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

• Label: 850.2.y
• Level: $850$
• Weight: $2$
• Character orbit: 850.y
• Rep. character: $\chi_{850}(21,\cdot)$
• Character field: $\Q(\zeta_{20})$
• Dimension: $368$
• Newform subspaces: $2$
• Sturm bound: $270$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 850 = 2 \cdot 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	850.y (of order \(20\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 425 \)
Character field:			\(\Q(\zeta_{20})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(270\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

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

	Total	New	Old
Modular forms	1104	368	736
Cusp forms	1040	368	672
Eisenstein series	64	0	64

Trace form

368 * q + 92 * q^4 - 2 * q^5 + 8 * q^7 - 6 * q^10 + 12 * q^11 + 16 * q^13 - 92 * q^16 + 4 * q^17 - 80 * q^18 + 12 * q^20 - 32 * q^21 - 24 * q^22 - 12 * q^23 - 60 * q^27 - 8 * q^28 - 12 * q^29 + 24 * q^33 - 16 * q^35 - 34 * q^37 + 16 * q^38 + 6 * q^40 - 12 * q^41 + 8 * q^44 + 18 * q^45 + 24 * q^46 + 120 * q^47 - 8 * q^50 - 16 * q^52 + 8 * q^55 - 32 * q^57 + 28 * q^58 - 36 * q^61 + 36 * q^62 - 28 * q^63 + 92 * q^64 - 50 * q^65 - 112 * q^67 - 4 * q^68 - 48 * q^69 - 4 * q^71 - 20 * q^72 - 52 * q^73 - 28 * q^74 + 148 * q^75 - 32 * q^78 + 48 * q^79 - 2 * q^80 + 124 * q^81 - 164 * q^82 - 88 * q^84 + 70 * q^85 - 40 * q^86 - 16 * q^88 - 50 * q^90 - 104 * q^91 - 8 * q^92 - 32 * q^95 - 44 * q^97 - 20 * q^98 - 40 * 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.y.a	$850$	$2$	850.y	425.ab	$20$	$176$	$22$	$6.787$		None		✓			850.2.y.a	$4$	$0$	\(0\)	\(0\)	\(-4\)	\(4\)		$\mathrm{SU}(2)[C_{20}]$
850.2.y.b	$850$	$2$	850.y	425.ab	$20$	$192$	$24$	$6.787$		None		✓	✓		850.2.y.b	$4$	$0$	\(0\)	\(0\)	\(2\)	\(4\)		$\mathrm{SU}(2)[C_{20}]$

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

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