Space of modular forms of level 9 and weight 22

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

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 - 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

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 available 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

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