Space of modular forms of level 385, weight 2, and Character 385.j

• Label: 385.2.j
• Level: $385$
• Weight: $2$
• Character orbit: 385.j
• Rep. character: $\chi_{385}(188,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $80$
• Newform subspaces: $4$
• Sturm bound: $96$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 385 = 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	385.j (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 35 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(96\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(2\), \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(385, [\chi])\).

	Total	New	Old
Modular forms	104	80	24
Cusp forms	88	80	8
Eisenstein series	16	0	16

Trace form

\( 80 q + 24 q^{8} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(385, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
385.2.j.a	$385$	$2$	385.j	35.f	$4$	$4$	$2$	$3.074$	\(\Q(\zeta_{12})\)	None		$2$	$1$	\(-4\)	\(-6\)	\(-2\)	\(-8\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-1-\zeta_{12}^{3})q^{2}+(-1-\zeta_{12}-\zeta_{12}^{2}+\cdots)q^{3}+\cdots\)
385.2.j.b	$385$	$2$	385.j	35.f	$4$	$4$	$2$	$3.074$	\(\Q(\zeta_{12})\)	None		$2$	$0$	\(-4\)	\(6\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-1+\zeta_{12}^{3})q^{2}+(1-\zeta_{12}+\zeta_{12}^{2}+\cdots)q^{3}+\cdots\)
385.2.j.c	$385$	$2$	385.j	35.f	$4$	$32$	$16$	$3.074$		None		$4$	$0$	\(8\)	\(0\)	\(0\)	\(8\)		$\mathrm{SU}(2)[C_{4}]$
385.2.j.d	$385$	$2$	385.j	35.f	$4$	$40$	$20$	$3.074$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$

Decomposition of \(S_{2}^{\mathrm{old}}(385, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(385, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 2}\)