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Properties

Label 9.38
Level 9
Weight 38
Dimension 87
Nonzero newspaces 2
Newform subspaces 5
Sturm bound 228
Trace bound 1

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Defining parameters

Level: \( N \) = \( 9 = 3^{2} \)
Weight: \( k \) = \( 38 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 5 \)
Sturm bound: \(228\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{38}(\Gamma_1(9))\).

Total New Old
Modular forms 115 92 23
Cusp forms 107 87 20
Eisenstein series 8 5 3

Trace form

\( 87 q + 329889 q^{2} - 401411892 q^{3} - 1619750875629 q^{4} + 18308365618722 q^{5} + 392737738672791 q^{6} + 2742373845211008 q^{7} - 154197865950929238 q^{8} - 160987063735768212 q^{9} + O(q^{10}) \) \( 87 q + 329889 q^{2} - 401411892 q^{3} - 1619750875629 q^{4} + 18308365618722 q^{5} + 392737738672791 q^{6} + 2742373845211008 q^{7} - 154197865950929238 q^{8} - 160987063735768212 q^{9} + 701811086045477904 q^{10} + 11545997776285928088 q^{11} + 205931182443362228004 q^{12} - 103319493076660821414 q^{13} + 3067223294721143275944 q^{14} + 21425611228622029637208 q^{15} - 95649770669017259211249 q^{16} - 8306234468091920602458 q^{17} + 82533387024967768624260 q^{18} + 270035797869373653325956 q^{19} + 6232134420005027125786980 q^{20} + 5838301440321983715229320 q^{21} + 9437426363670756221528775 q^{22} + 54255877390369102651683504 q^{23} - 65709136210581010081717371 q^{24} - 230854284144353401270225563 q^{25} + 122096071950165945112393428 q^{26} + 381958868294912176823572848 q^{27} - 955871471938320584845940004 q^{28} + 804132498646349946302415474 q^{29} - 601709628543234842558918376 q^{30} + 881225512446197435361370680 q^{31} - 18151730804860462796680992897 q^{32} - 38173301576979446099329160940 q^{33} + 27262880330075765854596958869 q^{34} - 200431901416098900571796822784 q^{35} + 243326989965809135416568490099 q^{36} - 98036062171463270199686544726 q^{37} + 1151092416460908800473807979859 q^{38} - 403802968711354024639660838160 q^{39} - 366940471346194657953056752368 q^{40} - 471706101506504473763896837398 q^{41} - 3341342390312122233865455923982 q^{42} - 442935772294851618625398423048 q^{43} - 10421187259538494087494836525142 q^{44} - 739318658750594406568464086952 q^{45} - 3144821351805580732190076216888 q^{46} + 25656224846167184337775202639232 q^{47} - 52356572848387126657978406782365 q^{48} - 61414101723917066503976153384733 q^{49} + 174211379023457416042116587774289 q^{50} - 203536505460286158473319755016852 q^{51} + 217730479730882346485559720698682 q^{52} - 562105116327675411606666144407598 q^{53} + 1010866361710929990292216974150009 q^{54} - 304419666763573840933982874642024 q^{55} + 523609600587293391484544540172750 q^{56} - 911741534435989274642508780045708 q^{57} - 1434283571032664998185636963157260 q^{58} + 1030987807918163364110176110195168 q^{59} + 1735895800328840301692845833732468 q^{60} - 2681528401088033533091914479580158 q^{61} + 9845798998683299339437765035327204 q^{62} - 12027424395451184167105611735489576 q^{63} + 24553200787814552000236270416344130 q^{64} + 377610413326934067670648372469436 q^{65} - 181835740431829108776682384900902 q^{66} + 1143324921773557096066935598695024 q^{67} - 11368913876393683623825562301429937 q^{68} + 45651766739864415186392523477009792 q^{69} - 28240947012852252451078152466078494 q^{70} - 38935502535802063850315881074884232 q^{71} - 41090783447791739841512902716364389 q^{72} - 27692624200493840540697160411976538 q^{73} + 99032525440396489596917857141509756 q^{74} + 170709895857321181267161602898401628 q^{75} - 66500879941432376353175950837131459 q^{76} + 342780164431500479532318352818878064 q^{77} - 276607517324500733525939302718153418 q^{78} - 379515845090436176152142826668618640 q^{79} + 1639829527648889210970557165430298368 q^{80} + 331293542492574451498143148213568148 q^{81} - 399372028015877543721045070361918538 q^{82} + 1500432873565728695616608098848685644 q^{83} + 670584552943002331558441172923019874 q^{84} - 1882364319763813075799410872225538932 q^{85} + 6103812648649635186903211512013123569 q^{86} - 1998354544933340665792185062503836096 q^{87} - 2069954387796229410093542440310184309 q^{88} + 6749162443888943821756576975670522166 q^{89} + 4815138213911653652259366571211256108 q^{90} - 6988899202022378884176125150365744896 q^{91} + 26245691438391562481391737835538463634 q^{92} - 4888442836513460260337741079738979632 q^{93} - 11457187503166588496184189861962510016 q^{94} + 35537636811651098189915166755679569424 q^{95} + 12347574341999101028342060805474522768 q^{96} - 39704159689023422777885224235664057582 q^{97} + 90377088367690491144263717562764476272 q^{98} - 15636137210022725768195532263739660984 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{38}^{\mathrm{new}}(\Gamma_1(9))\)

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
9.38.a \(\chi_{9}(1, \cdot)\) 9.38.a.a 2 1
9.38.a.b 3
9.38.a.c 4
9.38.a.d 6
9.38.c \(\chi_{9}(4, \cdot)\) 9.38.c.a 72 2

Decomposition of \(S_{38}^{\mathrm{old}}(\Gamma_1(9))\) into lower level spaces

\( S_{38}^{\mathrm{old}}(\Gamma_1(9)) \cong \) \(S_{38}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 3}\)\(\oplus\)\(S_{38}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 2}\)