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

• Label: 861.2.bc
• Level: $861$
• Weight: $2$
• Character orbit: 861.bc
• Rep. character: $\chi_{861}(146,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $432$
• Newform subspaces: $1$
• Sturm bound: $224$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 861 = 3 \cdot 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	861.bc (of order \(10\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 861 \)
Character field:			\(\Q(\zeta_{10})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(224\)
Trace bound:			\(0\)

Dimensions

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

	Total	New	Old
Modular forms	464	464	0
Cusp forms	432	432	0
Eisenstein series	32	32	0

Trace form

\( 432 q + 92 q^{4} - 10 q^{7} - 24 q^{9} + O(q^{10}) \)

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.bc.a	$861$	$2$	861.bc	861.ac	$10$	$432$	$108$	$6.875$		None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(-10\)		$\mathrm{SU}(2)[C_{10}]$