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

• Label: 805.2.c
• Level: $805$
• Weight: $2$
• Character orbit: 805.c
• Rep. character: $\chi_{805}(484,\cdot)$
• Character field: $\Q$
• Dimension: $68$
• Newform subspaces: $3$
• Sturm bound: $192$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 805 = 5 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	805.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(192\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

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

	Total	New	Old
Modular forms	100	68	32
Cusp forms	92	68	24
Eisenstein series	8	0	8

Trace form

\( 68 q - 72 q^{4} + 4 q^{5} - 72 q^{9} + O(q^{10}) \)

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.c.a	$805$	$2$	805.c	5.b	$2$	$2$	$2$	$6.428$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{3}+2q^{4}+(2-i)q^{5}+iq^{7}+2q^{9}+\cdots\)
805.2.c.b	$805$	$2$	805.c	5.b	$2$	$24$	$24$	$6.428$		None		$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$
805.2.c.c	$805$	$2$	805.c	5.b	$2$	$42$	$42$	$6.428$		None		$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

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

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