Space of modular forms of level 192, weight 11, and Character 192.l

• Label: 192.11.l
• Level: $192$
• Weight: $11$
• Character orbit: 192.l
• Rep. character: $\chi_{192}(79,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $80$
• Newform subspaces: $1$
• Sturm bound: $352$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 192 = 2^{6} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	192.l (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 16 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(352\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{11}(192, [\chi])\).

	Total	New	Old
Modular forms	656	80	576
Cusp forms	624	80	544
Eisenstein series	32	0	32

Trace form

\( 80 q + O(q^{10}) \)

Decomposition of \(S_{11}^{\mathrm{new}}(192, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
192.11.l.a	$192$	$11$	192.l	16.f	$4$	$80$	$40$	$121.989$		None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$

Decomposition of \(S_{11}^{\mathrm{old}}(192, [\chi])\) into lower level spaces

\( S_{11}^{\mathrm{old}}(192, [\chi]) \cong \) \(S_{11}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 2}\)