Space of modular forms of level 192, weight 3, and Character 192.l

• Label: 192.3.l
• Level: $192$
• Weight: $3$
• Character orbit: 192.l
• Rep. character: $\chi_{192}(79,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $16$
• Newform subspaces: $1$
• Sturm bound: $96$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 192 = 2^{6} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 3 \)
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:			\(96\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(192, [\chi])\).

	Total	New	Old
Modular forms	144	16	128
Cusp forms	112	16	96
Eisenstein series	32	0	32

Trace form

16 * q - 32 * q^11 + 32 * q^19 + 128 * q^23 + 32 * q^29 - 96 * q^35 - 96 * q^37 - 160 * q^43 + 112 * q^49 + 96 * q^51 - 160 * q^53 + 256 * q^55 + 128 * q^59 - 32 * q^61 - 32 * q^65 - 320 * q^67 + 96 * q^69 - 512 * q^71 - 192 * q^75 + 224 * q^77 - 144 * q^81 + 160 * q^83 + 160 * q^85 + 480 * q^91 - 96 * q^99

Decomposition of \(S_{3}^{\mathrm{new}}(192, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
192.3.l.a	$192$	$3$	192.l	16.f	$4$	$16$	$8$	$5.232$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None			✓	✓	48.3.l.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{24}$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{2}q^{3}-\beta _{9}q^{5}+\beta _{5}q^{7}-3\beta _{4}q^{9}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(192, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(192, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 2}\)