Space of modular forms of level 48, weight 7, and Character 48.g

• Label: 48.7.g
• Level: $48$
• Weight: $7$
• Character orbit: 48.g
• Rep. character: $\chi_{48}(31,\cdot)$
• Character field: $\Q$
• Dimension: $6$
• Newform subspaces: $3$
• Sturm bound: $56$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 48 = 2^{4} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	48.g (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 4 \)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(56\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(48, [\chi])\).

	Total	New	Old
Modular forms	54	6	48
Cusp forms	42	6	36
Eisenstein series	12	0	12

Trace form

\( 6 q + 132 q^{5} - 1458 q^{9} + O(q^{10}) \)

Decomposition of \(S_{7}^{\mathrm{new}}(48, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
48.7.g.a	$48$	$7$	48.g	4.b	$2$	$2$	$2$	$11.043$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-180\)	\(0\)	$2\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\zeta_{6}q^{3}-90q^{5}+12\zeta_{6}q^{7}-3^{5}q^{9}+\cdots\)
48.7.g.b	$48$	$7$	48.g	4.b	$2$	$2$	$2$	$11.043$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(12\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-9\zeta_{6}q^{3}+6q^{5}-116\zeta_{6}q^{7}-3^{5}q^{9}+\cdots\)
48.7.g.c	$48$	$7$	48.g	4.b	$2$	$2$	$2$	$11.043$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(300\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-9\zeta_{6}q^{3}+150q^{5}+188\zeta_{6}q^{7}-3^{5}q^{9}+\cdots\)

Decomposition of \(S_{7}^{\mathrm{old}}(48, [\chi])\) into lower level spaces

\( S_{7}^{\mathrm{old}}(48, [\chi]) \cong \) \(S_{7}^{\mathrm{new}}(4, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(8, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 2}\)