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

• Label: 310.2.k
• Level: $310$
• Weight: $2$
• Character orbit: 310.k
• Rep. character: $\chi_{310}(129,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $32$
• 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.k (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 155 \)
Character field:			\(\Q(\zeta_{6})\)
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	104	32	72
Cusp forms	88	32	56
Eisenstein series	16	0	16

Trace form

32 * q - 32 * q^4 - 2 * q^5 + 4 * q^6 + 8 * q^9 - 4 * q^10 + 4 * q^11 + 8 * q^15 + 32 * q^16 - 8 * q^19 + 2 * q^20 + 16 * q^21 - 4 * q^24 + 22 * q^25 + 12 * q^26 - 8 * q^29 + 28 * q^30 + 12 * q^31 - 12 * q^34 - 32 * q^35 - 8 * q^36 - 64 * q^39 + 4 * q^40 - 16 * q^41 - 4 * q^44 - 24 * q^45 - 8 * q^46 + 20 * q^49 - 40 * q^51 + 8 * q^54 - 8 * q^55 + 16 * q^59 - 8 * q^60 - 40 * q^61 - 32 * q^64 - 6 * q^65 - 24 * q^66 + 36 * q^69 + 36 * q^70 + 48 * q^71 - 28 * q^74 + 8 * q^75 + 8 * q^76 + 4 * q^79 - 2 * q^80 - 32 * q^81 - 16 * q^84 - 84 * q^85 + 12 * q^86 + 72 * q^89 + 40 * q^90 + 24 * q^91 + 16 * q^94 - 48 * q^95 + 4 * q^96 + 64 * q^99

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.k.a	$310$	$2$	310.k	155.j	$6$	$32$	$16$	$2.475$		None		✓	✓	✓	310.2.k.a	$4$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$

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

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