Space of modular forms of level 48, weight 3, and Character 48.e

• Label: 48.3.e
• Level: $48$
• Weight: $3$
• Character orbit: 48.e
• Rep. character: $\chi_{48}(17,\cdot)$
• Character field: $\Q$
• Dimension: $3$
• Newform subspaces: $2$
• Sturm bound: $24$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 48 = 2^{4} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	48.e (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 3 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(24\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(48, [\chi])\).

	Total	New	Old
Modular forms	22	5	17
Cusp forms	10	3	7
Eisenstein series	12	2	10

Trace form

\( 3 q + q^{3} + 10 q^{7} - 5 q^{9} + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(48, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
48.3.e.a	$48$	$3$	48.e	3.b	$2$	$1$	$1$	$1.308$	\(\Q\)	\(\Q(\sqrt{-3}) \)	✓	$2$	$0$	\(0\)	\(3\)	\(0\)	\(-2\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+3q^{3}-2q^{7}+9q^{9}-22q^{13}-26q^{19}+\cdots\)
48.3.e.b	$48$	$3$	48.e	3.b	$2$	$2$	$2$	$1.308$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(0\)	\(-2\)	\(0\)	\(12\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1+\beta )q^{3}+2\beta q^{5}+6q^{7}+(-7+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(48, [\chi])\) into lower level spaces

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