Space of modular forms of level 806, weight 2, and Character 806.d

• Label: 806.2.d
• Level: $806$
• Weight: $2$
• Character orbit: 806.d
• Rep. character: $\chi_{806}(311,\cdot)$
• Character field: $\Q$
• Dimension: $36$
• Newform subspaces: $4$
• Sturm bound: $224$
• Trace bound: $14$

Defining parameters

Level:	\( N \)	\(=\)	\( 806 = 2 \cdot 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	806.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 13 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(224\)
Trace bound:			\(14\)
Distinguishing \(T_p\):			\(3\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(806, [\chi])\).

	Total	New	Old
Modular forms	116	36	80
Cusp forms	108	36	72
Eisenstein series	8	0	8

Trace form

\( 36 q - 36 q^{4} + 56 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(806, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
806.2.d.a	$806$	$2$	806.d	13.b	$2$	$2$	$2$	$6.436$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{2}-q^{3}-q^{4}-iq^{5}+iq^{6}-iq^{7}+\cdots\)
806.2.d.b	$806$	$2$	806.d	13.b	$2$	$2$	$2$	$6.436$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{2}-q^{3}-q^{4}-iq^{5}+iq^{6}+5iq^{7}+\cdots\)
806.2.d.c	$806$	$2$	806.d	13.b	$2$	$10$	$10$	$6.436$	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	None		$2$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{3}q^{2}+\beta _{1}q^{3}-q^{4}-\beta _{6}q^{5}+\beta _{9}q^{6}+\cdots\)
806.2.d.d	$806$	$2$	806.d	13.b	$2$	$22$	$22$	$6.436$		None		$2$	$0$	\(0\)	\(6\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{2}^{\mathrm{old}}(806, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(806, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(26, [\chi])\)\(^{\oplus 2}\)