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

• Label: 380.2.be
• Level: $380$
• Weight: $2$
• Character orbit: 380.be
• Rep. character: $\chi_{380}(51,\cdot)$
• Character field: $\Q(\zeta_{18})$
• Dimension: $240$
• 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.be (of order \(18\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 76 \)
Character field:			\(\Q(\zeta_{18})\)
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	384	240	144
Cusp forms	336	240	96
Eisenstein series	48	0	48

Trace form

\( 240 q - 6 q^{4} + 6 q^{6} + 12 q^{9} + O(q^{10}) \)

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.be.a	$380$	$2$	380.be	76.k	$18$	$120$	$20$	$3.034$		None		$4$	$0$	\(-3\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{18}]$
380.2.be.b	$380$	$2$	380.be	76.k	$18$	$120$	$20$	$3.034$		None		$4$	$0$	\(3\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{18}]$

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

\( S_{2}^{\mathrm{old}}(380, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(76, [\chi])\)\(^{\oplus 2}\)