Space of modular forms of level 380, weight 2, and Character 380.d

• Label: 380.2.d
• Level: $380$
• Weight: $2$
• Character orbit: 380.d
• Rep. character: $\chi_{380}(379,\cdot)$
• Character field: $\Q$
• Dimension: $56$
• Newform subspaces: $2$
• Sturm bound: $120$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	380.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 380 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(120\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(380, [\chi])\).

	Total	New	Old
Modular forms	64	64	0
Cusp forms	56	56	0
Eisenstein series	8	8	0

Trace form

\( 56 q - 4 q^{5} + 8 q^{6} - 56 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(380, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
380.2.d.a	$380$	$2$	380.d	380.d	$2$	$16$	$16$	$3.034$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	\(\Q(\sqrt{-95}) \)		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{11}$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta _{1}q^{2}-\beta _{5}q^{3}+\beta _{2}q^{4}-\beta _{6}q^{5}+\cdots\)
380.2.d.b	$380$	$2$	380.d	380.d	$2$	$40$	$40$	$3.034$		None		$8$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$