Space of modular forms of level 6336, weight 2, and trivial character

• Label: 6336.2.a
• Level: $6336$
• Weight: $2$
• Character orbit: 6336.a
• Rep. character: $\chi_{6336}(1,\cdot)$
• Character field: $\Q$
• Dimension: $100$
• Newform subspaces: $80$
• Sturm bound: $2304$
• Trace bound: $13$

Defining parameters

Level:	\( N \)	\(=\)	\( 6336 = 2^{6} \cdot 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6336.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 80 \)
Sturm bound:			\(2304\)
Trace bound:			\(13\)
Distinguishing \(T_p\):			\(5\), \(7\), \(13\), \(17\), \(19\), \(23\), \(47\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(6336))\).

	Total	New	Old
Modular forms	1200	100	1100
Cusp forms	1105	100	1005
Eisenstein series	95	0	95

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

\(2\)	\(3\)	\(11\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	\(+\)	\(11\)
\(+\)	\(+\)	\(-\)	\(-\)	\(11\)
\(+\)	\(-\)	\(+\)	\(-\)	\(16\)
\(+\)	\(-\)	\(-\)	\(+\)	\(13\)
\(-\)	\(+\)	\(+\)	\(-\)	\(9\)
\(-\)	\(+\)	\(-\)	\(+\)	\(9\)
\(-\)	\(-\)	\(+\)	\(+\)	\(14\)
\(-\)	\(-\)	\(-\)	\(-\)	\(17\)
Plus space			\(+\)	\(47\)
Minus space			\(-\)	\(53\)

Trace form

\( 100 q + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6336))\) 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					A-L signs			Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		2	3	11
6336.2.a.a	$6336$	$2$	6336.a	1.a	$1$	$1$	$1$	$50.593$	\(\Q\)	None	✓				1056.2.a.a	$1$	$2$	\(0\)	\(0\)	\(-4\)	\(-2\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-4q^{5}-2q^{7}-q^{11}-4q^{13}-2q^{17}+\cdots\)
6336.2.a.b	$6336$	$2$	6336.a	1.a	$1$	$1$	$1$	$50.593$	\(\Q\)	None	✓				99.2.a.a	$1$	$1$	\(0\)	\(0\)	\(-4\)	\(-2\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-4q^{5}-2q^{7}-q^{11}+2q^{13}-2q^{17}+\cdots\)
6336.2.a.c	$6336$	$2$	6336.a	1.a	$1$	$1$	$1$	$50.593$	\(\Q\)	None	✓				66.2.a.c	$1$	$1$	\(0\)	\(0\)	\(-4\)	\(-2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-4q^{5}-2q^{7}+q^{11}-4q^{13}+2q^{17}+\cdots\)
6336.2.a.d	$6336$	$2$	6336.a	1.a	$1$	$1$	$1$	$50.593$	\(\Q\)	None	✓				66.2.a.c	$1$	$1$	\(0\)	\(0\)	\(-4\)	\(2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-4q^{5}+2q^{7}-q^{11}-4q^{13}+2q^{17}+\cdots\)
6336.2.a.e	$6336$	$2$	6336.a	1.a	$1$	$1$	$1$	$50.593$	\(\Q\)	None	✓				1056.2.a.a	$1$	$1$	\(0\)	\(0\)	\(-4\)	\(2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-4q^{5}+2q^{7}+q^{11}-4q^{13}-2q^{17}+\cdots\)
6336.2.a.f	$6336$	$2$	6336.a	1.a	$1$	$1$	$1$	$50.593$	\(\Q\)	None	✓				99.2.a.a	$1$	$1$	\(0\)	\(0\)	\(-4\)	\(2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-4q^{5}+2q^{7}+q^{11}+2q^{13}-2q^{17}+\cdots\)
6336.2.a.g	$6336$	$2$	6336.a	1.a	$1$	$1$	$1$	$50.593$	\(\Q\)	None	✓				352.2.a.b	$1$	$1$	\(0\)	\(0\)	\(-3\)	\(-4\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-3q^{5}-4q^{7}+q^{11}+2q^{13}+8q^{17}+\cdots\)
