Space of modular forms of level 861, weight 2, and Character 861.d

• Label: 861.2.d
• Level: $861$
• Weight: $2$
• Character orbit: 861.d
• Rep. character: $\chi_{861}(83,\cdot)$
• Character field: $\Q$
• Dimension: $108$
• Newform subspaces: $4$
• Sturm bound: $224$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 861 = 3 \cdot 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	861.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 21 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(224\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(2\), \(5\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(861, [\chi])\).

	Total	New	Old
Modular forms	116	108	8
Cusp forms	108	108	0
Eisenstein series	8	0	8

Trace form

\( 108 q - 112 q^{4} - 4 q^{7} + 4 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(861, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
861.2.d.a	$861$	$2$	861.d	21.c	$2$	$4$	$4$	$6.875$	\(\Q(\sqrt{-2}, \sqrt{3})\)	None		$2$	$0$	\(0\)	\(-4\)	\(0\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(-1-\beta _{1}+\beta _{3})q^{3}+\beta _{2}q^{4}+\cdots\)
861.2.d.b	$861$	$2$	861.d	21.c	$2$	$4$	$4$	$6.875$	\(\Q(\sqrt{-2}, \sqrt{3})\)	None		$2$	$0$	\(0\)	\(4\)	\(0\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(1+\beta _{1}-\beta _{3})q^{3}+\beta _{2}q^{4}+\cdots\)
861.2.d.c	$861$	$2$	861.d	21.c	$2$	$50$	$50$	$6.875$		None		$2$	$0$	\(0\)	\(-4\)	\(0\)	\(-6\)		$\mathrm{SU}(2)[C_{2}]$
861.2.d.d	$861$	$2$	861.d	21.c	$2$	$50$	$50$	$6.875$		None		$2$	$0$	\(0\)	\(4\)	\(0\)	\(-6\)		$\mathrm{SU}(2)[C_{2}]$