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

• Label: 845.2.n
• Level: $845$
• Weight: $2$
• Character orbit: 845.n
• Rep. character: $\chi_{845}(484,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $132$
• Newform subspaces: $9$
• Sturm bound: $182$
• Trace bound: $6$

Defining parameters

Level:	\( N \)	\(=\)	\( 845 = 5 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	845.n (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 65 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 9 \)
Sturm bound:			\(182\)
Trace bound:			\(6\)
Distinguishing \(T_p\):			\(2\), \(11\)

Dimensions

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

	Total	New	Old
Modular forms	212	172	40
Cusp forms	156	132	24
Eisenstein series	56	40	16

Trace form

\( 132 q + 56 q^{4} + 6 q^{5} + 10 q^{6} + 42 q^{9} + O(q^{10}) \)

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.n.a	$845$	$2$	845.n	65.n	$6$	$4$	$2$	$6.747$	\(\Q(\zeta_{12})\)	None		$4$	$1$	\(0\)	\(0\)	\(-8\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\zeta_{12}q^{2}-2\zeta_{12}q^{3}-\zeta_{12}^{2}q^{4}+(-2+\cdots)q^{5}+\cdots\)
845.2.n.b	$845$	$2$	845.n	65.n	$6$	$4$	$2$	$6.747$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(0\)	\(8\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\zeta_{12}q^{2}+2\zeta_{12}q^{3}-\zeta_{12}^{2}q^{4}+(2+\cdots)q^{5}+\cdots\)
845.2.n.c	$845$	$2$	845.n	65.n	$6$	$8$	$4$	$6.747$	8.0.49787136.1	None		$4$	$0$	\(-6\)	\(0\)	\(0\)	\(-12\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-1+\beta _{2}-\beta _{6})q^{2}-\beta _{3}q^{3}+(1-\beta _{2}+\cdots)q^{4}+\cdots\)
845.2.n.d	$845$	$2$	845.n	65.n	$6$	$8$	$4$	$6.747$	8.0.49787136.1	None		$4$	$0$	\(6\)	\(0\)	\(0\)	\(12\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(1-\beta _{2}+\beta _{6})q^{2}-\beta _{3}q^{3}+(1-\beta _{2}+\cdots)q^{4}+\cdots\)
845.2.n.e	$845$	$2$	845.n	65.n	$6$	$12$	$6$	$6.747$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(6\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta _{4}q^{2}+(-\beta _{4}+\beta _{11})q^{3}+(-\beta _{2}+\cdots)q^{4}+\cdots\)
845.2.n.f	$845$	$2$	845.n	65.n	$6$	$12$	$6$	$6.747$	12.0.\(\cdots\).1	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\beta _{3}+\beta _{4}-\beta _{5}-\beta _{9})q^{2}+(-\beta _{3}-\beta _{4}+\cdots)q^{3}+\cdots\)
845.2.n.g	$845$	$2$	845.n	65.n	$6$	$12$	$6$	$6.747$	12.0.\(\cdots\).1	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\beta _{3}+\beta _{4}-\beta _{5}-\beta _{9})q^{2}+(\beta _{3}+\beta _{4}+\cdots)q^{3}+\cdots\)
845.2.n.h	$845$	$2$	845.n	65.n	$6$	$36$	$18$	$6.747$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$
845.2.n.i	$845$	$2$	845.n	65.n	$6$	$36$	$18$	$6.747$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$

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

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