Properties

Label 21.41
Level 21
Weight 41
Dimension 450
Nonzero newspaces 4
Newform subspaces 6
Sturm bound 1312
Trace bound 1

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Defining parameters

Level: \( N \) = \( 21 = 3 \cdot 7 \)
Weight: \( k \) = \( 41 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 6 \)
Sturm bound: \(1312\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{41}(\Gamma_1(21))\).

Total New Old
Modular forms 652 458 194
Cusp forms 628 450 178
Eisenstein series 24 8 16

Trace form

\( 450 q - 2742619260 q^{3} + 13960793825242 q^{4} + 103264835143734 q^{5} - 16943724970655910 q^{6} - 143779844163826358 q^{7} - 7998612357433553262 q^{8} + 17307653119604768250 q^{9} + O(q^{10}) \) \( 450 q - 2742619260 q^{3} + 13960793825242 q^{4} + 103264835143734 q^{5} - 16943724970655910 q^{6} - 143779844163826358 q^{7} - 7998612357433553262 q^{8} + 17307653119604768250 q^{9} + 393514517582020222956 q^{10} - 1522708629531181387830 q^{11} + 9196429411619665948326 q^{12} - 13444212576818547044666 q^{13} + 431470275365546375107320 q^{14} + 128842483576031667608340 q^{15} - 14659837911152550100577022 q^{16} - 13348233696989394433999296 q^{17} - 21069492061147151920401900 q^{18} + 152064213909957984492000010 q^{19} + 189185670439125703353028134 q^{21} - 7117230967119569410850551740 q^{22} - 9424766274668033206968547200 q^{23} + 20064339933868978040309340666 q^{24} + 65921432179191509834296649592 q^{25} - 158952077818683056915673451590 q^{26} - 49302182531379886203142286952 q^{27} - 401486521578531464747385613302 q^{28} - 546411483341838960223400806212 q^{29} + 3707503419679261856784397028616 q^{30} - 3174782632259240367752884254722 q^{31} + 9869075489606696408124448042950 q^{32} + 1391655613763680368639558951804 q^{33} + 10049591577316403653837706574528 q^{34} + 47047170473132623771207494048246 q^{35} - 399265843444654424487206846691498 q^{36} - 12967599530928327721295835267412 q^{37} - 106828354801215611574360197742450 q^{38} + 36160944679934708628506930964774 q^{39} - 40561756010066012057870647866816 q^{40} + 190258707255253851496722884241264 q^{42} + 852867517250095084290092778466148 q^{43} + 1808419207701343888832251525491960 q^{44} - 43095759459746607841432846550292 q^{45} - 898277940465475902542540493981324 q^{46} + 63992014738201661530980958363494 q^{47} + 17578910427052609971454791763862934 q^{48} + 36011093087134938260288165910294252 q^{49} + 94847289846326276189298670902823974 q^{50} - 136329902837935297523831696959892166 q^{51} + 448738655271573123668308739465261464 q^{52} - 159761553350190191922226458022001244 q^{53} + 316781580999301441235114168657100948 q^{54} - 567702755775788090023246838095338876 q^{55} - 517701663487004095214313386461055982 q^{56} + 21862957429454679672241550220461520 q^{57} - 168784667585930278298952673387171488 q^{58} + 1146501442222766146857897789452459820 q^{59} + 1078408230005402648562396038092311156 q^{60} + 1247142771581014134811917248084590246 q^{61} - 1484357234640805142880508594875570588 q^{63} + 1484864206879390688492379443065069606 q^{64} - 20476569064781936857685312573036732682 q^{65} + 22383537217874099456389174803685119408 q^{66} - 58659909029658172963701244704765054402 q^{67} + 71445702191866661319149901146654271924 q^{68} - 70698711903948644692832166292908474852 q^{69} - 16742957078159978644441093804744644924 q^{70} + 24732402031777908772266924762699801048 q^{71} + 30902069880455891912914151903459483190 q^{72} + 19434132200604020103752772621722828296 q^{73} + 11798825275472177820357377145812761362 q^{74} - 165329880021704757276960256111077859836 q^{75} + 525343012690760478150253537389433017196 q^{76} + 47973692188357092229299648653057690664 q^{77} - 76362369145795140787402113640281539304 q^{78} + 1163512931088250335396646864256560678866 q^{79} - 1980763708128354911326070124836121197520 q^{80} + 57762535114963932404333135207857447734 q^{81} + 324689337054369594494120001956590014012 q^{82} + 1180465396421413916854691862850471863762 q^{84} + 1117960187787389287789472084082795809424 q^{85} + 1026065024094761906171831771124880793538 q^{86} - 4251312152712218918913914136865457412672 q^{87} + 4230832309186361703659086124793286197480 q^{88} + 902245436655905517356821941447117379164 q^{89} - 13266979683301547261277939306040130510316 q^{90} + 11821081699198230769971227132076922233052 q^{91} - 10941948756153835340097934973806279924500 q^{92} - 10773017161549213136591389876227760499826 q^{93} - 602236070019183253027344557985946004916 q^{94} + 13501383432310744396505594624091594532734 q^{95} - 88511717226415098012790417728838883324682 q^{96} + 71127198030945713443718356218333780508648 q^{97} - 50728965554903169755792830726700418617478 q^{98} - 58959938445347202124689394028824185672804 q^{99} + O(q^{100}) \)

Decomposition of \(S_{41}^{\mathrm{new}}(\Gamma_1(21))\)

We only show spaces with odd 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
21.41.b \(\chi_{21}(8, \cdot)\) 21.41.b.a 80 1
21.41.d \(\chi_{21}(13, \cdot)\) 21.41.d.a 54 1
21.41.f \(\chi_{21}(10, \cdot)\) 21.41.f.a 52 2
21.41.f.b 54
21.41.h \(\chi_{21}(2, \cdot)\) 21.41.h.a 2 2
21.41.h.b 208

Decomposition of \(S_{41}^{\mathrm{old}}(\Gamma_1(21))\) into lower level spaces

\( S_{41}^{\mathrm{old}}(\Gamma_1(21)) \cong \) \(S_{41}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 2}\)\(\oplus\)\(S_{41}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 2}\)