Space of modular forms of level 671, weight 2, and Character 671.i

• Label: 671.2.i
• Level: $671$
• Weight: $2$
• Character orbit: 671.i
• Rep. character: $\chi_{671}(34,\cdot)$
• Character field: $\Q(\zeta_{5})$
• Dimension: $216$
• Newform subspaces: $2$
• Sturm bound: $124$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 671 = 11 \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	671.i (of order \(5\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 61 \)
Character field:			\(\Q(\zeta_{5})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(124\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(671, [\chi])\).

	Total	New	Old
Modular forms	256	216	40
Cusp forms	240	216	24
Eisenstein series	16	0	16

Trace form

\( 216 q - 2 q^{2} - 4 q^{3} - 68 q^{4} + 8 q^{5} + 4 q^{6} + 18 q^{7} - 6 q^{8} - 50 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(671, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
671.2.i.a	$671$	$2$	671.i	61.e	$5$	$108$	$27$	$5.358$		None		$2$	$0$	\(-2\)	\(-2\)	\(4\)	\(8\)		$\mathrm{SU}(2)[C_{5}]$
671.2.i.b	$671$	$2$	671.i	61.e	$5$	$108$	$27$	$5.358$		None		$2$	$0$	\(0\)	\(-2\)	\(4\)	\(10\)		$\mathrm{SU}(2)[C_{5}]$

Decomposition of \(S_{2}^{\mathrm{old}}(671, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(671, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(61, [\chi])\)\(^{\oplus 2}\)