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

• Label: 6336.2.k
• Level: $6336$
• Weight: $2$
• Character orbit: 6336.k
• Rep. character: $\chi_{6336}(287,\cdot)$
• Character field: $\Q$
• Dimension: $80$
• Newform subspaces: $6$
• Sturm bound: $2304$
• Trace bound: $29$

Defining parameters

Level:	\( N \)	\(=\)	\( 6336 = 2^{6} \cdot 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6336.k (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 24 \)
Character field:			\(\Q\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(2304\)
Trace bound:			\(29\)
Distinguishing \(T_p\):			\(5\)

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.k.a	$6336$	$2$	6336.k	24.f	$2$	$4$	$4$	$50.593$	\(\Q(\zeta_{8})\)	None		$4$	$0$	\(0\)	\(0\)	\(-8\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-2q^{5}+4\zeta_{8}q^{7}+\zeta_{8}q^{11}+3\zeta_{8}^{2}q^{13}+\cdots\)
6336.2.k.b	$6336$	$2$	6336.k	24.f	$2$	$4$	$4$	$50.593$	\(\Q(\zeta_{8})\)	None		$4$	$0$	\(0\)	\(0\)	\(8\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+2q^{5}-4\zeta_{8}q^{7}+\zeta_{8}q^{11}-3\zeta_{8}^{2}q^{13}+\cdots\)
6336.2.k.c	$6336$	$2$	6336.k	24.f	$2$	$12$	$12$	$50.593$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(-8\)	\(0\)	$2^{11}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1+\beta _{2})q^{5}+(-\beta _{4}+\beta _{5})q^{7}-\beta _{4}q^{11}+\cdots\)
6336.2.k.d	$6336$	$2$	6336.k	24.f	$2$	$12$	$12$	$50.593$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(8\)	\(0\)	$2^{11}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(1-\beta _{2})q^{5}+(\beta _{4}-\beta _{5})q^{7}-\beta _{4}q^{11}+\cdots\)
6336.2.k.e	$6336$	$2$	6336.k	24.f	$2$	$24$	$24$	$50.593$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$
6336.2.k.f	$6336$	$2$	6336.k	24.f	$2$	$24$	$24$	$50.593$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

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

\( S_{2}^{\mathrm{old}}(6336, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(264, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(528, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(792, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1056, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1584, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2112, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(3168, [\chi])\)\(^{\oplus 2}\)