Space of modular forms of level 6336, weight 2, and Character 6336.b

• Label: 6336.2.b
• Level: $6336$
• Weight: $2$
• Character orbit: 6336.b
• Rep. character: $\chi_{6336}(2177,\cdot)$
• Character field: $\Q$
• Dimension: $96$
• Newform subspaces: $28$
• Sturm bound: $2304$
• Trace bound: $31$

Defining parameters

Level:	\( N \)	\(=\)	\( 6336 = 2^{6} \cdot 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6336.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 33 \)
Character field:			\(\Q\)
Newform subspaces:			\( 28 \)
Sturm bound:			\(2304\)
Trace bound:			\(31\)
Distinguishing \(T_p\):			\(5\), \(7\), \(13\), \(17\), \(31\), \(83\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(6336, [\chi])\).

	Total	New	Old
Modular forms	1200	96	1104
Cusp forms	1104	96	1008
Eisenstein series	96	0	96

Trace form

\( 96 q + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(6336, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
6336.2.b.a	$6336$	$2$	6336.b	33.d	$2$	$2$	$2$	$50.593$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2\beta q^{5}+(-3+\beta )q^{11}-3\beta q^{13}+\cdots\)
6336.2.b.b	$6336$	$2$	6336.b	33.d	$2$	$2$	$2$	$50.593$	\(\Q(\sqrt{-2}) \)	None		$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{5}+3\beta q^{7}+(-3+\beta )q^{11}-6q^{17}+\cdots\)
6336.2.b.c	$6336$	$2$	6336.b	33.d	$2$	$2$	$2$	$50.593$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{5}-\beta q^{7}+(-3+\beta )q^{11}-2\beta q^{13}+\cdots\)
6336.2.b.d	$6336$	$2$	6336.b	33.d	$2$	$2$	$2$	$50.593$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2\beta q^{7}+(-3+\beta )q^{11}+3\beta q^{13}+\cdots\)
6336.2.b.e	$6336$	$2$	6336.b	33.d	$2$	$2$	$2$	$50.593$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-2\beta q^{7}+(-3+\beta )q^{11}+3\beta q^{13}+\cdots\)
6336.2.b.f	$6336$	$2$	6336.b	33.d	$2$	$2$	$2$	$50.593$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2\beta q^{5}+(-3-\beta )q^{11}+3\beta q^{13}+\cdots\)
6336.2.b.g	$6336$	$2$	6336.b	33.d	$2$	$2$	$2$	$50.593$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{5}-\beta q^{7}+(-3-\beta )q^{11}+2\beta q^{13}+\cdots\)
6336.2.b.h	$6336$	$2$	6336.b	33.d	$2$	$2$	$2$	$50.593$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{5}+3\beta q^{7}+(-3-\beta )q^{11}+6q^{17}+\cdots\)
6336.2.b.i	$6336$	$2$	6336.b	33.d	$2$	$2$	$2$	$50.593$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2\beta q^{5}+(3-\beta )q^{11}-3\beta q^{13}-6q^{17}+\cdots\)
6336.2.b.j	$6336$	$2$	6336.b	33.d	$2$	$2$	$2$	$50.593$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{5}+\beta q^{7}+(3-\beta )q^{11}-2\beta q^{13}+\cdots\)
6336.2.b.k	$6336$	$2$	6336.b	33.d	$2$	$2$	$2$	$50.593$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{5}-3\beta q^{7}+(3-\beta )q^{11}-6q^{17}+\cdots\)
6336.2.b.l	$6336$	$2$	6336.b	33.d	$2$	$2$	$2$	$50.593$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-2\beta q^{7}+(3-\beta )q^{11}+3\beta q^{13}-2q^{17}+\cdots\)
6336.2.b.m	$6336$	$2$	6336.b	33.d	$2$	$2$	$2$	$50.593$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2\beta q^{7}+(3-\beta )q^{11}+3\beta q^{13}+2q^{17}+\cdots\)