6336.2.a.h	$6336$	$2$	6336.a	1.a	$1$	$1$	$1$	$50.593$	\(\Q\)	None	✓				88.2.a.a	$1$	$0$	\(0\)	\(0\)	\(-3\)	\(-2\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-3q^{5}-2q^{7}-q^{11}+6q^{17}-4q^{19}+\cdots\)
6336.2.a.i	$6336$	$2$	6336.a	1.a	$1$	$1$	$1$	$50.593$	\(\Q\)	None	✓				44.2.a.a	$1$	$0$	\(0\)	\(0\)	\(-3\)	\(-2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-3q^{5}-2q^{7}+q^{11}+4q^{13}-6q^{17}+\cdots\)
6336.2.a.j	$6336$	$2$	6336.a	1.a	$1$	$1$	$1$	$50.593$	\(\Q\)	None	✓				44.2.a.a	$1$	$0$	\(0\)	\(0\)	\(-3\)	\(2\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-3q^{5}+2q^{7}-q^{11}+4q^{13}-6q^{17}+\cdots\)
6336.2.a.k	$6336$	$2$	6336.a	1.a	$1$	$1$	$1$	$50.593$	\(\Q\)	None	✓				88.2.a.a	$1$	$0$	\(0\)	\(0\)	\(-3\)	\(2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-3q^{5}+2q^{7}+q^{11}+6q^{17}+4q^{19}+\cdots\)
6336.2.a.l	$6336$	$2$	6336.a	1.a	$1$	$1$	$1$	$50.593$	\(\Q\)	None	✓				352.2.a.b	$1$	$0$	\(0\)	\(0\)	\(-3\)	\(4\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-3q^{5}+4q^{7}-q^{11}+2q^{13}+8q^{17}+\cdots\)
6336.2.a.m	$6336$	$2$	6336.a	1.a	$1$	$1$	$1$	$50.593$	\(\Q\)	None	✓				3168.2.a.b	$1$	$2$	\(0\)	\(0\)	\(-2\)	\(-4\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}-4q^{7}-q^{11}-4q^{13}-6q^{17}+\cdots\)
6336.2.a.n	$6336$	$2$	6336.a	1.a	$1$	$1$	$1$	$50.593$	\(\Q\)	None	✓				33.2.a.a	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(-4\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}-4q^{7}-q^{11}+2q^{13}+2q^{17}+\cdots\)
6336.2.a.o	$6336$	$2$	6336.a	1.a	$1$	$1$	$1$	$50.593$	\(\Q\)	None	✓				264.2.a.b	$1$	$2$	\(0\)	\(0\)	\(-2\)	\(-4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}-4q^{7}+q^{11}-6q^{13}-6q^{17}+\cdots\)
6336.2.a.p	$6336$	$2$	6336.a	1.a	$1$	$1$	$1$	$50.593$	\(\Q\)	None	✓				1056.2.a.c	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(-2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}-2q^{7}+q^{11}+2q^{13}+2q^{19}+\cdots\)
6336.2.a.q	$6336$	$2$	6336.a	1.a	$1$	$1$	$1$	$50.593$	\(\Q\)	None	✓				3168.2.a.c	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}-q^{11}-2q^{17}-6q^{19}+6q^{23}+\cdots\)
6336.2.a.r	$6336$	$2$	6336.a	1.a	$1$	$1$	$1$	$50.593$	\(\Q\)	None	✓				1056.2.a.b	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}-q^{11}+6q^{13}-2q^{17}+4q^{19}+\cdots\)
6336.2.a.s	$6336$	$2$	6336.a	1.a	$1$	$1$	$1$	$50.593$	\(\Q\)	None	✓				3168.2.a.c	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}+q^{11}-2q^{17}+6q^{19}-6q^{23}+\cdots\)
6336.2.a.t	$6336$	$2$	6336.a	1.a	$1$	$1$	$1$	$50.593$	\(\Q\)	None	✓				1056.2.a.b	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}+q^{11}+6q^{13}-2q^{17}-4q^{19}+\cdots\)
6336.2.a.u	$6336$	$2$	6336.a	1.a	$1$	$1$	$1$	$50.593$	\(\Q\)	None	✓				1056.2.a.c	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}+2q^{7}-q^{11}+2q^{13}-2q^{19}+\cdots\)
