Defining parameters
Level: | \( N \) | \(=\) | \( 1368 = 2^{3} \cdot 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1368.j (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 24 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(480\) | ||
Trace bound: | \(4\) | ||
Distinguishing \(T_p\): | \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(1368, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 248 | 72 | 176 |
Cusp forms | 232 | 72 | 160 |
Eisenstein series | 16 | 0 | 16 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(1368, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
1368.2.j.a | $4$ | $10.924$ | \(\Q(\sqrt{-2}, \sqrt{-3})\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\beta _{1}q^{2}-2q^{4}-\beta _{2}q^{5}-\beta _{3}q^{7}-2\beta _{1}q^{8}+\cdots\) |
1368.2.j.b | $4$ | $10.924$ | \(\Q(\zeta_{8})\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\zeta_{8}^{3}q^{2}+2q^{4}+\zeta_{8}^{3}q^{5}+\zeta_{8}q^{7}+\cdots\) |
1368.2.j.c | $28$ | $10.924$ | None | \(0\) | \(0\) | \(0\) | \(0\) | ||
1368.2.j.d | $36$ | $10.924$ | None | \(0\) | \(0\) | \(0\) | \(0\) |
Decomposition of \(S_{2}^{\mathrm{old}}(1368, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(1368, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 4}\)