Space of modular forms of level 380, weight 3, and Character 380.bi

• Label: 380.3.bi
• Level: $380$
• Weight: $3$
• Character orbit: 380.bi
• Rep. character: $\chi_{380}(3,\cdot)$
• Character field: $\Q(\zeta_{36})$
• Dimension: $1392$
• Newform subspaces: $1$
• Sturm bound: $180$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	380.bi (of order \(36\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 380 \)
Character field:			\(\Q(\zeta_{36})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(180\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(380, [\chi])\).

	Total	New	Old
Modular forms	1488	1488	0
Cusp forms	1392	1392	0
Eisenstein series	96	96	0

Trace form

\( 1392 q - 12 q^{2} - 24 q^{5} + 12 q^{6} - 18 q^{8} + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(380, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
380.3.bi.a	$380$	$3$	380.bi	380.ai	$36$	$1392$	$116$	$10.354$		None		$8$	$0$	\(-12\)	\(0\)	\(-24\)	\(0\)		$\mathrm{SU}(2)[C_{36}]$