Space of modular forms of level 845, weight 2, and Character 845.bg

• Label: 845.2.bg
• Level: $845$
• Weight: $2$
• Character orbit: 845.bg
• Rep. character: $\chi_{845}(36,\cdot)$
• Character field: $\Q(\zeta_{78})$
• Dimension: $1440$
• Newform subspaces: $1$
• Sturm bound: $182$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 845 = 5 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	845.bg (of order \(78\) and degree \(24\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 169 \)
Character field:			\(\Q(\zeta_{78})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(182\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(845, [\chi])\).

	Total	New	Old
Modular forms	2256	1440	816
Cusp forms	2160	1440	720
Eisenstein series	96	0	96

Trace form

\( 1440 q - 2 q^{3} - 58 q^{4} + 18 q^{6} + 6 q^{7} + 60 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(845, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
845.2.bg.a	$845$	$2$	845.bg	169.k	$78$	$1440$	$60$	$6.747$		None		$2$	$0$	\(0\)	\(-2\)	\(0\)	\(6\)		$\mathrm{SU}(2)[C_{78}]$

Decomposition of \(S_{2}^{\mathrm{old}}(845, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(845, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(169, [\chi])\)\(^{\oplus 2}\)