Space of modular forms of level 48, weight 8, and Character 48.c

• Label: 48.8.c
• Level: $48$
• Weight: $8$
• Character orbit: 48.c
• Rep. character: $\chi_{48}(47,\cdot)$
• Character field: $\Q$
• Dimension: $14$
• Newform subspaces: $3$
• Sturm bound: $64$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 48 = 2^{4} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	48.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 12 \)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(64\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(48, [\chi])\).

	Total	New	Old
Modular forms	62	14	48
Cusp forms	50	14	36
Eisenstein series	12	0	12

Trace form

\( 14 q - 3354 q^{9} + O(q^{10}) \)

Decomposition of \(S_{8}^{\mathrm{new}}(48, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
48.8.c.a	$48$	$8$	48.c	12.b	$2$	$2$	$2$	$14.994$	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{U}(1)[D_{2}]$	\(q-3^{3}\zeta_{6}q^{3}+1006\zeta_{6}q^{7}-3^{7}q^{9}+\cdots\)
48.8.c.b	$48$	$8$	48.c	12.b	$2$	$4$	$4$	$14.994$	\(\Q(\sqrt{30}, \sqrt{-123})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{3}+\beta _{3}q^{5}+(-\beta _{1}-3\beta _{2})q^{7}+\cdots\)
48.8.c.c	$48$	$8$	48.c	12.b	$2$	$8$	$8$	$14.994$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{30}\cdot 3^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{1}-\beta _{2})q^{3}+\beta _{3}q^{5}+(-20\beta _{1}-10\beta _{2}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{8}^{\mathrm{old}}(48, [\chi])\) into lower level spaces

\( S_{8}^{\mathrm{old}}(48, [\chi]) \cong \)