6336.2.b.n	$6336$	$2$	6336.b	33.d	$2$	$2$	$2$	$50.593$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2\beta q^{5}+(3+\beta )q^{11}+3\beta q^{13}+6q^{17}+\cdots\)
6336.2.b.o	$6336$	$2$	6336.b	33.d	$2$	$2$	$2$	$50.593$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{5}-3\beta q^{7}+(3+\beta )q^{11}+6q^{17}+\cdots\)
6336.2.b.p	$6336$	$2$	6336.b	33.d	$2$	$2$	$2$	$50.593$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{5}+\beta q^{7}+(3+\beta )q^{11}+2\beta q^{13}+\cdots\)
6336.2.b.q	$6336$	$2$	6336.b	33.d	$2$	$4$	$4$	$50.593$	\(\Q(\sqrt{-2}, \sqrt{5})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q-2\beta _{1}q^{5}+(-1+\beta _{2})q^{11}-\beta _{2}q^{13}+\cdots\)
6336.2.b.r	$6336$	$2$	6336.b	33.d	$2$	$4$	$4$	$50.593$	\(\Q(\sqrt{-2}, \sqrt{5})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{5}+3\beta _{1}q^{7}+(-1+\beta _{2})q^{11}+\cdots\)
6336.2.b.s	$6336$	$2$	6336.b	33.d	$2$	$4$	$4$	$50.593$	\(\Q(\sqrt{-2}, \sqrt{3})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{5}-\beta _{3}q^{7}+(-2\beta _{1}+\beta _{2})q^{11}+\cdots\)
6336.2.b.t	$6336$	$2$	6336.b	33.d	$2$	$4$	$4$	$50.593$	\(\Q(\sqrt{-2}, \sqrt{3})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{5}+\beta _{3}q^{7}+(2\beta _{1}-\beta _{2})q^{11}+\cdots\)
6336.2.b.u	$6336$	$2$	6336.b	33.d	$2$	$4$	$4$	$50.593$	\(\Q(\sqrt{-2}, \sqrt{5})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q-2\beta _{1}q^{5}+(1+\beta _{2})q^{11}+\beta _{2}q^{13}+\cdots\)
6336.2.b.v	$6336$	$2$	6336.b	33.d	$2$	$4$	$4$	$50.593$	\(\Q(\sqrt{-2}, \sqrt{5})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{5}-3\beta _{1}q^{7}+(1+\beta _{2})q^{11}-2\beta _{2}q^{13}+\cdots\)
6336.2.b.w	$6336$	$2$	6336.b	33.d	$2$	$6$	$6$	$50.593$	6.0.12781568.1	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{5}+(\beta _{2}+\beta _{4})q^{7}+(\beta _{3}+\beta _{4})q^{11}+\cdots\)
6336.2.b.x	$6336$	$2$	6336.b	33.d	$2$	$6$	$6$	$50.593$	6.0.12781568.1	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{5}+(\beta _{2}+\beta _{4})q^{7}+(\beta _{3}-\beta _{4})q^{11}+\cdots\)
6336.2.b.y	$6336$	$2$	6336.b	33.d	$2$	$6$	$6$	$50.593$	6.0.12781568.1	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{5}+(-\beta _{2}-\beta _{4})q^{7}+(-\beta _{3}-\beta _{4}+\cdots)q^{11}+\cdots\)
6336.2.b.z	$6336$	$2$	6336.b	33.d	$2$	$6$	$6$	$50.593$	6.0.12781568.1	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{5}+(-\beta _{2}-\beta _{4})q^{7}+(-\beta _{3}+\beta _{4}+\cdots)q^{11}+\cdots\)
6336.2.b.ba	$6336$	$2$	6336.b	33.d	$2$	$8$	$8$	$50.593$	8.0.4956160000.6	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{5}-\beta _{7}q^{7}+\beta _{4}q^{11}+2\beta _{5}q^{13}+\cdots\)
6336.2.b.bb	$6336$	$2$	6336.b	33.d	$2$	$8$	$8$	$50.593$	8.0.4956160000.6	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{5}+\beta _{7}q^{7}+\beta _{3}q^{11}-2\beta _{5}q^{13}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(6336, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(6336, [\chi]) \cong \)