Space of modular forms of level 1380, weight 4, and Character 1380.f

• Label: 1380.4.f
• Level: $1380$
• Weight: $4$
• Character orbit: 1380.f
• Rep. character: $\chi_{1380}(829,\cdot)$
• Character field: $\Q$
• Dimension: $68$
• Newform subspaces: $2$
• Sturm bound: $1152$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 1380 = 2^{2} \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1380.f (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(1152\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1380, [\chi])\).

	Total	New	Old
Modular forms	876	68	808
Cusp forms	852	68	784
Eisenstein series	24	0	24

Trace form

\( 68 q + 24 q^{5} - 612 q^{9} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(1380, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1380.4.f.a	$1380$	$4$	1380.f	5.b	$2$	$30$	$30$	$81.423$		None		$2$	$0$	\(0\)	\(0\)	\(12\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$
1380.4.f.b	$1380$	$4$	1380.f	5.b	$2$	$38$	$38$	$81.423$		None		$2$	$0$	\(0\)	\(0\)	\(12\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{4}^{\mathrm{old}}(1380, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1380, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(10, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 4}\)