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

• Label: 48.3.i
• Level: $48$
• Weight: $3$
• Character orbit: 48.i
• Rep. character: $\chi_{48}(5,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $28$
• 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.i (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 48 \)
Character field:			\(\Q(i)\)
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	36	36	0
Cusp forms	28	28	0
Eisenstein series	8	8	0

Trace form

\( 28 q - 2 q^{3} - 4 q^{4} + 4 q^{6} + O(q^{10}) \)

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.i.a	$48$	$3$	48.i	48.i	$4$	$8$	$4$	$1.308$	8.0.629407744.1	None		$4$	$0$	\(0\)	\(4\)	\(0\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{4}q^{2}+(\beta _{1}+\beta _{2}+\beta _{3}-\beta _{4})q^{3}+\cdots\)
48.3.i.b	$48$	$3$	48.i	48.i	$4$	$20$	$10$	$1.308$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		$4$	$0$	\(0\)	\(-6\)	\(0\)	\(0\)	$2^{13}$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{15}q^{2}+\beta _{4}q^{3}+(\beta _{1}+\beta _{8}-\beta _{12}+\cdots)q^{4}+\cdots\)