Properties

Label 21.32
Level 21
Weight 32
Dimension 356
Nonzero newspaces 4
Newform subspaces 9
Sturm bound 1024
Trace bound 1

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Defining parameters

Level: \( N \) = \( 21 = 3 \cdot 7 \)
Weight: \( k \) = \( 32 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 9 \)
Sturm bound: \(1024\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{32}(\Gamma_1(21))\).

Total New Old
Modular forms 508 368 140
Cusp forms 484 356 128
Eisenstein series 24 12 12

Trace form

\( 356 q + 94308 q^{2} + 14348904 q^{3} + 555012274 q^{4} - 228128447574 q^{5} - 1905592245228 q^{6} + 435624284434 q^{7} + 574400376268374 q^{8} - 514201400442330 q^{9} + O(q^{10}) \) \( 356 q + 94308 q^{2} + 14348904 q^{3} + 555012274 q^{4} - 228128447574 q^{5} - 1905592245228 q^{6} + 435624284434 q^{7} + 574400376268374 q^{8} - 514201400442330 q^{9} + 14423144515714608 q^{10} + 28695923344880610 q^{11} + 116700127371994848 q^{12} + 108101403351455178 q^{13} + 1044779141948033928 q^{14} - 358777355748755508 q^{15} - 23219895035018825806 q^{16} + 16421209825538291232 q^{17} - 39299587496338780782 q^{18} + 51278796645161839350 q^{19} + 963270017397708117924 q^{20} - 2219166747837452940 q^{21} - 1743897119114085692064 q^{22} + 2068187732465620712328 q^{23} + 14807944732387594308768 q^{24} - 20681761993301037437386 q^{25} + 19355448360169549009242 q^{26} - 5908625413101667397286 q^{27} + 145472215826826046049642 q^{28} + 88547308069064595705960 q^{29} - 29647170483503834264490 q^{30} + 152301600418126761849606 q^{31} - 1522827454011533233540530 q^{32} + 1028834959106003282274798 q^{33} - 3137598568490865479804796 q^{34} + 5753231946575934293089314 q^{35} + 27780042145884479254666410 q^{36} + 752037953751510941824244 q^{37} + 17569886326409070608759382 q^{38} - 7849403861988388758333558 q^{39} + 92535557461184844511254696 q^{40} - 39096466006428114527622348 q^{41} + 2304847484498661857019486 q^{42} - 83495864807869866049224160 q^{43} + 70351979794316956882004184 q^{44} - 300167143176355026743947194 q^{45} + 465656815723189445816924580 q^{46} - 406520381790775097915684034 q^{47} - 165356846154763189179484320 q^{48} + 1324410883193353422201489662 q^{49} - 1274020333264893864079569198 q^{50} + 2013756524378774508734649108 q^{51} - 839945880957784576074252936 q^{52} - 2620318528587705022214662020 q^{53} + 1477531855177747609261599306 q^{54} - 6028778317540080013583049240 q^{55} - 4622329648101443153612851758 q^{56} + 9573084612292984352026028964 q^{57} - 6102124967673600817012501464 q^{58} - 7264717968913538519278912692 q^{59} + 17136587030684880562534295460 q^{60} - 15458077327724006307093372414 q^{61} - 9371371376808471742218877500 q^{62} + 20239883343617968827936569418 q^{63} - 46555896322912178786117793914 q^{64} - 54471403485507127681923013326 q^{65} + 122375200517390666346184290186 q^{66} - 40862125309029804010462551974 q^{67} + 10346041436852345731416708000 q^{68} + 7376567594787432769568062968 q^{69} + 100914764399020312383414890256 q^{70} - 35035370001700814867818375668 q^{71} - 208015577855113800761254043586 q^{72} - 240435558226550250457605090840 q^{73} + 568675726228770473921031295494 q^{74} - 11006562430807801680222340854 q^{75} - 1608497754811531743119382421944 q^{76} - 419878106939260200827053134048 q^{77} + 135942424661773802847558586752 q^{78} - 1946649808442081405797072520834 q^{79} - 3319688323818334503648605810184 q^{80} - 370068342615459467284082193126 q^{81} - 2473691443252911250924511686824 q^{82} + 1560923437713928976400548857308 q^{83} - 3080382178243191007388729452692 q^{84} + 2909850970653154930302580628208 q^{85} + 355451004924465149822214472998 q^{86} - 2289169083673727775490260689316 q^{87} + 16589672061972709057784715572844 q^{88} + 6352585495281160470615748640136 q^{89} - 5700402695464712498374228575720 q^{90} + 11488651500283898333191435804248 q^{91} + 23940405500980677045268671520704 q^{92} - 21348846320552039450129771772852 q^{93} - 31603888618124357027524725059736 q^{94} + 54656338958625004800130318955034 q^{95} + 5519312767629479638866960351252 q^{96} - 83655982971018680233597057299444 q^{97} + 29444452183843704364576201512870 q^{98} + 7717587546967150897593395444124 q^{99} + O(q^{100}) \)

Decomposition of \(S_{32}^{\mathrm{new}}(\Gamma_1(21))\)

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
21.32.a \(\chi_{21}(1, \cdot)\) 21.32.a.a 7 1
21.32.a.b 8
21.32.a.c 8
21.32.a.d 9
21.32.c \(\chi_{21}(20, \cdot)\) 21.32.c.a 80 1
21.32.e \(\chi_{21}(4, \cdot)\) 21.32.e.a 40 2
21.32.e.b 42
21.32.g \(\chi_{21}(5, \cdot)\) 21.32.g.a 2 2
21.32.g.b 160

Decomposition of \(S_{32}^{\mathrm{old}}(\Gamma_1(21))\) into lower level spaces

\( S_{32}^{\mathrm{old}}(\Gamma_1(21)) \cong \) \(S_{32}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{32}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 2}\)\(\oplus\)\(S_{32}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 2}\)