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

• Label: 380.2.l
• Level: $380$
• Weight: $2$
• Character orbit: 380.l
• Rep. character: $\chi_{380}(37,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $20$
• 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.l (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 95 \)
Character field:			\(\Q(i)\)
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	132	20	112
Cusp forms	108	20	88
Eisenstein series	24	0	24

Trace form

\( 20 q + 2 q^{5} - 2 q^{7} + O(q^{10}) \)

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.l.a	$380$	$2$	380.l	95.g	$4$	$8$	$4$	$3.034$	8.0.2702336256.1	\(\Q(\sqrt{-19}) \)		$4$	$0$	\(0\)	\(0\)	\(-2\)	\(-6\)	$2^{2}\cdot 5$	$\mathrm{U}(1)[D_{4}]$	\(q+\beta _{6}q^{5}+(-1+\beta _{3}+\beta _{5}-\beta _{6}+\beta _{7})q^{7}+\cdots\)
380.2.l.b	$380$	$2$	380.l	95.g	$4$	$12$	$6$	$3.034$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(4\)	\(4\)	$2^{6}$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{2}q^{3}+(\beta _{3}-\beta _{8})q^{5}+\beta _{6}q^{7}+(\beta _{3}+\cdots)q^{9}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(380, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(95, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(190, [\chi])\)\(^{\oplus 2}\)