Properties

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

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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

\( 58 q + 8145 q^{2} - 335640 q^{3} - 165608621 q^{4} + 528567372 q^{5} + 8407960119 q^{6} - 40344592000 q^{7} - 45513033750 q^{8} + 1107247155912 q^{9} + O(q^{10}) \) \( 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} + O(q^{100}) \)

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 the 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

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