Space of modular forms of level 48, weight 6, and Character 48.c

• Label: 48.6.c
• Level: $48$
• Weight: $6$
• Character orbit: 48.c
• Rep. character: $\chi_{48}(47,\cdot)$
• Character field: $\Q$
• Dimension: $10$
• Newform subspaces: $4$
• Sturm bound: $48$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 48 = 2^{4} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	48.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 12 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(48\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(5\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(48, [\chi])\).

	Total	New	Old
Modular forms	46	10	36
Cusp forms	34	10	24
Eisenstein series	12	0	12

Trace form

\( 10 q + 66 q^{9} + O(q^{10}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(48, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
48.6.c.a	$48$	$6$	48.c	12.b	$2$	$2$	$2$	$7.698$	\(\Q(\sqrt{-11}) \)	None		$2$	$1$	\(0\)	\(-24\)	\(0\)	\(0\)	$2\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-12-\beta )q^{3}-8\beta q^{5}+18\beta q^{7}+\cdots\)
48.6.c.b	$48$	$6$	48.c	12.b	$2$	$2$	$2$	$7.698$	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{U}(1)[D_{2}]$	\(q-9\zeta_{6}q^{3}-62\zeta_{6}q^{7}-3^{5}q^{9}-1202q^{13}+\cdots\)
48.6.c.c	$48$	$6$	48.c	12.b	$2$	$2$	$2$	$7.698$	\(\Q(\sqrt{-11}) \)	None		$2$	$0$	\(0\)	\(24\)	\(0\)	\(0\)	$2\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	\(q+(12+\beta )q^{3}-8\beta q^{5}-18\beta q^{7}+(45+\cdots)q^{9}+\cdots\)
48.6.c.d	$48$	$6$	48.c	12.b	$2$	$4$	$4$	$7.698$	\(\Q(\sqrt{-3}, \sqrt{-14})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	\(q+(2\beta _{1}-\beta _{2})q^{3}-\beta _{3}q^{5}+11\beta _{1}q^{7}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(48, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(48, [\chi]) \cong \)