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

• Label: 380.2.n
• Level: $380$
• Weight: $2$
• Character orbit: 380.n
• Rep. character: $\chi_{380}(31,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $80$
• Newform subspaces: $2$
• Sturm bound: $120$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	380.n (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 76 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(120\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(3\)

Dimensions

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

	Total	New	Old
Modular forms	128	80	48
Cusp forms	112	80	32
Eisenstein series	16	0	16

Trace form

\( 80 q + 2 q^{4} - 2 q^{6} - 44 q^{9} + O(q^{10}) \)

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.n.a	$380$	$2$	380.n	76.f	$6$	$40$	$20$	$3.034$		None		$4$	$0$	\(-3\)	\(0\)	\(20\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$
380.2.n.b	$380$	$2$	380.n	76.f	$6$	$40$	$20$	$3.034$		None		$4$	$0$	\(3\)	\(0\)	\(-20\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{2}^{\mathrm{old}}(380, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(380, [\chi]) \cong \)