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

• Label: 850.2.c
• Level: $850$
• Weight: $2$
• Character orbit: 850.c
• Rep. character: $\chi_{850}(749,\cdot)$
• Character field: $\Q$
• Dimension: $24$
• Newform subspaces: $10$
• Sturm bound: $270$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 850 = 2 \cdot 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	850.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 10 \)
Sturm bound:			\(270\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(3\), \(7\), \(11\), \(13\)

Dimensions

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

	Total	New	Old
Modular forms	148	24	124
Cusp forms	124	24	100
Eisenstein series	24	0	24

Trace form

\( 24 q - 24 q^{4} + 4 q^{6} - 24 q^{9} + O(q^{10}) \)

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.c.a	$850$	$2$	850.c	5.b	$2$	$2$	$2$	$6.787$	\(\Q(\sqrt{-1}) \)	None		$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}+3iq^{3}-q^{4}-3q^{6}-2iq^{7}+\cdots\)
850.2.c.b	$850$	$2$	850.c	5.b	$2$	$2$	$2$	$6.787$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}+2iq^{3}-q^{4}-2q^{6}-4iq^{7}+\cdots\)
850.2.c.c	$850$	$2$	850.c	5.b	$2$	$2$	$2$	$6.787$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}+iq^{3}-q^{4}-q^{6}-2iq^{7}+\cdots\)
850.2.c.d	$850$	$2$	850.c	5.b	$2$	$2$	$2$	$6.787$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}+iq^{3}-q^{4}-q^{6}+5iq^{7}+\cdots\)
850.2.c.e	$850$	$2$	850.c	5.b	$2$	$2$	$2$	$6.787$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{2}+iq^{3}-q^{4}+q^{6}-2iq^{7}+\cdots\)
850.2.c.f	$850$	$2$	850.c	5.b	$2$	$2$	$2$	$6.787$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{2}+2iq^{3}-q^{4}+2q^{6}-2iq^{7}+\cdots\)
850.2.c.g	$850$	$2$	850.c	5.b	$2$	$2$	$2$	$6.787$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{2}+2iq^{3}-q^{4}+2q^{6}+2iq^{7}+\cdots\)
850.2.c.h	$850$	$2$	850.c	5.b	$2$	$2$	$2$	$6.787$	\(\Q(\sqrt{-1}) \)	None		$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{2}+3iq^{3}-q^{4}+3q^{6}-iq^{7}+\cdots\)
850.2.c.i	$850$	$2$	850.c	5.b	$2$	$4$	$4$	$6.787$	\(\Q(i, \sqrt{17})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{2}+\beta _{1}q^{3}-q^{4}+(-1+\beta _{3})q^{6}+\cdots\)
850.2.c.j	$850$	$2$	850.c	5.b	$2$	$4$	$4$	$6.787$	\(\Q(\zeta_{8})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\zeta_{8}q^{2}+(\zeta_{8}+\zeta_{8}^{2})q^{3}-q^{4}+(1+\zeta_{8}^{3})q^{6}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(850, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(85, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(170, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(425, [\chi])\)\(^{\oplus 2}\)