6336.2.a.v	$6336$	$2$	6336.a	1.a	$1$	$1$	$1$	$50.593$	\(\Q\)	None	✓				264.2.a.b	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(4\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}+4q^{7}-q^{11}-6q^{13}-6q^{17}+\cdots\)
6336.2.a.w	$6336$	$2$	6336.a	1.a	$1$	$1$	$1$	$50.593$	\(\Q\)	None	✓				3168.2.a.b	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(4\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}+4q^{7}+q^{11}-4q^{13}-6q^{17}+\cdots\)
6336.2.a.x	$6336$	$2$	6336.a	1.a	$1$	$1$	$1$	$50.593$	\(\Q\)	None	✓				33.2.a.a	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(4\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}+4q^{7}+q^{11}+2q^{13}+2q^{17}+\cdots\)
6336.2.a.y	$6336$	$2$	6336.a	1.a	$1$	$1$	$1$	$50.593$	\(\Q\)	None	✓				1056.2.a.d	$1$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{7}-q^{11}-4q^{13}+2q^{17}+2q^{23}+\cdots\)
6336.2.a.z	$6336$	$2$	6336.a	1.a	$1$	$1$	$1$	$50.593$	\(\Q\)	None	✓				198.2.a.b	$1$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{7}-q^{11}-2q^{13}-6q^{17}+2q^{19}+\cdots\)
6336.2.a.ba	$6336$	$2$	6336.a	1.a	$1$	$1$	$1$	$50.593$	\(\Q\)	None	✓				264.2.a.c	$1$	$1$	\(0\)	\(0\)	\(0\)	\(-2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{7}-q^{11}+2q^{17}+8q^{19}-2q^{23}+\cdots\)
6336.2.a.bb	$6336$	$2$	6336.a	1.a	$1$	$1$	$1$	$50.593$	\(\Q\)	None	✓				3168.2.a.k	$1$	$1$	\(0\)	\(0\)	\(0\)	\(-2\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{7}-q^{11}+2q^{13}+2q^{17}-6q^{19}+\cdots\)
6336.2.a.bc	$6336$	$2$	6336.a	1.a	$1$	$1$	$1$	$50.593$	\(\Q\)	None	✓				792.2.a.c	$1$	$1$	\(0\)	\(0\)	\(0\)	\(-2\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{7}-q^{11}+6q^{13}-6q^{17}+2q^{19}+\cdots\)
6336.2.a.bd	$6336$	$2$	6336.a	1.a	$1$	$1$	$1$	$50.593$	\(\Q\)	None	✓				198.2.a.b	$1$	$1$	\(0\)	\(0\)	\(0\)	\(-2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{7}+q^{11}-2q^{13}+6q^{17}+2q^{19}+\cdots\)
6336.2.a.be	$6336$	$2$	6336.a	1.a	$1$	$1$	$1$	$50.593$	\(\Q\)	None	✓				3168.2.a.k	$1$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{7}+q^{11}+2q^{13}-2q^{17}-6q^{19}+\cdots\)
6336.2.a.bf	$6336$	$2$	6336.a	1.a	$1$	$1$	$1$	$50.593$	\(\Q\)	None	✓				66.2.a.a	$1$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{7}+q^{11}+4q^{13}+6q^{17}-4q^{19}+\cdots\)
6336.2.a.bg	$6336$	$2$	6336.a	1.a	$1$	$1$	$1$	$50.593$	\(\Q\)	None	✓				792.2.a.c	$1$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{7}+q^{11}+6q^{13}+6q^{17}+2q^{19}+\cdots\)
6336.2.a.bh	$6336$	$2$	6336.a	1.a	$1$	$1$	$1$	$50.593$	\(\Q\)	None	✓				198.2.a.b	$1$	$1$	\(0\)	\(0\)	\(0\)	\(2\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{7}-q^{11}-2q^{13}+6q^{17}-2q^{19}+\cdots\)
6336.2.a.bi	$6336$	$2$	6336.a	1.a	$1$	$1$	$1$	$50.593$	\(\Q\)	None	✓				3168.2.a.k	$1$	$1$	\(0\)	\(0\)	\(0\)	\(2\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{7}-q^{11}+2q^{13}-2q^{17}+6q^{19}+\cdots\)
