Defining parameters
Level: | \( N \) | \(=\) | \( 192 = 2^{6} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 192.e (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 3 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 6 \) | ||
Sturm bound: | \(96\) | ||
Trace bound: | \(9\) | ||
Distinguishing \(T_p\): | \(5\), \(7\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(192, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 76 | 18 | 58 |
Cusp forms | 52 | 14 | 38 |
Eisenstein series | 24 | 4 | 20 |
Trace form
Decomposition of \(S_{3}^{\mathrm{new}}(192, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
192.3.e.a | $1$ | $5.232$ | \(\Q\) | \(\Q(\sqrt{-3}) \) | \(0\) | \(-3\) | \(0\) | \(-2\) | \(q-3q^{3}-2q^{7}+9q^{9}+22q^{13}+26q^{19}+\cdots\) |
192.3.e.b | $1$ | $5.232$ | \(\Q\) | \(\Q(\sqrt{-3}) \) | \(0\) | \(3\) | \(0\) | \(2\) | \(q+3q^{3}+2q^{7}+9q^{9}+22q^{13}-26q^{19}+\cdots\) |
192.3.e.c | $2$ | $5.232$ | \(\Q(\sqrt{-2}) \) | None | \(0\) | \(-2\) | \(0\) | \(-12\) | \(q+(-1+\beta )q^{3}-2\beta q^{5}-6q^{7}+(-7+\cdots)q^{9}+\cdots\) |
192.3.e.d | $2$ | $5.232$ | \(\Q(\sqrt{-2}) \) | None | \(0\) | \(2\) | \(0\) | \(12\) | \(q+(1+\beta )q^{3}+2\beta q^{5}+6q^{7}+(-7+2\beta )q^{9}+\cdots\) |
192.3.e.e | $4$ | $5.232$ | \(\Q(\sqrt{-2}, \sqrt{3})\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\beta _{1}q^{3}-\beta _{2}q^{5}+(-2\beta _{1}+\beta _{3})q^{7}+\cdots\) |
192.3.e.f | $4$ | $5.232$ | \(\Q(\sqrt{-2}, \sqrt{7})\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+(\beta _{1}+\beta _{3})q^{3}+\beta _{2}q^{5}+(\beta _{1}+2\beta _{3})q^{7}+\cdots\) |
Decomposition of \(S_{3}^{\mathrm{old}}(192, [\chi])\) into lower level spaces
\( S_{3}^{\mathrm{old}}(192, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 2}\)