Space of modular forms of level 516, weight 2, and Character 516.m

• Label: 516.2.m
• Level: $516$
• Weight: $2$
• Character orbit: 516.m
• Rep. character: $\chi_{516}(7,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $88$
• Newform subspaces: $2$
• Sturm bound: $176$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 516 = 2^{2} \cdot 3 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	516.m (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 172 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(176\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(516, [\chi])\).

	Total	New	Old
Modular forms	184	88	96
Cusp forms	168	88	80
Eisenstein series	16	0	16

Trace form

88 * q - 4 * q^4 - 44 * q^9 - 4 * q^10 + 12 * q^12 + 4 * q^13 - 10 * q^14 + 4 * q^16 - 6 * q^18 + 24 * q^20 + 8 * q^21 + 44 * q^25 - 6 * q^28 + 48 * q^29 + 12 * q^30 + 24 * q^34 + 2 * q^36 + 12 * q^37 - 28 * q^38 - 4 * q^40 + 68 * q^44 - 42 * q^46 - 32 * q^49 + 84 * q^50 - 32 * q^52 + 32 * q^53 - 10 * q^56 - 24 * q^57 - 6 * q^58 + 10 * q^60 - 48 * q^62 + 32 * q^64 + 8 * q^66 + 26 * q^68 - 36 * q^73 - 52 * q^74 - 90 * q^76 - 72 * q^77 - 20 * q^78 - 30 * q^80 - 44 * q^81 - 48 * q^84 + 14 * q^86 + 8 * q^90 - 16 * q^92 - 12 * q^93 + 30 * q^96 - 64 * q^97 + 6 * q^98

Decomposition of \(S_{2}^{\mathrm{new}}(516, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
516.2.m.a	$516$	$2$	516.m	172.f	$6$	$44$	$22$	$4.120$		None		✓			516.2.m.a	$2$	$0$	\(0\)	\(-22\)	\(0\)	\(-2\)		$\mathrm{SU}(2)[C_{6}]$
516.2.m.b	$516$	$2$	516.m	172.f	$6$	$44$	$22$	$4.120$		None		✓			516.2.m.a	$2$	$0$	\(0\)	\(22\)	\(0\)	\(2\)		$\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{2}^{\mathrm{old}}(516, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(516, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(172, [\chi])\)\(^{\oplus 2}\)