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

• Label: 192.11.b
• Level: $192$
• Weight: $11$
• Character orbit: 192.b
• Rep. character: $\chi_{192}(31,\cdot)$
• Character field: $\Q$
• Dimension: $40$
• Newform subspaces: $3$
• Sturm bound: $352$
• Trace bound: $17$

Defining parameters

Level:	\( N \)	\(=\)	\( 192 = 2^{6} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	192.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 8 \)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(352\)
Trace bound:			\(17\)
Distinguishing \(T_p\):			\(5\)

Dimensions

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

	Total	New	Old
Modular forms	332	40	292
Cusp forms	308	40	268
Eisenstein series	24	0	24

Trace form

\( 40 q + 787320 q^{9} + O(q^{10}) \)

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.b.a	$192$	$11$	192.b	8.d	$2$	$12$	$12$	$121.989$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{48}\cdot 3^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+3^{4}\beta _{6}q^{3}+(5\beta _{1}-\beta _{3})q^{5}+(-117\beta _{7}+\cdots)q^{7}+\cdots\)
192.11.b.b	$192$	$11$	192.b	8.d	$2$	$12$	$12$	$121.989$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{48}\cdot 3^{18}$	$\mathrm{SU}(2)[C_{2}]$	\(q-3\beta _{6}q^{3}+(\beta _{1}-\beta _{2})q^{5}+(-57\beta _{7}+\cdots)q^{7}+\cdots\)
192.11.b.c	$192$	$11$	192.b	8.d	$2$	$16$	$16$	$121.989$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{88}\cdot 3^{14}\cdot 7^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+3^{4}\beta _{8}q^{3}+(7\beta _{2}+\beta _{5})q^{5}+(8\beta _{9}-\beta _{11}+\cdots)q^{7}+\cdots\)

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

\( S_{11}^{\mathrm{old}}(192, [\chi]) \cong \) \(S_{11}^{\mathrm{new}}(8, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 2}\)