6336.2.a.bj	$6336$	$2$	6336.a	1.a	$1$	$1$	$1$	$50.593$	\(\Q\)	None	✓				66.2.a.a	$1$	$0$	\(0\)	\(0\)	\(0\)	\(2\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{7}-q^{11}+4q^{13}+6q^{17}+4q^{19}+\cdots\)
6336.2.a.bk	$6336$	$2$	6336.a	1.a	$1$	$1$	$1$	$50.593$	\(\Q\)	None	✓				792.2.a.c	$1$	$0$	\(0\)	\(0\)	\(0\)	\(2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{7}-q^{11}+6q^{13}+6q^{17}-2q^{19}+\cdots\)
6336.2.a.bl	$6336$	$2$	6336.a	1.a	$1$	$1$	$1$	$50.593$	\(\Q\)	None	✓				1056.2.a.d	$1$	$1$	\(0\)	\(0\)	\(0\)	\(2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{7}+q^{11}-4q^{13}+2q^{17}-2q^{23}+\cdots\)
6336.2.a.bm	$6336$	$2$	6336.a	1.a	$1$	$1$	$1$	$50.593$	\(\Q\)	None	✓				198.2.a.b	$1$	$0$	\(0\)	\(0\)	\(0\)	\(2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{7}+q^{11}-2q^{13}-6q^{17}-2q^{19}+\cdots\)
6336.2.a.bn	$6336$	$2$	6336.a	1.a	$1$	$1$	$1$	$50.593$	\(\Q\)	None	✓				264.2.a.c	$1$	$1$	\(0\)	\(0\)	\(0\)	\(2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{7}+q^{11}+2q^{17}-8q^{19}+2q^{23}+\cdots\)
6336.2.a.bo	$6336$	$2$	6336.a	1.a	$1$	$1$	$1$	$50.593$	\(\Q\)	None	✓				3168.2.a.k	$1$	$0$	\(0\)	\(0\)	\(0\)	\(2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{7}+q^{11}+2q^{13}+2q^{17}+6q^{19}+\cdots\)
6336.2.a.bp	$6336$	$2$	6336.a	1.a	$1$	$1$	$1$	$50.593$	\(\Q\)	None	✓				792.2.a.c	$1$	$1$	\(0\)	\(0\)	\(0\)	\(2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{7}+q^{11}+6q^{13}-6q^{17}-2q^{19}+\cdots\)
6336.2.a.bq	$6336$	$2$	6336.a	1.a	$1$	$1$	$1$	$50.593$	\(\Q\)	None	✓				352.2.a.c	$1$	$1$	\(0\)	\(0\)	\(1\)	\(-4\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-4q^{7}-q^{11}+2q^{13}-2q^{19}+\cdots\)
6336.2.a.br	$6336$	$2$	6336.a	1.a	$1$	$1$	$1$	$50.593$	\(\Q\)	None	✓				11.2.a.a	$1$	$1$	\(0\)	\(0\)	\(1\)	\(-2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-2q^{7}+q^{11}-4q^{13}+2q^{17}+\cdots\)
6336.2.a.bs	$6336$	$2$	6336.a	1.a	$1$	$1$	$1$	$50.593$	\(\Q\)	None	✓				352.2.a.a	$1$	$1$	\(0\)	\(0\)	\(1\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-q^{11}+6q^{13}+4q^{17}-6q^{19}+\cdots\)
6336.2.a.bt	$6336$	$2$	6336.a	1.a	$1$	$1$	$1$	$50.593$	\(\Q\)	None	✓				352.2.a.a	$1$	$0$	\(0\)	\(0\)	\(1\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+q^{11}+6q^{13}+4q^{17}+6q^{19}+\cdots\)
6336.2.a.bu	$6336$	$2$	6336.a	1.a	$1$	$1$	$1$	$50.593$	\(\Q\)	None	✓				11.2.a.a	$1$	$1$	\(0\)	\(0\)	\(1\)	\(2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+2q^{7}-q^{11}-4q^{13}+2q^{17}+\cdots\)
6336.2.a.bv	$6336$	$2$	6336.a	1.a	$1$	$1$	$1$	$50.593$	\(\Q\)	None	✓				352.2.a.c	$1$	$0$	\(0\)	\(0\)	\(1\)	\(4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+4q^{7}+q^{11}+2q^{13}+2q^{19}+\cdots\)
6336.2.a.bw	$6336$	$2$	6336.a	1.a	$1$	$1$	$1$	$50.593$	\(\Q\)	None	✓				66.2.a.b	$1$	$0$	\(0\)	\(0\)	\(2\)	\(-4\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}-4q^{7}-q^{11}+6q^{13}-2q^{17}+\cdots\)
