Space of modular forms of level 93, weight 3, and Character 93.j

• Label: 93.3.j
• Level: $93$
• Weight: $3$
• Character orbit: 93.j
• Rep. character: $\chi_{93}(46,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $40$
• Newform subspaces: $1$
• Sturm bound: $32$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 93 = 3 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	93.j (of order \(10\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 31 \)
Character field:			\(\Q(\zeta_{10})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(32\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(93, [\chi])\).

	Total	New	Old
Modular forms	96	40	56
Cusp forms	80	40	40
Eisenstein series	16	0	16

Trace form

40 * q - 20 * q^4 - 4 * q^7 - 6 * q^8 + 30 * q^9 - 18 * q^10 + 10 * q^11 - 30 * q^13 + 10 * q^14 + 84 * q^16 - 80 * q^17 - 36 * q^19 + 68 * q^20 + 120 * q^21 - 230 * q^22 - 70 * q^23 - 120 * q^24 + 136 * q^25 - 54 * q^28 - 20 * q^29 - 172 * q^31 - 124 * q^32 + 90 * q^33 + 440 * q^34 + 88 * q^35 - 180 * q^36 + 210 * q^38 - 12 * q^39 + 452 * q^40 + 58 * q^41 + 120 * q^42 - 90 * q^43 - 440 * q^44 + 230 * q^46 + 20 * q^47 - 546 * q^49 - 452 * q^50 + 6 * q^51 + 60 * q^52 + 60 * q^53 - 90 * q^54 - 440 * q^55 - 36 * q^56 - 250 * q^58 + 64 * q^59 + 150 * q^60 + 242 * q^62 - 48 * q^63 + 674 * q^64 - 20 * q^65 + 96 * q^66 - 184 * q^67 - 144 * q^69 + 150 * q^70 + 748 * q^71 + 18 * q^72 + 130 * q^73 - 60 * q^74 - 60 * q^75 + 114 * q^76 + 1080 * q^77 + 204 * q^78 - 590 * q^79 - 350 * q^80 - 90 * q^81 + 202 * q^82 - 180 * q^84 - 480 * q^85 - 280 * q^86 - 96 * q^87 + 30 * q^89 + 54 * q^90 + 240 * q^91 - 288 * q^93 - 308 * q^94 + 458 * q^95 + 810 * q^96 + 762 * q^97 + 660 * q^98

Decomposition of \(S_{3}^{\mathrm{new}}(93, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
93.3.j.a	$93$	$3$	93.j	31.f	$10$	$40$	$10$	$2.534$		None		✓	✓	✓	93.3.j.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)		$\mathrm{SU}(2)[C_{10}]$

Decomposition of \(S_{3}^{\mathrm{old}}(93, [\chi])\) into lower level spaces

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