Space of modular forms of level 192, weight 13, and Character 192.g

• Label: 192.13.g
• Level: $192$
• Weight: $13$
• Character orbit: 192.g
• Rep. character: $\chi_{192}(127,\cdot)$
• Character field: $\Q$
• Dimension: $48$
• Newform subspaces: $6$
• Sturm bound: $416$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 192 = 2^{6} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 13 \)
Character orbit:	\([\chi]\)	\(=\)	192.g (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 4 \)
Character field:			\(\Q\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(416\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{13}(192, [\chi])\).

	Total	New	Old
Modular forms	396	48	348
Cusp forms	372	48	324
Eisenstein series	24	0	24

Trace form

\( 48 q - 8503056 q^{9} + O(q^{10}) \)

Decomposition of \(S_{13}^{\mathrm{new}}(192, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
192.13.g.a	$192$	$13$	192.g	4.b	$2$	$4$	$4$	$175.487$	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(-30456\)	\(0\)	$2^{10}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-3^{5}\beta _{1}q^{3}+(-7614-\beta _{2})q^{5}+(-15668\beta _{1}+\cdots)q^{7}+\cdots\)
192.13.g.b	$192$	$13$	192.g	4.b	$2$	$4$	$4$	$175.487$	\(\Q(\sqrt{-3}, \sqrt{-2803})\)	None		$2$	$0$	\(0\)	\(0\)	\(-22392\)	\(0\)	$2^{10}\cdot 3^{11}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+(-5598+\beta _{2})q^{5}+(63\beta _{1}+\cdots)q^{7}+\cdots\)
192.13.g.c	$192$	$13$	192.g	4.b	$2$	$4$	$4$	$175.487$	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(21960\)	\(0\)	$2^{10}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-3^{5}\beta _{1}q^{3}+(5490+5\beta _{2})q^{5}+(5372\beta _{1}+\cdots)q^{7}+\cdots\)
192.13.g.d	$192$	$13$	192.g	4.b	$2$	$12$	$12$	$175.487$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(-17160\)	\(0\)	$2^{102}\cdot 3^{28}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{7}q^{3}+(-1430+\beta _{1})q^{5}+(-18\beta _{6}+\cdots)q^{7}+\cdots\)
192.13.g.e	$192$	$13$	192.g	4.b	$2$	$12$	$12$	$175.487$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(10296\)	\(0\)	$2^{126}\cdot 3^{25}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+(858+\beta _{2})q^{5}+(-35\beta _{1}+\cdots)q^{7}+\cdots\)
192.13.g.f	$192$	$13$	192.g	4.b	$2$	$12$	$12$	$175.487$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(37752\)	\(0\)	$2^{102}\cdot 3^{22}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+(3146+\beta _{2})q^{5}+(63\beta _{1}-13\beta _{3}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{13}^{\mathrm{old}}(192, [\chi])\) into lower level spaces

\( S_{13}^{\mathrm{old}}(192, [\chi]) \simeq \) \(S_{13}^{\mathrm{new}}(4, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{13}^{\mathrm{new}}(8, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{13}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{13}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{13}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{13}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{13}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{13}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{13}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 2}\)