Space of modular forms of level 350, weight 2, and Character 350.x

• Label: 350.2.x
• Level: $350$
• Weight: $2$
• Character orbit: 350.x
• Rep. character: $\chi_{350}(3,\cdot)$
• Character field: $\Q(\zeta_{60})$
• Dimension: $320$
• Newform subspaces: $1$
• Sturm bound: $120$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 350 = 2 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	350.x (of order \(60\) and degree \(16\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 175 \)
Character field:			\(\Q(\zeta_{60})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(120\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(350, [\chi])\).

	Total	New	Old
Modular forms	1024	320	704
Cusp forms	896	320	576
Eisenstein series	128	0	128

Trace form

320 * q + 12 * q^5 - 8 * q^7 + 12 * q^10 - 16 * q^15 - 40 * q^16 + 36 * q^17 + 8 * q^18 - 72 * q^22 + 44 * q^23 - 12 * q^25 - 24 * q^28 - 80 * q^29 + 20 * q^30 - 48 * q^33 - 28 * q^35 + 80 * q^36 - 4 * q^37 - 24 * q^38 - 40 * q^39 - 36 * q^42 + 88 * q^43 - 228 * q^45 - 12 * q^47 + 32 * q^50 - 52 * q^53 + 152 * q^57 + 32 * q^58 - 120 * q^59 - 8 * q^60 + 136 * q^63 + 8 * q^65 - 32 * q^67 - 144 * q^68 + 92 * q^70 + 8 * q^72 + 12 * q^73 - 432 * q^75 + 144 * q^77 - 16 * q^78 + 12 * q^80 - 40 * q^81 - 192 * q^82 + 60 * q^84 - 24 * q^85 + 24 * q^87 + 4 * q^88 - 300 * q^89 - 8 * q^92 - 68 * q^93 + 20 * q^95 - 40 * q^98

Decomposition of \(S_{2}^{\mathrm{new}}(350, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
350.2.x.a	$350$	$2$	350.x	175.x	$60$	$320$	$20$	$2.795$		None		✓	✓	✓	350.2.x.a	$4$	$0$	\(0\)	\(0\)	\(12\)	\(-8\)		$\mathrm{SU}(2)[C_{60}]$

Decomposition of \(S_{2}^{\mathrm{old}}(350, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(350, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(175, [\chi])\)\(^{\oplus 2}\)