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

• Label: 6336.2.d
• Level: $6336$
• Weight: $2$
• Character orbit: 6336.d
• Rep. character: $\chi_{6336}(3455,\cdot)$
• Character field: $\Q$
• Dimension: $80$
• Newform subspaces: $10$
• 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.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 12 \)
Character field:			\(\Q\)
Newform subspaces:			\( 10 \)
Sturm bound:			\(2304\)
Trace bound:			\(13\)
Distinguishing \(T_p\):			\(5\), \(23\)

Dimensions

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

	Total	New	Old
Modular forms	1200	80	1120
Cusp forms	1104	80	1024
Eisenstein series	96	0	96

Trace form

\( 80 q + O(q^{10}) \)

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.d.a	$6336$	$2$	6336.d	12.b	$2$	$2$	$2$	$50.593$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{5}-2\beta q^{7}-q^{11}-\beta q^{17}+2\beta q^{19}+\cdots\)
6336.2.d.b	$6336$	$2$	6336.d	12.b	$2$	$2$	$2$	$50.593$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{5}+2\beta q^{7}+q^{11}-\beta q^{17}-2\beta q^{19}+\cdots\)
6336.2.d.c	$6336$	$2$	6336.d	12.b	$2$	$8$	$8$	$50.593$	8.0.1768034304.5	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{8}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{4}q^{5}-\beta _{4}q^{7}-q^{11}+(1-\beta _{3})q^{13}+\cdots\)
6336.2.d.d	$6336$	$2$	6336.d	12.b	$2$	$8$	$8$	$50.593$	8.0.110166016.2	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{1}-\beta _{3})q^{5}+(-\beta _{1}+\beta _{3})q^{7}-q^{11}+\cdots\)
6336.2.d.e	$6336$	$2$	6336.d	12.b	$2$	$8$	$8$	$50.593$	8.0.1768034304.5	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{8}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{4}q^{5}+\beta _{4}q^{7}+q^{11}+(1-\beta _{3})q^{13}+\cdots\)
6336.2.d.f	$6336$	$2$	6336.d	12.b	$2$	$8$	$8$	$50.593$	8.0.110166016.2	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{1}-\beta _{3})q^{5}+(\beta _{1}-\beta _{3})q^{7}+q^{11}+\cdots\)
6336.2.d.g	$6336$	$2$	6336.d	12.b	$2$	$10$	$10$	$50.593$	10.0.\(\cdots\).1	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{9}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{5}-\beta _{9}q^{7}-q^{11}+(-1+\beta _{7}+\cdots)q^{13}+\cdots\)
6336.2.d.h	$6336$	$2$	6336.d	12.b	$2$	$10$	$10$	$50.593$	10.0.\(\cdots\).1	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{9}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{5}+\beta _{9}q^{7}+q^{11}+(-1+\beta _{7}+\cdots)q^{13}+\cdots\)
6336.2.d.i	$6336$	$2$	6336.d	12.b	$2$	$12$	$12$	$50.593$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{12}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{4}q^{5}+\beta _{10}q^{7}-q^{11}+\beta _{8}q^{13}+\cdots\)
6336.2.d.j	$6336$	$2$	6336.d	12.b	$2$	$12$	$12$	$50.593$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{12}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{4}q^{5}+\beta _{10}q^{7}+q^{11}+\beta _{8}q^{13}+\cdots\)

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

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