Properties

Label 9.22
Level 9
Weight 22
Dimension 48
Nonzero newspaces 2
Newform subspaces 7
Sturm bound 132
Trace bound 1

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Defining parameters

Level: \( N \) = \( 9 = 3^{2} \)
Weight: \( k \) = \( 22 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 7 \)
Sturm bound: \(132\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{22}(\Gamma_1(9))\).

Total New Old
Modular forms 67 53 14
Cusp forms 59 48 11
Eisenstein series 8 5 3

Trace form

\( 48 q + 1761 q^{2} + 128841 q^{3} - 12173037 q^{4} + 47999847 q^{5} + 187115031 q^{6} - 290151387 q^{7} + 8255204778 q^{8} + 10117230687 q^{9} + O(q^{10}) \) \( 48 q + 1761 q^{2} + 128841 q^{3} - 12173037 q^{4} + 47999847 q^{5} + 187115031 q^{6} - 290151387 q^{7} + 8255204778 q^{8} + 10117230687 q^{9} - 16895949936 q^{10} + 70455589638 q^{11} - 287594221404 q^{12} - 63755310321 q^{13} + 2142597894888 q^{14} - 5069511951597 q^{15} - 14781361946097 q^{16} - 9986997763800 q^{17} + 35716321080900 q^{18} - 20431085383254 q^{19} + 90916646798820 q^{20} - 25195769607435 q^{21} - 84776391850809 q^{22} + 965898363216999 q^{23} + 410684147823429 q^{24} - 2044325787458253 q^{25} + 7499011802958804 q^{26} - 3576595918397832 q^{27} - 653423799548964 q^{28} + 2902496833420917 q^{29} + 3993479924773464 q^{30} - 7326297106898679 q^{31} + 60058028234416383 q^{32} - 4293613576965348 q^{33} - 11305352220309099 q^{34} - 7661898032523834 q^{35} + 85851013073070195 q^{36} + 1551842388247740 q^{37} + 40860518476035027 q^{38} - 87846860189874705 q^{39} - 54286511239324848 q^{40} + 27686270849937600 q^{41} + 337199075744914674 q^{42} - 30486370146318504 q^{43} - 148258122126917718 q^{44} - 626346227021430807 q^{45} + 83927831151126216 q^{46} - 229409857646053167 q^{47} - 2063048917232418717 q^{48} - 1108270134864421365 q^{49} - 2048666820532107951 q^{50} + 2354897151685709901 q^{51} + 148312543669324410 q^{52} - 6659333188769384226 q^{53} + 99342864988461945 q^{54} + 6489676565022689886 q^{55} + 13339816058020724430 q^{56} - 13459209464247889803 q^{57} - 11689258639528713612 q^{58} + 13765658304146828394 q^{59} + 51156044998564987188 q^{60} - 10680237427975940259 q^{61} - 37652888926244288796 q^{62} - 13230441185793947541 q^{63} + 49715901928530104898 q^{64} + 54012765594723896931 q^{65} - 123823169645858161830 q^{66} - 35725392182261978820 q^{67} + 149403402029899788687 q^{68} + 150864702504537503655 q^{69} - 41217366141732052254 q^{70} - 235255188881302206840 q^{71} - 48892048794664809957 q^{72} + 113662884764914359450 q^{73} + 116162706747602203068 q^{74} - 257510560866332897127 q^{75} - 27246365185995290307 q^{76} + 120823311655124036949 q^{77} + 427374495269366745654 q^{78} + 87556943942019043767 q^{79} - 1321238267116739953152 q^{80} - 257436670304083233285 q^{81} + 683257030398511048758 q^{82} + 195247664484342609759 q^{83} - 475322036714517671646 q^{84} - 324599312515478456502 q^{85} - 771643406043802382991 q^{86} + 656183537067073653567 q^{87} + 384591127830516035211 q^{88} + 830249342078464225422 q^{89} - 317064997814377319892 q^{90} - 984002259191464371762 q^{91} + 1492482588168196042770 q^{92} + 580984338398858289255 q^{93} + 1254358343494182739200 q^{94} + 2964122687442617239524 q^{95} - 4879256367050568317232 q^{96} - 1461370422568740953094 q^{97} + 5478488837438118468912 q^{98} + 1652708587690791985041 q^{99} + O(q^{100}) \)

Decomposition of \(S_{22}^{\mathrm{new}}(\Gamma_1(9))\)

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
9.22.a \(\chi_{9}(1, \cdot)\) 9.22.a.a 1 1
9.22.a.b 1
9.22.a.c 1
9.22.a.d 1
9.22.a.e 2
9.22.a.f 2
9.22.c \(\chi_{9}(4, \cdot)\) 9.22.c.a 40 2

Decomposition of \(S_{22}^{\mathrm{old}}(\Gamma_1(9))\) into lower level spaces

\( S_{22}^{\mathrm{old}}(\Gamma_1(9)) \cong \) \(S_{22}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 3}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 2}\)