Space of modular forms of level 9 and weight 26

• Label: 9.26
• Level: 9
• Weight: 26
• Dimension: 58
• Nonzero newspaces: 2
• Newform subspaces: 5
• Sturm bound: 156
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 9 = 3^{2} \)
Weight:	\( k \)	=	\( 26 \)
Nonzero newspaces:			\( 2 \)
Newform subspaces:			\( 5 \)
Sturm bound:			\(156\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{26}(\Gamma_1(9))\).

	Total	New	Old
Modular forms	79	63	16
Cusp forms	71	58	13
Eisenstein series	8	5	3

Trace form

58 * q + 8145 * q^2 - 335640 * q^3 - 165608621 * q^4 + 528567372 * q^5 + 8407960119 * q^6 - 40344592000 * q^7 - 45513033750 * q^8 + 1107247155912 * q^9 - 11208997789776 * q^10 + 30897962134992 * q^11 + 21776654328900 * q^12 - 43916287514020 * q^13 + 199322239014936 * q^14 - 411307254415152 * q^15 - 341004514754801 * q^16 - 11799562433704380 * q^17 + 16742683171458900 * q^18 - 7338992206458376 * q^19 + 78742936105393860 * q^20 - 9061344856902480 * q^21 - 71190724780791225 * q^22 + 261878030121394080 * q^23 - 539698742708635179 * q^24 + 85753868082359182 * q^25 - 853812609614415468 * q^26 + 2244815908037091360 * q^27 - 3320723418915317860 * q^28 + 7994047879182590316 * q^29 - 6180151691356095096 * q^30 - 12904778214116589040 * q^31 + 7769944377505088415 * q^32 + 6844879295440307640 * q^33 - 44865547357811707179 * q^34 + 113632329818393519616 * q^35 - 202234747913227031949 * q^36 + 4237226137040882300 * q^37 + 230546255890468180275 * q^38 + 18165046500500633760 * q^39 - 739454808045022676928 * q^40 + 799616808202615570908 * q^41 - 810045233869642905870 * q^42 + 58166694755614392080 * q^43 - 153628137013688177238 * q^44 + 1510420538601874883088 * q^45 - 3555834871038095173752 * q^46 + 3209108843891957293440 * q^47 - 1962204915727265383965 * q^48 - 6374737236494954155902 * q^49 + 6621118963010788624209 * q^50 + 2082080428860125777832 * q^51 - 7950799395334801211350 * q^52 + 3897029707296920001900 * q^53 - 7730938792096003258119 * q^54 + 19880761052623959087696 * q^55 - 24139028465082732101490 * q^56 - 12978619220310720341640 * q^57 + 54590903548106814136980 * q^58 - 10372977213698045757888 * q^59 + 11349211438365362976708 * q^60 - 19957326612251537777332 * q^61 - 25897372382398545180 * q^62 - 11134480408245484495920 * q^63 + 221597896921760731083970 * q^64 - 33962377706326822728024 * q^65 - 102891096761697746859078 * q^66 - 49661666196316254521440 * q^67 - 107527931405889258310785 * q^68 + 260240669263018032997248 * q^69 + 530988770471850935308386 * q^70 - 903207284715438643444848 * q^71 - 142928938327501523856645 * q^72 + 210578805003733322492420 * q^73 + 1153322249441487095045484 * q^74 - 1238796883078188815944632 * q^75 - 2593136794108544507023171 * q^76 + 1792830050150046377150880 * q^77 + 4418391944477821188586230 * q^78 - 1613510944766974147203040 * q^79 - 1783196392981657155291072 * q^80 - 2284960422274645165030728 * q^81 + 2582212655823059908087830 * q^82 + 3402740137126123205896680 * q^83 - 10698113826113438268340494 * q^84 - 3071154100304634745503672 * q^85 + 9996838278445384244533521 * q^86 + 6682205310148152051315840 * q^87 - 2403890658116755581789045 * q^88 - 23894088481822114426542876 * q^89 + 2827591278614830928476908 * q^90 + 4216389071070157164641536 * q^91 + 30542621240302452256769010 * q^92 - 20735230897402365717993120 * q^93 - 19559568886829464701938544 * q^94 + 17147970288935508252505824 * q^95 + 84563965218716865427897152 * q^96 - 11139980556317273059979380 * q^97 - 125972252395240060387961280 * q^98 - 20822691689608762075940496 * q^99

Decomposition of \(S_{26}^{\mathrm{new}}(\Gamma_1(9))\)

We only show spaces with even parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list available newforms together with their dimension.

Label	\(\chi\)	Newforms	Dimension	\(\chi\) degree
9.26.a	\(\chi_{9}(1, \cdot)\)	9.26.a.a	1	1
		9.26.a.b	2
		9.26.a.c	3
		9.26.a.d	4
9.26.c	\(\chi_{9}(4, \cdot)\)	9.26.c.a	48	2

Decomposition of \(S_{26}^{\mathrm{old}}(\Gamma_1(9))\) into lower level spaces

\( S_{26}^{\mathrm{old}}(\Gamma_1(9)) \cong \) \(S_{26}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 3}\)\(\oplus\)\(S_{26}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 2}\)