Defining parameters
Level: | \( N \) | \(=\) | \( 1152 = 2^{7} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1152.f (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 24 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(384\) | ||
Trace bound: | \(25\) | ||
Distinguishing \(T_p\): | \(5\), \(7\), \(23\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(1152, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 224 | 16 | 208 |
Cusp forms | 160 | 16 | 144 |
Eisenstein series | 64 | 0 | 64 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(1152, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
1152.2.f.a | $4$ | $9.199$ | \(\Q(\zeta_{8})\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\zeta_{8}^{3}q^{5}-2\zeta_{8}^{2}q^{7}+2\zeta_{8}q^{11}-\zeta_{8}q^{13}+\cdots\) |
1152.2.f.b | $4$ | $9.199$ | \(\Q(\zeta_{8})\) | \(\Q(\sqrt{-1}) \) | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\zeta_{8}^{2}q^{5}+\zeta_{8}q^{13}+\zeta_{8}^{3}q^{17}-3q^{25}+\cdots\) |
1152.2.f.c | $4$ | $9.199$ | \(\Q(\zeta_{8})\) | \(\Q(\sqrt{-1}) \) | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\zeta_{8}^{3}q^{5}-\zeta_{8}q^{13}-5\zeta_{8}^{2}q^{17}+13q^{25}+\cdots\) |
1152.2.f.d | $4$ | $9.199$ | \(\Q(\zeta_{8})\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\zeta_{8}^{3}q^{5}-2\zeta_{8}^{2}q^{7}+2\zeta_{8}q^{11}+\zeta_{8}q^{13}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(1152, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(1152, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 10}\)