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

• Label: 385.2.h
• Level: $385$
• Weight: $2$
• Character orbit: 385.h
• Rep. character: $\chi_{385}(384,\cdot)$
• Character field: $\Q$
• Dimension: $44$
• Newform subspaces: $3$
• Sturm bound: $96$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 385 = 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	385.h (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 385 \)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(96\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

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

	Total	New	Old
Modular forms	52	52	0
Cusp forms	44	44	0
Eisenstein series	8	8	0

Trace form

\( 44 q + 32 q^{4} + 24 q^{9} + O(q^{10}) \)

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.h.a	$385$	$2$	385.h	385.h	$2$	$4$	$4$	$3.074$	\(\Q(\sqrt{5}, \sqrt{-7})\)	\(\Q(\sqrt{-35}) \)		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{U}(1)[D_{2}]$	\(q+(\beta _{1}+\beta _{3})q^{3}-2q^{4}+(\beta _{1}+\beta _{3})q^{5}+\cdots\)
385.2.h.b	$385$	$2$	385.h	385.h	$2$	$8$	$8$	$3.074$	8.0.\(\cdots\).19	\(\Q(\sqrt{-55}) \)		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta _{6}q^{2}+(2+\beta _{5})q^{4}+\beta _{1}q^{5}-\beta _{2}q^{7}+\cdots\)
385.2.h.c	$385$	$2$	385.h	385.h	$2$	$32$	$32$	$3.074$		None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$