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

• Label: 845.2.t
• Level: $845$
• Weight: $2$
• Character orbit: 845.t
• Rep. character: $\chi_{845}(188,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $268$
• 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.t (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 65 \)
Character field:			\(\Q(\zeta_{12})\)
Newform subspaces:			\( 9 \)
Sturm bound:			\(182\)
Trace bound:			\(6\)
Distinguishing \(T_p\):			\(2\), \(3\), \(7\)

Dimensions

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

	Total	New	Old
Modular forms	420	348	72
Cusp forms	308	268	40
Eisenstein series	112	80	32

Trace form

\( 268 q + 6 q^{2} + 2 q^{3} + 114 q^{4} + 8 q^{6} + 2 q^{7} - 12 q^{9} + O(q^{10}) \)

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
845.2.t.a	$845$	$2$	845.t	65.t	$12$	$4$	$1$	$6.747$	\(\Q(\zeta_{12})\)	None					65.2.f.a	$4$	$0$	\(0\)	\(-2\)	\(-8\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+(-\zeta_{12}+\zeta_{12}^{3})q^{2}+(\zeta_{12}-\zeta_{12}^{2}+\cdots)q^{3}+\cdots\)
845.2.t.b	$845$	$2$	845.t	65.t	$12$	$4$	$1$	$6.747$	\(\Q(\zeta_{12})\)	None					65.2.f.a	$4$	$0$	\(0\)	\(-2\)	\(8\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+(\zeta_{12}-\zeta_{12}^{3})q^{2}+(\zeta_{12}-\zeta_{12}^{2}-\zeta_{12}^{3})q^{3}+\cdots\)
845.2.t.c	$845$	$2$	845.t	65.t	$12$	$16$	$4$	$6.747$	16.0.\(\cdots\).1	None					65.2.f.b	$4$	$0$	\(0\)	\(6\)	\(-4\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{12}]$	\(q+(\beta _{5}+\beta _{6}-\beta _{8}+\beta _{9})q^{2}+(1+\beta _{2}+\cdots)q^{3}+\cdots\)
845.2.t.d	$845$	$2$	845.t	65.t	$12$	$16$	$4$	$6.747$	16.0.\(\cdots\).1	None					65.2.f.b	$4$	$0$	\(0\)	\(6\)	\(4\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{12}]$	\(q+(\beta _{5}+\beta _{6}-\beta _{8}+\beta _{9})q^{2}+(1+\beta _{4}+\cdots)q^{3}+\cdots\)
845.2.t.e	$845$	$2$	845.t	65.t	$12$	$20$	$5$	$6.747$	\(\mathbb{Q}[x]/(x^{20} + \cdots)\)	None					65.2.o.a	$2$	$0$	\(-6\)	\(-2\)	\(0\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+\beta _{1}q^{2}+(\beta _{2}+\beta _{4}+\beta _{8}-\beta _{12}-\beta _{14}+\cdots)q^{3}+\cdots\)
845.2.t.f	$845$	$2$	845.t	65.t	$12$	$20$	$5$	$6.747$	\(\mathbb{Q}[x]/(x^{20} + \cdots)\)	None					65.2.o.a	$2$	$0$	\(6\)	\(-2\)	\(0\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+\beta _{2}q^{2}+(\beta _{1}+\beta _{2}-\beta _{3}+\beta _{4}-\beta _{6}+\cdots)q^{3}+\cdots\)
845.2.t.g	$845$	$2$	845.t	65.t	$12$	$20$	$5$	$6.747$	\(\mathbb{Q}[x]/(x^{20} + \cdots)\)	None					65.2.o.a	$2$	$0$	\(6\)	\(-2\)	\(0\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+\beta _{2}q^{2}+(-\beta _{2}-\beta _{4}-\beta _{8}+\beta _{12}+\cdots)q^{3}+\cdots\)
845.2.t.h	$845$	$2$	845.t	65.t	$12$	$24$	$6$	$6.747$		None		✓			845.2.f.c	$8$	$0$	\(0\)	\(-4\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{12}]$
845.2.t.i	$845$	$2$	845.t	65.t	$12$	$144$	$36$	$6.747$		None		✓	✓		845.2.f.f	$8$	$0$	\(0\)	\(4\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{12}]$

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

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