Space of modular forms of level 539, weight 2, and Character 539.r

• Label: 539.2.r
• Level: $539$
• Weight: $2$
• Character orbit: 539.r
• Rep. character: $\chi_{539}(23,\cdot)$
• Character field: $\Q(\zeta_{21})$
• Dimension: $552$
• Newform subspaces: $2$
• Sturm bound: $112$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 539 = 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	539.r (of order \(21\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 49 \)
Character field:			\(\Q(\zeta_{21})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(112\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(539, [\chi])\).

	Total	New	Old
Modular forms	696	552	144
Cusp forms	648	552	96
Eisenstein series	48	0	48

Trace form

552 * q + 2 * q^3 + 44 * q^4 + 4 * q^5 - 20 * q^6 - 2 * q^7 + 12 * q^8 + 12 * q^9 - 6 * q^10 - 76 * q^12 + 16 * q^13 - 70 * q^14 + 12 * q^15 + 36 * q^16 - 6 * q^17 - 10 * q^18 - 2 * q^19 - 40 * q^20 + 2 * q^21 + 8 * q^24 + 42 * q^25 + 10 * q^26 - 16 * q^27 - 16 * q^28 - 52 * q^29 - 32 * q^30 - 78 * q^31 - 116 * q^32 + 4 * q^33 - 108 * q^34 + 6 * q^35 - 112 * q^36 - 46 * q^37 + 8 * q^38 + 4 * q^39 - 112 * q^40 + 48 * q^41 - 8 * q^42 + 20 * q^43 - 32 * q^44 - 6 * q^45 + 126 * q^46 - 62 * q^47 + 128 * q^48 + 24 * q^49 - 188 * q^50 - 32 * q^51 + 114 * q^52 + 26 * q^53 + 142 * q^54 - 16 * q^55 - 76 * q^56 - 18 * q^57 + 22 * q^58 + 64 * q^59 - 44 * q^60 - 54 * q^61 - 20 * q^62 - 116 * q^63 - 92 * q^64 - 14 * q^65 - 72 * q^66 - 24 * q^67 - 16 * q^68 - 36 * q^69 - 158 * q^70 - 62 * q^71 - 260 * q^72 - 14 * q^73 - 12 * q^74 - 218 * q^75 - 114 * q^76 + 2 * q^77 - 54 * q^78 - 12 * q^79 - 172 * q^80 - 198 * q^81 + 38 * q^82 + 66 * q^83 - 180 * q^84 - 48 * q^85 + 130 * q^86 + 6 * q^87 - 14 * q^89 + 500 * q^90 + 118 * q^91 + 22 * q^92 + 202 * q^93 + 242 * q^94 - 44 * q^95 + 254 * q^96 + 4 * q^97 - 12 * q^98

Decomposition of \(S_{2}^{\mathrm{new}}(539, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
539.2.r.a	$539$	$2$	539.r	49.g	$21$	$276$	$23$	$4.304$		None		✓			539.2.r.a	$2$	$0$	\(0\)	\(-1\)	\(-2\)	\(-2\)		$\mathrm{SU}(2)[C_{21}]$
539.2.r.b	$539$	$2$	539.r	49.g	$21$	$276$	$23$	$4.304$		None		✓			539.2.r.b	$2$	$0$	\(0\)	\(3\)	\(6\)	\(0\)		$\mathrm{SU}(2)[C_{21}]$

Decomposition of \(S_{2}^{\mathrm{old}}(539, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(539, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 2}\)