Defining parameters
Level: | \( N \) | \(=\) | \( 192 = 2^{6} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 192.g (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 4 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 3 \) | ||
Sturm bound: | \(96\) | ||
Trace bound: | \(5\) | ||
Distinguishing \(T_p\): | \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(192, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 76 | 8 | 68 |
Cusp forms | 52 | 8 | 44 |
Eisenstein series | 24 | 0 | 24 |
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.g.a | $2$ | $5.232$ | \(\Q(\sqrt{-3}) \) | None | \(0\) | \(0\) | \(-12\) | \(0\) | \(q-\zeta_{6}q^{3}-6q^{5}+4\zeta_{6}q^{7}-3q^{9}+12\zeta_{6}q^{11}+\cdots\) |
192.3.g.b | $2$ | $5.232$ | \(\Q(\sqrt{-3}) \) | None | \(0\) | \(0\) | \(4\) | \(0\) | \(q-\zeta_{6}q^{3}+2q^{5}-4\zeta_{6}q^{7}-3q^{9}-4\zeta_{6}q^{11}+\cdots\) |
192.3.g.c | $4$ | $5.232$ | \(\Q(\zeta_{12})\) | None | \(0\) | \(0\) | \(8\) | \(0\) | \(q-\zeta_{12}^{2}q^{3}+(2-\zeta_{12}^{3})q^{5}+(-\zeta_{12}+\cdots)q^{7}+\cdots\) |
Decomposition of \(S_{3}^{\mathrm{old}}(192, [\chi])\) into lower level spaces
\( S_{3}^{\mathrm{old}}(192, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 2}\)