6336.2.a.bx	$6336$	$2$	6336.a	1.a	$1$	$1$	$1$	$50.593$	\(\Q\)	None	✓				3168.2.a.b	$1$	$1$	\(0\)	\(0\)	\(2\)	\(-4\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}-4q^{7}+q^{11}-4q^{13}+6q^{17}+\cdots\)
6336.2.a.by	$6336$	$2$	6336.a	1.a	$1$	$1$	$1$	$50.593$	\(\Q\)	None	✓				1056.2.a.e	$1$	$1$	\(0\)	\(0\)	\(2\)	\(-4\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}-4q^{7}+q^{11}+2q^{13}-2q^{17}+\cdots\)
6336.2.a.bz	$6336$	$2$	6336.a	1.a	$1$	$1$	$1$	$50.593$	\(\Q\)	None	✓				132.2.a.a	$1$	$0$	\(0\)	\(0\)	\(2\)	\(-2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}-2q^{7}+q^{11}-6q^{13}+4q^{17}+\cdots\)
6336.2.a.ca	$6336$	$2$	6336.a	1.a	$1$	$1$	$1$	$50.593$	\(\Q\)	None	✓				132.2.a.b	$1$	$1$	\(0\)	\(0\)	\(2\)	\(-2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}-2q^{7}+q^{11}+2q^{13}-4q^{17}+\cdots\)
6336.2.a.cb	$6336$	$2$	6336.a	1.a	$1$	$1$	$1$	$50.593$	\(\Q\)	None	✓				264.2.a.a	$1$	$1$	\(0\)	\(0\)	\(2\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}-q^{11}-2q^{13}-6q^{17}+4q^{23}+\cdots\)
6336.2.a.cc	$6336$	$2$	6336.a	1.a	$1$	$1$	$1$	$50.593$	\(\Q\)	None	✓				3168.2.a.c	$1$	$0$	\(0\)	\(0\)	\(2\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}-q^{11}+2q^{17}+6q^{19}+6q^{23}+\cdots\)
6336.2.a.cd	$6336$	$2$	6336.a	1.a	$1$	$1$	$1$	$50.593$	\(\Q\)	None	✓				264.2.a.a	$1$	$1$	\(0\)	\(0\)	\(2\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}+q^{11}-2q^{13}-6q^{17}-4q^{23}+\cdots\)
6336.2.a.ce	$6336$	$2$	6336.a	1.a	$1$	$1$	$1$	$50.593$	\(\Q\)	None	✓				3168.2.a.c	$1$	$1$	\(0\)	\(0\)	\(2\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}+q^{11}+2q^{17}-6q^{19}-6q^{23}+\cdots\)
6336.2.a.cf	$6336$	$2$	6336.a	1.a	$1$	$1$	$1$	$50.593$	\(\Q\)	None	✓				132.2.a.a	$1$	$0$	\(0\)	\(0\)	\(2\)	\(2\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}+2q^{7}-q^{11}-6q^{13}+4q^{17}+\cdots\)
6336.2.a.cg	$6336$	$2$	6336.a	1.a	$1$	$1$	$1$	$50.593$	\(\Q\)	None	✓				132.2.a.b	$1$	$1$	\(0\)	\(0\)	\(2\)	\(2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}+2q^{7}-q^{11}+2q^{13}-4q^{17}+\cdots\)
6336.2.a.ch	$6336$	$2$	6336.a	1.a	$1$	$1$	$1$	$50.593$	\(\Q\)	None	✓				3168.2.a.b	$1$	$0$	\(0\)	\(0\)	\(2\)	\(4\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}+4q^{7}-q^{11}-4q^{13}+6q^{17}+\cdots\)
6336.2.a.ci	$6336$	$2$	6336.a	1.a	$1$	$1$	$1$	$50.593$	\(\Q\)	None	✓				1056.2.a.e	$1$	$0$	\(0\)	\(0\)	\(2\)	\(4\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}+4q^{7}-q^{11}+2q^{13}-2q^{17}+\cdots\)
6336.2.a.cj	$6336$	$2$	6336.a	1.a	$1$	$1$	$1$	$50.593$	\(\Q\)	None	✓				66.2.a.b	$1$	$0$	\(0\)	\(0\)	\(2\)	\(4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}+4q^{7}+q^{11}+6q^{13}-2q^{17}+\cdots\)
6336.2.a.ck	$6336$	$2$	6336.a	1.a	$1$	$1$	$1$	$50.593$	\(\Q\)	None	✓				264.2.a.d	$1$	$0$	\(0\)	\(0\)	\(4\)	\(-2\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+4q^{5}-2q^{7}-q^{11}+6q^{17}-4q^{19}+\cdots\)
