1344.2.s.b | $4$ | $10.732$ | \(\Q(\zeta_{8})\) | None | \(0\) | \(4\) | \(-4\) | \(4\) | \(q+(1-\zeta_{8}^{2})q^{3}+(-1-\zeta_{8}+\zeta_{8}^{2}+\zeta_{8}^{3})q^{5}+\cdots\) |
1344.2.s.c | $40$ | $10.732$ | None | \(0\) | \(-4\) | \(0\) | \(40\) | ||
1344.2.s.d | $48$ | $10.732$ | None | \(0\) | \(0\) | \(0\) | \(-48\) |
Decomposition of \(S_{2}^{\mathrm{old}}(1344, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(1344, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 2}\)