Space of modular forms of level 805, weight 2, and Character 805.f

• Label: 805.2.f
• Level: $805$
• Weight: $2$
• Character orbit: 805.f
• Rep. character: $\chi_{805}(321,\cdot)$
• Character field: $\Q$
• Dimension: $64$
• Newform subspaces: $2$
• Sturm bound: $192$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 805 = 5 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	805.f (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 161 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(192\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(805, [\chi])\).

	Total	New	Old
Modular forms	100	64	36
Cusp forms	92	64	28
Eisenstein series	8	0	8

Trace form

\( 64 q - 4 q^{2} + 68 q^{4} - 12 q^{8} - 56 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(805, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
805.2.f.a	$805$	$2$	805.f	161.c	$2$	$32$	$32$	$6.428$		None		$2$	$0$	\(-2\)	\(0\)	\(-32\)	\(-3\)		$\mathrm{SU}(2)[C_{2}]$
805.2.f.b	$805$	$2$	805.f	161.c	$2$	$32$	$32$	$6.428$		None		$2$	$0$	\(-2\)	\(0\)	\(32\)	\(3\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{2}^{\mathrm{old}}(805, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(805, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(161, [\chi])\)\(^{\oplus 2}\)