6336.2.a.cl	$6336$	$2$	6336.a	1.a	$1$	$1$	$1$	$50.593$	\(\Q\)	None	✓				99.2.a.a	$1$	$0$	\(0\)	\(0\)	\(4\)	\(-2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+4q^{5}-2q^{7}+q^{11}+2q^{13}+2q^{17}+\cdots\)
6336.2.a.cm	$6336$	$2$	6336.a	1.a	$1$	$1$	$1$	$50.593$	\(\Q\)	None	✓				99.2.a.a	$1$	$0$	\(0\)	\(0\)	\(4\)	\(2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+4q^{5}+2q^{7}-q^{11}+2q^{13}+2q^{17}+\cdots\)
6336.2.a.cn	$6336$	$2$	6336.a	1.a	$1$	$1$	$1$	$50.593$	\(\Q\)	None	✓				264.2.a.d	$1$	$0$	\(0\)	\(0\)	\(4\)	\(2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+4q^{5}+2q^{7}+q^{11}+6q^{17}+4q^{19}+\cdots\)
6336.2.a.co	$6336$	$2$	6336.a	1.a	$1$	$2$	$2$	$50.593$	\(\Q(\sqrt{2}) \)	None	✓		✓		792.2.a.i	$1$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)		$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta q^{5}+(-2-\beta )q^{7}-q^{11}+(-2+\cdots)q^{13}+\cdots\)
6336.2.a.cp	$6336$	$2$	6336.a	1.a	$1$	$2$	$2$	$50.593$	\(\Q(\sqrt{2}) \)	None	✓		✓		792.2.a.i	$1$	$1$	\(0\)	\(0\)	\(0\)	\(-4\)		$-$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+\beta q^{5}+(-2+\beta )q^{7}+q^{11}+(-2+\cdots)q^{13}+\cdots\)
6336.2.a.cq	$6336$	$2$	6336.a	1.a	$1$	$2$	$2$	$50.593$	\(\Q(\sqrt{2}) \)	None	✓				792.2.a.i	$1$	$1$	\(0\)	\(0\)	\(0\)	\(4\)		$+$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+\beta q^{5}+(2-\beta )q^{7}-q^{11}+(-2-\beta )q^{13}+\cdots\)
6336.2.a.cr	$6336$	$2$	6336.a	1.a	$1$	$2$	$2$	$50.593$	\(\Q(\sqrt{2}) \)	None	✓				792.2.a.i	$1$	$0$	\(0\)	\(0\)	\(0\)	\(4\)		$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta q^{5}+(2+\beta )q^{7}+q^{11}+(-2+\beta )q^{13}+\cdots\)
6336.2.a.cs	$6336$	$2$	6336.a	1.a	$1$	$2$	$2$	$50.593$	\(\Q(\sqrt{5}) \)	None	✓				1056.2.a.k	$1$	$0$	\(0\)	\(0\)	\(2\)	\(-2\)		$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{5}+(-1+\beta )q^{7}+q^{11}+(-3+\cdots)q^{13}+\cdots\)
6336.2.a.ct	$6336$	$2$	6336.a	1.a	$1$	$2$	$2$	$50.593$	\(\Q(\sqrt{5}) \)	None	✓				1056.2.a.k	$1$	$1$	\(0\)	\(0\)	\(2\)	\(2\)		$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{5}+(1-\beta )q^{7}-q^{11}+(-3+\cdots)q^{13}+\cdots\)
6336.2.a.cu	$6336$	$2$	6336.a	1.a	$1$	$2$	$2$	$50.593$	\(\Q(\sqrt{17}) \)	None	✓				88.2.a.b	$1$	$0$	\(0\)	\(0\)	\(3\)	\(-2\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{5}+(-2+2\beta )q^{7}-q^{11}+\cdots\)
6336.2.a.cv	$6336$	$2$	6336.a	1.a	$1$	$2$	$2$	$50.593$	\(\Q(\sqrt{17}) \)	None	✓				352.2.a.g	$1$	$0$	\(0\)	\(0\)	\(3\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{5}-q^{11}-2q^{13}+(-4+2\beta )q^{17}+\cdots\)
6336.2.a.cw	$6336$	$2$	6336.a	1.a	$1$	$2$	$2$	$50.593$	\(\Q(\sqrt{17}) \)	None	✓		✓		352.2.a.g	$1$	$1$	\(0\)	\(0\)	\(3\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{5}+q^{11}-2q^{13}+(-4+2\beta )q^{17}+\cdots\)
