Space of modular forms of level 192, weight 6, and trivial character

• Label: 192.6.a
• Level: $192$
• Weight: $6$
• Character orbit: 192.a
• Rep. character: $\chi_{192}(1,\cdot)$
• Character field: $\Q$
• Dimension: $20$
• Newform subspaces: $18$
• Sturm bound: $192$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 192 = 2^{6} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	192.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 18 \)
Sturm bound:			\(192\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_0(192))\).

	Total	New	Old
Modular forms	172	20	152
Cusp forms	148	20	128
Eisenstein series	24	0	24

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)	\(3\)	Fricke	Dim
\(+\)	\(+\)	$+$	\(5\)
\(+\)	\(-\)	$-$	\(6\)
\(-\)	\(+\)	$-$	\(5\)
\(-\)	\(-\)	$+$	\(4\)
Plus space		\(+\)	\(9\)
Minus space		\(-\)	\(11\)

Trace form

\( 20 q + 1620 q^{9} + O(q^{10}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_0(192))\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces					A-L signs		Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		2	3
192.6.a.a	$192$	$6$	192.a	1.a	$1$	$1$	$1$	$30.794$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-9\)	\(-94\)	\(-144\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-9q^{3}-94q^{5}-12^{2}q^{7}+3^{4}q^{9}+\cdots\)
192.6.a.b	$192$	$6$	192.a	1.a	$1$	$1$	$1$	$30.794$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-9\)	\(-38\)	\(120\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-9q^{3}-38q^{5}+120q^{7}+3^{4}q^{9}+\cdots\)
192.6.a.c	$192$	$6$	192.a	1.a	$1$	$1$	$1$	$30.794$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-9\)	\(-26\)	\(36\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-9q^{3}-26q^{5}+6^{2}q^{7}+3^{4}q^{9}-180q^{11}+\cdots\)
192.6.a.d	$192$	$6$	192.a	1.a	$1$	$1$	$1$	$30.794$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-9\)	\(-6\)	\(-40\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-9q^{3}-6q^{5}-40q^{7}+3^{4}q^{9}+564q^{11}+\cdots\)
192.6.a.e	$192$	$6$	192.a	1.a	$1$	$1$	$1$	$30.794$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-9\)	\(14\)	\(-100\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-9q^{3}+14q^{5}-10^{2}q^{7}+3^{4}q^{9}+\cdots\)
192.6.a.f	$192$	$6$	192.a	1.a	$1$	$1$	$1$	$30.794$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-9\)	\(34\)	\(240\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-9q^{3}+34q^{5}+240q^{7}+3^{4}q^{9}+\cdots\)
192.6.a.g	$192$	$6$	192.a	1.a	$1$	$1$	$1$	$30.794$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-9\)	\(66\)	\(-176\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-9q^{3}+66q^{5}-176q^{7}+3^{4}q^{9}+\cdots\)
192.6.a.h	$192$	$6$	192.a	1.a	$1$	$1$	$1$	$30.794$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-9\)	\(86\)	\(180\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-9q^{3}+86q^{5}+180q^{7}+3^{4}q^{9}+\cdots\)
192.6.a.i	$192$	$6$	192.a	1.a	$1$	$1$	$1$	$30.794$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(9\)	\(-94\)	\(144\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+9q^{3}-94q^{5}+12^{2}q^{7}+3^{4}q^{9}+\cdots\)
192.6.a.j	$192$	$6$	192.a	1.a	$1$	$1$	$1$	$30.794$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(9\)	\(-38\)	\(-120\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+9q^{3}-38q^{5}-120q^{7}+3^{4}q^{9}+\cdots\)
192.6.a.k	$192$	$6$	192.a	1.a	$1$	$1$	$1$	$30.794$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(9\)	\(-26\)	\(-36\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+9q^{3}-26q^{5}-6^{2}q^{7}+3^{4}q^{9}+180q^{11}+\cdots\)
192.6.a.l	$192$	$6$	192.a	1.a	$1$	$1$	$1$	$30.794$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(9\)	\(-6\)	\(40\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+9q^{3}-6q^{5}+40q^{7}+3^{4}q^{9}-564q^{11}+\cdots\)
192.6.a.m	$192$	$6$	192.a	1.a	$1$	$1$	$1$	$30.794$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(9\)	\(14\)	\(100\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+9q^{3}+14q^{5}+10^{2}q^{7}+3^{4}q^{9}+\cdots\)
192.6.a.n	$192$	$6$	192.a	1.a	$1$	$1$	$1$	$30.794$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(9\)	\(34\)	\(-240\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+9q^{3}+34q^{5}-240q^{7}+3^{4}q^{9}+\cdots\)
192.6.a.o	$192$	$6$	192.a	1.a	$1$	$1$	$1$	$30.794$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(9\)	\(66\)	\(176\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+9q^{3}+66q^{5}+176q^{7}+3^{4}q^{9}+\cdots\)
192.6.a.p	$192$	$6$	192.a	1.a	$1$	$1$	$1$	$30.794$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(9\)	\(86\)	\(-180\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+9q^{3}+86q^{5}-180q^{7}+3^{4}q^{9}+\cdots\)
192.6.a.q	$192$	$6$	192.a	1.a	$1$	$2$	$2$	$30.794$	\(\Q(\sqrt{31}) \)	None	✓	$1$	$1$	\(0\)	\(-18\)	\(-36\)	\(120\)		$+$	$+$	$+$	$2^{4}$	$\mathrm{SU}(2)$	\(q-9q^{3}+(-18+\beta )q^{5}+(60-\beta )q^{7}+\cdots\)
192.6.a.r	$192$	$6$	192.a	1.a	$1$	$2$	$2$	$30.794$	\(\Q(\sqrt{31}) \)	None	✓	$1$	$0$	\(0\)	\(18\)	\(-36\)	\(-120\)		$+$	$-$	$-$	$2^{4}$	$\mathrm{SU}(2)$	\(q+9q^{3}+(-18+\beta )q^{5}+(-60+\beta )q^{7}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_0(192))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_0(192)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_0(3))\)\(^{\oplus 7}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(4))\)\(^{\oplus 10}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(6))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(8))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(12))\)\(^{\oplus 5}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(16))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(64))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(96))\)\(^{\oplus 2}\)