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

• Label: 850.2.v
• Level: $850$
• Weight: $2$
• Character orbit: 850.v
• Rep. character: $\chi_{850}(107,\cdot)$
• Character field: $\Q(\zeta_{16})$
• Dimension: $216$
• Newform subspaces: $6$
• Sturm bound: $270$
• Trace bound: $13$

Defining parameters

Level:	\( N \)	\(=\)	\( 850 = 2 \cdot 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	850.v (of order \(16\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 85 \)
Character field:			\(\Q(\zeta_{16})\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(270\)
Trace bound:			\(13\)
Distinguishing \(T_p\):			\(3\)

Dimensions

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

	Total	New	Old
Modular forms	1176	216	960
Cusp forms	984	216	768
Eisenstein series	192	0	192

Trace form

216 * q - 48 * q^27 + 16 * q^28 + 64 * q^31 - 32 * q^33 - 64 * q^34 + 32 * q^37 + 128 * q^39 - 40 * q^41 + 48 * q^42 + 32 * q^52 - 32 * q^53 + 144 * q^57 - 112 * q^59 + 48 * q^62 + 48 * q^63 - 32 * q^67 - 64 * q^71 - 40 * q^72 - 120 * q^73 + 40 * q^74 - 48 * q^77 - 64 * q^78 + 64 * q^79 - 192 * q^81 - 64 * q^82 - 32 * q^83 - 64 * q^86 - 176 * q^87 - 32 * q^88 - 192 * q^91 - 16 * q^92 + 16 * q^93 + 32 * q^97 - 72 * q^98 - 192 * q^99

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
850.2.v.a	$850$	$2$	850.v	85.r	$16$	$24$	$3$	$6.787$		None		✓			850.2.s.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{16}]$
850.2.v.b	$850$	$2$	850.v	85.r	$16$	$24$	$3$	$6.787$		None		✓			850.2.s.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{16}]$
850.2.v.c	$850$	$2$	850.v	85.r	$16$	$32$	$4$	$6.787$		None					170.2.o.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{16}]$
850.2.v.d	$850$	$2$	850.v	85.r	$16$	$40$	$5$	$6.787$		None					170.2.o.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{16}]$
850.2.v.e	$850$	$2$	850.v	85.r	$16$	$48$	$6$	$6.787$		None		✓			850.2.s.e	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{16}]$
850.2.v.f	$850$	$2$	850.v	85.r	$16$	$48$	$6$	$6.787$		None		✓			850.2.s.e	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{16}]$

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

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