Defining parameters
Level: | \( N \) | \(=\) | \( 1248 = 2^{5} \cdot 3 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1248.n (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 156 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 5 \) | ||
Sturm bound: | \(448\) | ||
Trace bound: | \(5\) | ||
Distinguishing \(T_p\): | \(5\), \(7\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(1248, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 240 | 56 | 184 |
Cusp forms | 208 | 56 | 152 |
Eisenstein series | 32 | 0 | 32 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(1248, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
1248.2.n.a | $4$ | $9.965$ | \(\Q(\zeta_{8})\) | None | \(0\) | \(-4\) | \(-8\) | \(8\) | \(q+(-1-\zeta_{8}^{2})q^{3}+(-2+\zeta_{8}^{3})q^{5}+\cdots\) |
1248.2.n.b | $4$ | $9.965$ | \(\Q(\zeta_{8})\) | None | \(0\) | \(-4\) | \(8\) | \(-8\) | \(q+(-1+\zeta_{8}^{2})q^{3}+(2+\zeta_{8}^{3})q^{5}+(-2+\cdots)q^{7}+\cdots\) |
1248.2.n.c | $4$ | $9.965$ | \(\Q(\zeta_{8})\) | None | \(0\) | \(4\) | \(-8\) | \(-8\) | \(q+(1+\zeta_{8}^{2})q^{3}+(-2+\zeta_{8}^{3})q^{5}+(-2+\cdots)q^{7}+\cdots\) |
1248.2.n.d | $4$ | $9.965$ | \(\Q(\zeta_{8})\) | None | \(0\) | \(4\) | \(8\) | \(8\) | \(q+(1-\zeta_{8}^{2})q^{3}+(2-\zeta_{8}^{3})q^{5}+(2-\zeta_{8}^{3})q^{7}+\cdots\) |
1248.2.n.e | $40$ | $9.965$ | None | \(0\) | \(0\) | \(0\) | \(0\) |
Decomposition of \(S_{2}^{\mathrm{old}}(1248, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(1248, [\chi]) \cong \)