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

• Label: 845.2.c
• Level: $845$
• Weight: $2$
• Character orbit: 845.c
• Rep. character: $\chi_{845}(506,\cdot)$
• Character field: $\Q$
• Dimension: $50$
• Newform subspaces: $8$
• Sturm bound: $182$
• Trace bound: $4$

Defining parameters

Level:	\( N \)	\(=\)	\( 845 = 5 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	845.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 13 \)
Character field:			\(\Q\)
Newform subspaces:			\( 8 \)
Sturm bound:			\(182\)
Trace bound:			\(4\)
Distinguishing \(T_p\):			\(2\)

Dimensions

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

	Total	New	Old
Modular forms	106	50	56
Cusp forms	78	50	28
Eisenstein series	28	0	28

Trace form

\( 50 q + 4 q^{3} - 46 q^{4} + 50 q^{9} + O(q^{10}) \)

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.c.a	$845$	$2$	845.c	13.b	$2$	$2$	$2$	$6.747$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(-4\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}-2q^{3}+q^{4}+iq^{5}-2iq^{6}+\cdots\)
845.2.c.b	$845$	$2$	845.c	13.b	$2$	$4$	$4$	$6.747$	\(\Q(\zeta_{8})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\zeta_{8}+\zeta_{8}^{2})q^{2}-\zeta_{8}^{3}q^{3}+(-1-2\zeta_{8}^{3})q^{4}+\cdots\)
845.2.c.c	$845$	$2$	845.c	13.b	$2$	$4$	$4$	$6.747$	\(\Q(i, \sqrt{5})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(1+2\beta _{2})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
845.2.c.d	$845$	$2$	845.c	13.b	$2$	$4$	$4$	$6.747$	\(\Q(i, \sqrt{13})\)	None		$2$	$0$	\(0\)	\(4\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+q^{3}+(-2+\beta _{3})q^{4}-\beta _{2}q^{5}+\cdots\)
845.2.c.e	$845$	$2$	845.c	13.b	$2$	$4$	$4$	$6.747$	\(\Q(\zeta_{12})\)	None		$2$	$0$	\(0\)	\(4\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\zeta_{12}^{2}q^{2}+(1-\zeta_{12}^{3})q^{3}-q^{4}+\zeta_{12}q^{5}+\cdots\)
845.2.c.f	$845$	$2$	845.c	13.b	$2$	$6$	$6$	$6.747$	6.0.153664.1	None		$2$	$0$	\(0\)	\(-10\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(-1-\beta _{2}-\beta _{4})q^{3}+\beta _{2}q^{4}+\cdots\)
845.2.c.g	$845$	$2$	845.c	13.b	$2$	$8$	$8$	$6.747$	8.0.22581504.2	None		$2$	$0$	\(0\)	\(-4\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(-1-\beta _{3})q^{3}+(-1+\beta _{2}+\cdots)q^{4}+\cdots\)
845.2.c.h	$845$	$2$	845.c	13.b	$2$	$18$	$18$	$6.747$	\(\mathbb{Q}[x]/(x^{18} + \cdots)\)	None		$2$	$0$	\(0\)	\(14\)	\(0\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\beta _{1}+\beta _{6})q^{2}+(1+\beta _{11})q^{3}+(-2+\cdots)q^{4}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(845, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(65, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(169, [\chi])\)\(^{\oplus 2}\)