Space of modular forms of level 310, weight 2, and Character 310.w

• Label: 310.2.w
• Level: $310$
• Weight: $2$
• Character orbit: 310.w
• Rep. character: $\chi_{310}(3,\cdot)$
• Character field: $\Q(\zeta_{60})$
• Dimension: $256$
• Newform subspaces: $1$
• Sturm bound: $96$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 310 = 2 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	310.w (of order \(60\) and degree \(16\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 155 \)
Character field:			\(\Q(\zeta_{60})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(96\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(310, [\chi])\).

	Total	New	Old
Modular forms	832	256	576
Cusp forms	704	256	448
Eisenstein series	128	0	128

Trace form

256 * q - 24 * q^7 - 8 * q^10 + 64 * q^16 + 4 * q^20 + 32 * q^21 - 52 * q^22 + 20 * q^23 + 20 * q^25 - 180 * q^27 + 4 * q^28 + 8 * q^31 - 44 * q^33 + 48 * q^35 + 128 * q^36 - 108 * q^37 - 52 * q^38 - 32 * q^41 + 8 * q^42 - 48 * q^43 - 28 * q^45 + 40 * q^46 + 20 * q^47 + 20 * q^48 - 48 * q^50 + 16 * q^51 + 28 * q^53 - 80 * q^55 - 24 * q^57 - 20 * q^60 + 20 * q^62 - 256 * q^63 - 8 * q^65 - 56 * q^66 + 4 * q^67 - 40 * q^70 + 88 * q^71 + 32 * q^73 - 32 * q^75 - 96 * q^76 + 20 * q^77 - 112 * q^78 + 48 * q^81 + 8 * q^82 - 108 * q^83 - 120 * q^85 - 24 * q^86 + 8 * q^87 - 108 * q^88 - 32 * q^90 - 80 * q^91 - 260 * q^93 + 64 * q^95 - 88 * q^97 - 112 * q^98

Decomposition of \(S_{2}^{\mathrm{new}}(310, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
310.2.w.a	$310$	$2$	310.w	155.x	$60$	$256$	$16$	$2.475$		None		✓	✓	✓	310.2.w.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-24\)		$\mathrm{SU}(2)[C_{60}]$

Decomposition of \(S_{2}^{\mathrm{old}}(310, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(310, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(155, [\chi])\)\(^{\oplus 2}\)