Defining parameters
Level: | \( N \) | \(=\) | \( 192 = 2^{6} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 192.f (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 24 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(128\) | ||
Trace bound: | \(15\) | ||
Distinguishing \(T_p\): | \(5\), \(23\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(192, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 108 | 24 | 84 |
Cusp forms | 84 | 24 | 60 |
Eisenstein series | 24 | 0 | 24 |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(192, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
192.4.f.a | $4$ | $11.328$ | \(\Q(\zeta_{12})\) | \(\Q(\sqrt{-6}) \) | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\zeta_{12}^{2}q^{3}-\zeta_{12}^{3}q^{5}-17\zeta_{12}q^{7}+\cdots\) |
192.4.f.b | $4$ | $11.328$ | \(\Q(\zeta_{12})\) | \(\Q(\sqrt{-3}) \) | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\zeta_{12}q^{3}-5\zeta_{12}^{2}q^{7}+3^{3}q^{9}+3\zeta_{12}^{3}q^{13}+\cdots\) |
192.4.f.c | $8$ | $11.328$ | 8.0.1731891456.1 | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\beta _{3}q^{3}+(3\beta _{1}-\beta _{3}+\beta _{5})q^{5}+\beta _{7}q^{7}+\cdots\) |
192.4.f.d | $8$ | $11.328$ | 8.0.1731891456.1 | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\beta _{3}q^{3}+(3\beta _{1}-\beta _{3}+\beta _{5})q^{5}-\beta _{7}q^{7}+\cdots\) |
Decomposition of \(S_{4}^{\mathrm{old}}(192, [\chi])\) into lower level spaces
\( S_{4}^{\mathrm{old}}(192, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 4}\)