6336.2.a.cx	$6336$	$2$	6336.a	1.a	$1$	$2$	$2$	$50.593$	\(\Q(\sqrt{17}) \)	None	✓				88.2.a.b	$1$	$0$	\(0\)	\(0\)	\(3\)	\(2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{5}+(2-2\beta )q^{7}+q^{11}+2\beta q^{13}+\cdots\)
6336.2.a.cy	$6336$	$2$	6336.a	1.a	$1$	$3$	$3$	$50.593$	3.3.229.1	None	✓		✓		1056.2.a.m	$1$	$1$	\(0\)	\(0\)	\(0\)	\(-4\)		$-$	$-$	$+$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{5}+(-1-\beta _{2})q^{7}-q^{11}+\beta _{1}q^{13}+\cdots\)
6336.2.a.cz	$6336$	$2$	6336.a	1.a	$1$	$3$	$3$	$50.593$	3.3.229.1	None	✓		✓		1056.2.a.m	$1$	$0$	\(0\)	\(0\)	\(0\)	\(4\)		$-$	$-$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{5}+(1+\beta _{2})q^{7}+q^{11}+\beta _{1}q^{13}+\cdots\)
6336.2.a.da	$6336$	$2$	6336.a	1.a	$1$	$4$	$4$	$50.593$	\(\Q(\zeta_{24})^+\)	None	✓		✓		3168.2.a.bi	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$+$	$+$	$2^{4}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{5}+\beta _{3}q^{7}-q^{11}+(-2-\beta _{2}+\cdots)q^{13}+\cdots\)
6336.2.a.db	$6336$	$2$	6336.a	1.a	$1$	$4$	$4$	$50.593$	\(\Q(\zeta_{24})^+\)	None	✓		✓		3168.2.a.bi	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$-$	$-$	$2^{4}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{5}+\beta _{3}q^{7}+q^{11}+(-2+\beta _{2}+\cdots)q^{13}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(6336))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(6336)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 21}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(22))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(44))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(64))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(66))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(72))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(88))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(96))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(99))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(132))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(144))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(176))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(192))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(198))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(264))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(288))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(352))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(396))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(528))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(576))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(704))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(792))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1056))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1584))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2112))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3168))\)\(^{\oplus 2}\)