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

• Label: 845.2.k
• Level: $845$
• Weight: $2$
• Character orbit: 845.k
• Rep. character: $\chi_{845}(268,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $134$
• Newform subspaces: $6$
• Sturm bound: $182$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 845 = 5 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	845.k (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 65 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(182\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

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

	Total	New	Old
Modular forms	210	174	36
Cusp forms	154	134	20
Eisenstein series	56	40	16

Trace form

\( 134 q + 2 q^{2} + 4 q^{3} + 114 q^{4} + 4 q^{6} + 6 q^{8} + O(q^{10}) \)

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.k.a	$845$	$2$	845.k	65.k	$4$	$2$	$1$	$6.747$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(-2\)	\(2\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q-q^{2}+(1+i)q^{3}-q^{4}+(1+2i)q^{5}+\cdots\)
845.2.k.b	$845$	$2$	845.k	65.k	$4$	$8$	$4$	$6.747$	8.0.619810816.2	None		$2$	$0$	\(4\)	\(-6\)	\(-2\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{5}q^{2}+(-1-\beta _{2}+\beta _{3})q^{3}+(1+\beta _{4}+\cdots)q^{4}+\cdots\)
845.2.k.c	$845$	$2$	845.k	65.k	$4$	$12$	$6$	$6.747$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		$4$	$0$	\(0\)	\(4\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{10}q^{2}+\beta _{6}q^{3}-\beta _{11}q^{4}+(\beta _{1}-\beta _{9}+\cdots)q^{5}+\cdots\)
845.2.k.d	$845$	$2$	845.k	65.k	$4$	$20$	$10$	$6.747$	\(\mathbb{Q}[x]/(x^{20} + \cdots)\)	None		$2$	$0$	\(-8\)	\(4\)	\(6\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{2}q^{2}-\beta _{10}q^{3}+(-\beta _{3}+\beta _{4}+\beta _{8}+\cdots)q^{4}+\cdots\)
845.2.k.e	$845$	$2$	845.k	65.k	$4$	$20$	$10$	$6.747$	\(\mathbb{Q}[x]/(x^{20} + \cdots)\)	None		$2$	$0$	\(8\)	\(4\)	\(-6\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{2}q^{2}+\beta _{9}q^{3}+(-\beta _{3}+\beta _{4}+\beta _{8}+\cdots)q^{4}+\cdots\)
845.2.k.f	$845$	$2$	845.k	65.k	$4$	$72$	$36$	$6.747$		None		$4$	$0$	\(0\)	\(-4\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$

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

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