Defining parameters
Level: | \( N \) | \(=\) | \( 192 = 2^{6} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 192.c (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 12 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(128\) | ||
Trace bound: | \(9\) | ||
Distinguishing \(T_p\): | \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(192, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 108 | 26 | 82 |
Cusp forms | 84 | 22 | 62 |
Eisenstein series | 24 | 4 | 20 |
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.c.a | $2$ | $11.328$ | \(\Q(\sqrt{-3}) \) | \(\Q(\sqrt{-3}) \) | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\beta q^{3}-6\beta q^{7}-27 q^{9}-70 q^{13}+\cdots\) |
192.4.c.b | $4$ | $11.328$ | \(\Q(\sqrt{3}, \sqrt{-5})\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\beta _{3}q^{3}+\beta _{2}q^{5}+(\beta _{1}-\beta _{3})q^{7}+(-3+\cdots)q^{9}+\cdots\) |
192.4.c.c | $4$ | $11.328$ | \(\Q(\sqrt{-2}, \sqrt{-3})\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\beta _{2}q^{3}+\beta _{3}q^{5}-5\beta _{1}q^{7}+(21-\beta _{3})q^{9}+\cdots\) |
192.4.c.d | $12$ | $11.328$ | 12.0.\(\cdots\).1 | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\beta _{4}q^{3}+\beta _{8}q^{5}+\beta _{1}q^{7}+(-2+\beta _{5}+\cdots)q^{9}+\cdots\) |
Decomposition of \(S_{4}^{\mathrm{old}}(192, [\chi])\) into lower level spaces
\( S_{4}^{\mathrm{old}}(192, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 2}\)