Space of modular forms of level 192, weight 8, and Character 192.c

• Label: 192.8.c
• Level: $192$
• Weight: $8$
• Character orbit: 192.c
• Rep. character: $\chi_{192}(191,\cdot)$
• Character field: $\Q$
• Dimension: $54$
• Newform subspaces: $6$
• Sturm bound: $256$
• Trace bound: $9$

Defining parameters

Level:	\( N \)	\(=\)	\( 192 = 2^{6} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	192.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 12 \)
Character field:			\(\Q\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(256\)
Trace bound:			\(9\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(192, [\chi])\).

	Total	New	Old
Modular forms	236	58	178
Cusp forms	212	54	158
Eisenstein series	24	4	20

Trace form

\( 54 q - 2 q^{9} + O(q^{10}) \)

Decomposition of \(S_{8}^{\mathrm{new}}(192, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
192.8.c.a	$192$	$8$	192.c	12.b	$2$	$2$	$2$	$59.978$	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{U}(1)[D_{2}]$	\(q-3^{3}\zeta_{6}q^{3}-1006\zeta_{6}q^{7}-3^{7}q^{9}+\cdots\)
192.8.c.b	$192$	$8$	192.c	12.b	$2$	$4$	$4$	$59.978$	\(\Q(\sqrt{3}, \sqrt{-5})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-3\beta _{2}q^{3}-23\beta _{1}q^{5}+(-43\beta _{2}-43\beta _{3})q^{7}+\cdots\)
192.8.c.c	$192$	$8$	192.c	12.b	$2$	$4$	$4$	$59.978$	\(\Q(\sqrt{30}, \sqrt{-123})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{3}+\beta _{2}q^{5}+(3\beta _{1}+\beta _{3})q^{7}+(-3^{3}+\cdots)q^{9}+\cdots\)
192.8.c.d	$192$	$8$	192.c	12.b	$2$	$8$	$8$	$59.978$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{30}\cdot 3^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\beta _{1}-\beta _{2})q^{3}+\beta _{4}q^{5}+(-20\beta _{1}+\cdots)q^{7}+\cdots\)
192.8.c.e	$192$	$8$	192.c	12.b	$2$	$8$	$8$	$59.978$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{30}\cdot 3^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+\beta _{3}q^{5}+(-9\beta _{1}+3\beta _{2}-\beta _{5}+\cdots)q^{7}+\cdots\)
192.8.c.f	$192$	$8$	192.c	12.b	$2$	$28$	$28$	$59.978$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{8}^{\mathrm{old}}(192, [\chi])\) into lower level spaces

\( S_{8}^{\mathrm{old}}(192, [\chi]) \cong \)