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Properties

Label 21.34
Level 21
Weight 34
Dimension 378
Nonzero newspaces 4
Newform subspaces 9
Sturm bound 1088
Trace bound 1

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Defining parameters

Level: \( N \) = \( 21 = 3 \cdot 7 \)
Weight: \( k \) = \( 34 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 9 \)
Sturm bound: \(1088\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{34}(\Gamma_1(21))\).

Total New Old
Modular forms 540 390 150
Cusp forms 516 378 138
Eisenstein series 24 12 12

Trace form

\( 378 q - 355644 q^{2} - 86093445 q^{3} - 26964175662 q^{4} + 794626592064 q^{5} + 25141523493492 q^{6} + 183856583281170 q^{7} - 4275658311220314 q^{8} - 14836588382427657 q^{9} + O(q^{10}) \) \( 378 q - 355644 q^{2} - 86093445 q^{3} - 26964175662 q^{4} + 794626592064 q^{5} + 25141523493492 q^{6} + 183856583281170 q^{7} - 4275658311220314 q^{8} - 14836588382427657 q^{9} - 171057633394524144 q^{10} + 31710339468278064 q^{11} + 61219500743343912 q^{12} + 8172043558490191164 q^{13} - 14425835302706081160 q^{14} - 62883497345550578982 q^{15} + 458341920187425986418 q^{16} + 159168043077238406676 q^{17} - 1485970670375364321918 q^{18} + 4713373600329281598126 q^{19} - 1211580774101338920252 q^{20} - 7196915651627270148639 q^{21} + 175291390509659992724016 q^{22} - 44191161174962903624904 q^{23} - 157122498960945641293128 q^{24} + 415839033673957896019674 q^{25} - 1861326171115541026474998 q^{26} + 319065772307490039453444 q^{27} - 1605299822218315046326710 q^{28} + 2937648108784085429871024 q^{29} - 13050926787028049435591442 q^{30} - 4523747917988023471869342 q^{31} + 9825935883911270133217950 q^{32} - 49836285002564379729328653 q^{33} + 111165848352754064378846052 q^{34} + 4593046798427096130921492 q^{35} + 1084048986194987430483615642 q^{36} + 571233942750611082167459550 q^{37} + 242462009772282087451180422 q^{38} - 46004717258478547398026484 q^{39} - 1756799844505703397259284552 q^{40} + 1942293161004206132704306920 q^{41} - 1464901167710522478933255114 q^{42} + 8429080358942640117921213168 q^{43} - 6982036079092871896563809064 q^{44} + 5085522200420471426781070251 q^{45} - 1539909082305546608599803324 q^{46} - 5016026886151029115572110664 q^{47} + 26617968603882662320841976288 q^{48} + 5431044376902127879344889026 q^{49} + 67503342268791620873765852850 q^{50} - 90397948857816856090886151741 q^{51} - 180980077461540512318788304040 q^{52} + 11363184404295772897172450172 q^{53} - 182758703553511246130062109742 q^{54} - 230653673683349342541162655308 q^{55} + 96877271097790839481228550130 q^{56} - 441230806334128690210656828150 q^{57} + 1431433113743069475099996168264 q^{58} - 544337520271291291575726594672 q^{59} - 1639172222673325431788973239316 q^{60} + 2196451209882922986263521084410 q^{61} - 3992012832652641879747158946972 q^{62} + 1929248147293498736709026627067 q^{63} - 9316927119035074333047017024922 q^{64} + 5814425144883174090866782848648 q^{65} - 1332807930725186127001471454430 q^{66} - 5639893353629784806484260446650 q^{67} + 4099153314445262729602577541456 q^{68} - 5864710291574874000880553761320 q^{69} + 4774025684212652925081614747664 q^{70} + 9061562168667995132704741449972 q^{71} + 13235718937196589988038237036198 q^{72} - 13904270990133778166218375328094 q^{73} + 33490588819882465384729805535078 q^{74} + 10217564365733514201721320424776 q^{75} + 74593861474944409788230594758920 q^{76} - 82486217163523310002577939546268 q^{77} - 18992945070747525287133183861360 q^{78} - 32979828836550015642554370300846 q^{79} + 159270695085527245834221811350024 q^{80} - 841973911908949498937549306157 q^{81} + 879536174123888343972051435720 q^{82} + 166256362313497347972120493855464 q^{83} + 199596862569144918755896458799692 q^{84} - 851194008333095195894008241659620 q^{85} + 499702146783507631864657652940630 q^{86} - 216413218938219988818598481953512 q^{87} - 1609106056023186509276167049766228 q^{88} + 102414776190444922621462723328928 q^{89} + 454025009527077813103304438564952 q^{90} + 68203336582087098352738320050388 q^{91} - 4476588785784198854064171393868128 q^{92} + 391228196967598150703570170222083 q^{93} + 1076052446580717598478585646039288 q^{94} - 2584078235369132482401546070348608 q^{95} - 2899352220172802603229758195606652 q^{96} + 5794568251055266841251147704199212 q^{97} - 1143241214766901840340938861681242 q^{98} - 6078089767895744000739948804262302 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{34}^{\mathrm{new}}(\Gamma_1(21))\)

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 available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
21.34.a \(\chi_{21}(1, \cdot)\) 21.34.a.a 7 1
21.34.a.b 8
21.34.a.c 8
21.34.a.d 9
21.34.c \(\chi_{21}(20, \cdot)\) 21.34.c.a 2 1
21.34.c.b 84
21.34.e \(\chi_{21}(4, \cdot)\) 21.34.e.a 42 2
21.34.e.b 46
21.34.g \(\chi_{21}(5, \cdot)\) 21.34.g.a 172 2

Decomposition of \(S_{34}^{\mathrm{old}}(\Gamma_1(21))\) into lower level spaces

\( S_{34}^{\mathrm{old}}(\Gamma_1(21)) \cong \) \(S_{34}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{34}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 2}\)\(\oplus\)\(S_{34}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 2}\)