Space of modular forms of level 946, weight 2, and Character 946.h

• Label: 946.2.h
• Level: $946$
• Weight: $2$
• Character orbit: 946.h
• Rep. character: $\chi_{946}(351,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $88$
• Newform subspaces: $6$
• Sturm bound: $264$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 946 = 2 \cdot 11 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	946.h (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 473 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(264\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(946, [\chi])\).

	Total	New	Old
Modular forms	272	88	184
Cusp forms	256	88	168
Eisenstein series	16	0	16

Trace form

\( 88 q + 88 q^{4} + 40 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(946, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
946.2.h.a	$946$	$2$	946.h	473.i	$6$	$4$	$2$	$7.554$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	None		$2$	$1$	\(-4\)	\(-6\)	\(-6\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q-q^{2}+(-2+\beta _{1}+\beta _{2}-\beta _{3})q^{3}+q^{4}+\cdots\)
946.2.h.b	$946$	$2$	946.h	473.i	$6$	$4$	$2$	$7.554$	\(\Q(\sqrt{-3}, \sqrt{-11})\)	None		$2$	$0$	\(-4\)	\(3\)	\(-3\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q-q^{2}+(1-\beta _{1})q^{3}+q^{4}+(-1+\beta _{1}+\cdots)q^{5}+\cdots\)
946.2.h.c	$946$	$2$	946.h	473.i	$6$	$4$	$2$	$7.554$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	None		$2$	$1$	\(4\)	\(-6\)	\(-6\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+q^{2}+(-2+\beta _{1}+\beta _{2}-\beta _{3})q^{3}+q^{4}+\cdots\)
946.2.h.d	$946$	$2$	946.h	473.i	$6$	$4$	$2$	$7.554$	\(\Q(\sqrt{-3}, \sqrt{-11})\)	None		$2$	$0$	\(4\)	\(3\)	\(-3\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+q^{2}+(1-\beta _{1})q^{3}+q^{4}+(-1+\beta _{1}+\cdots)q^{5}+\cdots\)
946.2.h.e	$946$	$2$	946.h	473.i	$6$	$36$	$18$	$7.554$		None		$2$	$0$	\(-36\)	\(3\)	\(9\)	\(-3\)		$\mathrm{SU}(2)[C_{6}]$
946.2.h.f	$946$	$2$	946.h	473.i	$6$	$36$	$18$	$7.554$		None		$2$	$0$	\(36\)	\(3\)	\(9\)	\(3\)		$\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{2}^{\mathrm{old}}(946, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(946, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(473, [\chi])\)\(^{\oplus 2}\)