Space of modular forms of level 279, weight 3, and Character 279.v

• Label: 279.3.v
• Level: $279$
• Weight: $3$
• Character orbit: 279.v
• Rep. character: $\chi_{279}(46,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $100$
• Newform subspaces: $3$
• Sturm bound: $96$
• Trace bound: $8$

Defining parameters

Level:	\( N \)	\(=\)	\( 279 = 3^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	279.v (of order \(10\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 31 \)
Character field:			\(\Q(\zeta_{10})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(96\)
Trace bound:			\(8\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(279, [\chi])\).

	Total	New	Old
Modular forms	272	108	164
Cusp forms	240	100	140
Eisenstein series	32	8	24

Trace form

100 * q + 3 * q^2 - 51 * q^4 + 14 * q^5 - 9 * q^7 + 25 * q^8 - 60 * q^10 + 10 * q^13 - 10 * q^14 - 31 * q^16 + 45 * q^17 - 25 * q^19 + 57 * q^20 - 10 * q^22 - 5 * q^23 + 306 * q^25 + 88 * q^28 + 15 * q^29 - 67 * q^31 - 102 * q^32 - 105 * q^34 - 38 * q^35 - 218 * q^38 + 102 * q^40 + 40 * q^41 + 65 * q^43 + 60 * q^44 + 15 * q^46 + 167 * q^47 - 260 * q^49 + 496 * q^50 - 15 * q^52 - 85 * q^53 - 210 * q^55 - 28 * q^56 - 165 * q^58 + 109 * q^59 - 202 * q^62 + 99 * q^64 + 365 * q^65 + 260 * q^67 + 265 * q^70 - 281 * q^71 - 235 * q^73 + 15 * q^74 - 113 * q^76 - 760 * q^77 - 680 * q^79 - 680 * q^80 + 126 * q^82 + 50 * q^83 + 380 * q^85 - 845 * q^86 - 85 * q^89 - 120 * q^91 - 506 * q^94 + 101 * q^95 + 543 * q^97 + 340 * q^98

Decomposition of \(S_{3}^{\mathrm{new}}(279, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
279.3.v.a	$279$	$3$	279.v	31.f	$10$	$20$	$5$	$7.602$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None					31.3.f.a	$2$	$0$	\(3\)	\(0\)	\(14\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{10}]$	\(q+\beta _{10}q^{2}+(3\beta _{11}+\beta _{19})q^{4}+(2-\beta _{4}+\cdots)q^{5}+\cdots\)
279.3.v.b	$279$	$3$	279.v	31.f	$10$	$40$	$10$	$7.602$		None		✓			279.3.v.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)		$\mathrm{SU}(2)[C_{10}]$
279.3.v.c	$279$	$3$	279.v	31.f	$10$	$40$	$10$	$7.602$		None					93.3.j.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)		$\mathrm{SU}(2)[C_{10}]$

Decomposition of \(S_{3}^{\mathrm{old}}(279, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(279, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(31, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(93, [\chi])\)\(^{\oplus 2}\)