Space of modular forms of level 5148, weight 2, and Character 5148.ba

• Label: 5148.2.ba
• Level: $5148$
• Weight: $2$
• Character orbit: 5148.ba
• Rep. character: $\chi_{5148}(2465,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $88$
• Newform subspaces: $2$
• Sturm bound: $2016$
• Trace bound: $13$

Defining parameters

Level:	\( N \)	\(=\)	\( 5148 = 2^{2} \cdot 3^{2} \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5148.ba (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 39 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(2016\)
Trace bound:			\(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(5148, [\chi])\).

	Total	New	Old
Modular forms	2064	88	1976
Cusp forms	1968	88	1880
Eisenstein series	96	0	96

Trace form

\( 88 q + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(5148, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
5148.2.ba.a	$5148$	$2$	5148.ba	39.f	$4$	$44$	$22$	$41.107$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$
5148.2.ba.b	$5148$	$2$	5148.ba	39.f	$4$	$44$	$22$	$41.107$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$

Decomposition of \(S_{2}^{\mathrm{old}}(5148, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(5148, [\chi]) \cong \)