Space of modular forms of level 850, weight 2, and Character 850.d

• Label: 850.2.d
• Level: $850$
• Weight: $2$
• Character orbit: 850.d
• Rep. character: $\chi_{850}(849,\cdot)$
• Character field: $\Q$
• Dimension: $28$
• Newform subspaces: $10$
• Sturm bound: $270$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 850 = 2 \cdot 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	850.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 85 \)
Character field:			\(\Q\)
Newform subspaces:			\( 10 \)
Sturm bound:			\(270\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(3\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(850, [\chi])\).

	Total	New	Old
Modular forms	148	28	120
Cusp forms	124	28	96
Eisenstein series	24	0	24

Trace form

\( 28 q - 28 q^{4} + 16 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(850, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
850.2.d.a	$850$	$2$	850.d	85.c	$2$	$2$	$2$	$6.787$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(-6\)	\(0\)	\(-8\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}-3q^{3}-q^{4}-3iq^{6}-4q^{7}+\cdots\)
850.2.d.b	$850$	$2$	850.d	85.c	$2$	$2$	$2$	$6.787$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}-q^{3}-q^{4}-iq^{6}-iq^{8}-2q^{9}+\cdots\)
850.2.d.c	$850$	$2$	850.d	85.c	$2$	$2$	$2$	$6.787$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(-2\)	\(0\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}-q^{3}-q^{4}-iq^{6}+3q^{7}-iq^{8}+\cdots\)
850.2.d.d	$850$	$2$	850.d	85.c	$2$	$2$	$2$	$6.787$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}-q^{4}-2q^{7}-iq^{8}-3q^{9}+\cdots\)
850.2.d.e	$850$	$2$	850.d	85.c	$2$	$2$	$2$	$6.787$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}-q^{4}+2q^{7}-iq^{8}-3q^{9}+\cdots\)
850.2.d.f	$850$	$2$	850.d	85.c	$2$	$2$	$2$	$6.787$	\(\Q(\sqrt{-1}) \)	None		$2$	$1$	\(0\)	\(2\)	\(0\)	\(-6\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}+q^{3}-q^{4}+iq^{6}-3q^{7}-iq^{8}+\cdots\)
850.2.d.g	$850$	$2$	850.d	85.c	$2$	$2$	$2$	$6.787$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{2}+q^{3}-q^{4}-iq^{6}+iq^{8}-2q^{9}+\cdots\)
850.2.d.h	$850$	$2$	850.d	85.c	$2$	$2$	$2$	$6.787$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(6\)	\(0\)	\(8\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{2}+3q^{3}-q^{4}-3iq^{6}+4q^{7}+\cdots\)
850.2.d.i	$850$	$2$	850.d	85.c	$2$	$4$	$4$	$6.787$	\(\Q(\zeta_{8})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\zeta_{8}q^{2}+\zeta_{8}^{3}q^{3}-q^{4}-\zeta_{8}^{2}q^{6}+\cdots\)
850.2.d.j	$850$	$2$	850.d	85.c	$2$	$8$	$8$	$6.787$	8.0.\(\cdots\).2	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{6}q^{2}-\beta _{3}q^{3}-q^{4}-\beta _{2}q^{6}+(-\beta _{1}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(850, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(850, [\chi]) \cong \)