Space of modular forms of level 9, weight 26, and Character 9.c

• Label: 9.26.c
• Level: $9$
• Weight: $26$
• Character orbit: 9.c
• Rep. character: $\chi_{9}(4,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $48$
• Newform subspaces: $1$
• Sturm bound: $26$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 9 = 3^{2} \)
Weight:	\( k \)	\(=\)	\( 26 \)
Character orbit:	\([\chi]\)	\(=\)	9.c (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 9 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(26\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{26}(9, [\chi])\).

	Total	New	Old
Modular forms	52	52	0
Cusp forms	48	48	0
Eisenstein series	4	4	0

Trace form

48 * q + 4095 * q^2 - 335640 * q^3 - 385875969 * q^4 + 194286528 * q^5 + 8407960119 * q^6 + 574239120 * q^7 - 333604719630 * q^8 + 1107247155912 * q^9 + 67108860 * q^10 + 15182693684712 * q^11 + 21776654328900 * q^12 + 30845059234080 * q^13 + 479129042149992 * q^14 - 411307254415152 * q^15 - 5910974544478209 * q^16 - 8135564625756720 * q^17 + 16742683171458900 * q^18 + 13878744667200240 * q^19 + 26635801757562684 * q^20 - 9061344856902480 * q^21 - 732960793309185 * q^22 + 251666092773863280 * q^23 - 539698742708635179 * q^24 - 1047666649082618904 * q^25 - 702052508042165736 * q^26 + 2244815908037091360 * q^27 - 74821270268542980 * q^28 + 5220261078588471312 * q^29 - 6180151691356095096 * q^30 - 4871733080330211600 * q^31 - 14346274527923994945 * q^32 + 6844879295440307640 * q^33 - 17649919089751817511 * q^34 + 74205726885943934976 * q^35 - 202234747913227031949 * q^36 - 14031220470666087360 * q^37 - 87993955311387889365 * q^38 + 18165046500500633760 * q^39 - 81619631915220593136 * q^40 + 18471304489307321016 * q^41 - 810045233869642905870 * q^42 + 21191123340670055640 * q^43 - 2407639037928001544934 * q^44 + 1510420538601874883088 * q^45 - 1614552401623441661640 * q^46 + 967366710540351803520 * q^47 - 1962204915727265383965 * q^48 - 4177818896069700336888 * q^49 - 2139162477396260964957 * q^50 + 2082080428860125777832 * q^51 + 2645834018601132828690 * q^52 + 3468745325709252563040 * q^53 - 7730938792096003258119 * q^54 + 5931102931014788138880 * q^55 - 6671736954115138854450 * q^56 - 12978619220310720341640 * q^57 + 15146980591398835974480 * q^58 + 34880994479740153028184 * q^59 + 11349211438365362976708 * q^60 - 12448173624138010494624 * q^61 + 75257474718885502490820 * q^62 - 11134480408245484495920 * q^63 + 113095766787720725565570 * q^64 + 103853667366020207651904 * q^65 - 102891096761697746859078 * q^66 - 11956762573729517477640 * q^67 + 280664072512591978314855 * q^68 + 260240669263018032997248 * q^69 + 191494390399606344137346 * q^70 - 712239369898260675110976 * q^71 - 142928938327501523856645 * q^72 - 255100554432640949097360 * q^73 + 627122932974024306341760 * q^74 - 1238796883078188815944632 * q^75 - 558098160899208793458771 * q^76 + 535920202928886577195680 * q^77 + 4418391944477821188586230 * q^78 - 182227576547765569432224 * q^79 - 4955870382137361308865888 * q^80 - 2284960422274645165030728 * q^81 - 73506470593885838390070 * q^82 + 1534749348551697224456400 * q^83 - 10698113826113438268340494 * q^84 + 456636154086222234954336 * q^85 + 7847551530281482122014361 * q^86 + 6682205310148152051315840 * q^87 + 535500638574266257628715 * q^88 - 26886810966882595462369728 * q^89 + 2827591278614830928476908 * q^90 - 3527798844197845716057312 * q^91 + 33002001992117379253447890 * q^92 - 20735230897402365717993120 * q^93 - 408713704573659762260304 * q^94 + 24000354674106690001359888 * q^95 + 84563965218716865427897152 * q^96 - 11572360842857754432513720 * q^97 - 87782489388760196350751490 * q^98 - 20822691689608762075940496 * q^99

Decomposition of \(S_{26}^{\mathrm{new}}(9, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
9.26.c.a	$9$	$26$	9.c	9.c	$3$	$48$	$24$	$35.640$		None		✓	✓	✓	9.26.c.a	$2$	$0$	\(4095\)	\(-335640\)	\(194286528\)	\(574239120\)		$\mathrm{SU}(2)[C_{3}]$