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

• Label: 380.2.y
• Level: $380$
• Weight: $2$
• Character orbit: 380.y
• Rep. character: $\chi_{380}(217,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $40$
• 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.y (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 95 \)
Character field:			\(\Q(\zeta_{12})\)
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	264	40	224
Cusp forms	216	40	176
Eisenstein series	48	0	48

Trace form

\( 40 q - 2 q^{5} - 4 q^{7} + O(q^{10}) \)

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.y.a	$380$	$2$	380.y	95.l	$12$	$4$	$1$	$3.034$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(6\)	\(2\)	\(-8\)	$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+(1+\zeta_{12}+\zeta_{12}^{2}-2\zeta_{12}^{3})q^{3}+(1+\cdots)q^{5}+\cdots\)
380.2.y.b	$380$	$2$	380.y	95.l	$12$	$36$	$9$	$3.034$		None		$4$	$0$	\(0\)	\(-6\)	\(-4\)	\(4\)		$\mathrm{SU}(2)[C_{12}]$

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

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