Properties

Label 21.30.a
Level $21$
Weight $30$
Character orbit 21.a
Rep. character $\chi_{21}(1,\cdot)$
Character field $\Q$
Dimension $28$
Newform subspaces $4$
Sturm bound $80$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 21 = 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 30 \)
Character orbit: \([\chi]\) \(=\) 21.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(80\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{30}(\Gamma_0(21))\).

Total New Old
Modular forms 80 28 52
Cusp forms 76 28 48
Eisenstein series 4 0 4

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(3\)\(7\)FrickeDim.
\(+\)\(+\)\(+\)\(7\)
\(+\)\(-\)\(-\)\(7\)
\(-\)\(+\)\(-\)\(8\)
\(-\)\(-\)\(+\)\(6\)
Plus space\(+\)\(13\)
Minus space\(-\)\(15\)

Trace form

\( 28q + 50050q^{2} + 5725675522q^{4} - 47133524848q^{5} - 382847970636q^{6} - 1356446145698q^{7} + 16864624126350q^{8} + 640550188738908q^{9} + O(q^{10}) \) \( 28q + 50050q^{2} + 5725675522q^{4} - 47133524848q^{5} - 382847970636q^{6} - 1356446145698q^{7} + 16864624126350q^{8} + 640550188738908q^{9} + 67758897384108q^{10} - 1409527146769672q^{11} - 10401106719052008q^{12} + 36411565066322072q^{13} + 54676987686940682q^{14} - 181641390569271864q^{15} - 27639092963413358q^{16} - 2888932810381716528q^{17} + 1144983462370798050q^{18} - 1402410564715601872q^{19} - 500701357602020900q^{20} - 6487839865043017362q^{21} - 3732700255101173664q^{22} + 75151689905616899736q^{23} - 55621318180372725348q^{24} + 459186895718644748452q^{25} + 411997920223742233396q^{26} - 479069233308652910714q^{28} + 3078374906583286172072q^{29} + 5506598594254191410088q^{30} + 10149013569896566323392q^{31} - 495946672725576915850q^{32} - 8065891212786760071960q^{33} + 53462407997041901461404q^{34} - 18111075044234737636484q^{35} + 130985090581244485164642q^{36} + 80169423998315581294568q^{37} + 9054288926988284501488q^{38} - 84631878068124191419440q^{39} - 474240427617637621356444q^{40} - 550220237965107796429568q^{41} - 106296768348864796459008q^{42} + 1845478782292041833921600q^{43} + 2343139745931468646214752q^{44} - 1078263865618443214370928q^{45} - 6320804441126815759469112q^{46} + 5006143877227481306819856q^{47} - 11226536246386554596493840q^{48} + 12879623023252718907350428q^{49} + 23418723975704108164019102q^{50} - 3090117373925177142279432q^{51} + 3182447193590861421760868q^{52} - 17324018940126692125339560q^{53} - 8758333566042775280525196q^{54} - 18328350441876081451534032q^{55} + 28267295606020552764041058q^{56} - 44568817675574444325880128q^{57} - 77029252774319335990221540q^{58} + 272748131455868283335578224q^{59} - 318119348335570567670456208q^{60} - 23724206457570985490890744q^{61} + 955605894187972194827383104q^{62} - 31031136951464935708907778q^{63} - 589289580135480054978727286q^{64} + 482528023441453332839521088q^{65} + 529829335840894667751244824q^{66} - 369691065287906620572319600q^{67} + 161700798960968226592789692q^{68} - 17820966677766886209742344q^{69} - 724442120013094427049933156q^{70} - 1025634004890420624535994136q^{71} + 385808505969436926348322350q^{72} + 4257549037714932344955464936q^{73} - 5768175814678945889870844804q^{74} + 5045812754211080989706315808q^{75} - 7972593288979383136157624608q^{76} - 1496184178736861270339426240q^{77} + 3100251446607251445268497696q^{78} + 4342046561262556088801352032q^{79} + 3121245573372384040107536668q^{80} + 14653733724766095041978322588q^{81} + 30702635773120378802280758172q^{82} - 38682157214123173428369049152q^{83} - 5224698757883402475553161216q^{84} + 631176205996378193064477648q^{85} + 3404855402872203723824906168q^{86} + 13872805661751426312689308320q^{87} + 6345047997026617801047645072q^{88} + 70591364596308189827662064000q^{89} + 1550106232433238534307159788q^{90} - 26474487075793362313137126844q^{91} - 52574900294650243491825057144q^{92} - 2130080510409903001582627968q^{93} - 76945989973742971513534831008q^{94} - 165189920445301082916592215040q^{95} - 32678118762202774832687567532q^{96} + 194873177704814562581338754888q^{97} + 23022326154064235046888890050q^{98} - 32245459996283138473700742792q^{99} + O(q^{100}) \)

Decomposition of \(S_{30}^{\mathrm{new}}(\Gamma_0(21))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 3 7
21.30.a.a \(6\) \(111.884\) \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(4464\) \(28697814\) \(-34057000980\) \(40\!\cdots\!94\) \(-\) \(-\) \(q+(744+\beta _{1})q^{2}+3^{14}q^{3}+(51420432+\cdots)q^{4}+\cdots\)
21.30.a.b \(7\) \(111.884\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(4177\) \(-33480783\) \(-1716792694\) \(-4\!\cdots\!43\) \(+\) \(+\) \(q+(597-\beta _{1})q^{2}-3^{14}q^{3}+(249858685+\cdots)q^{4}+\cdots\)
21.30.a.c \(7\) \(111.884\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(60870\) \(-33480783\) \(-2861618502\) \(47\!\cdots\!43\) \(+\) \(-\) \(q+(8696-\beta _{1})q^{2}-3^{14}q^{3}+(314449162+\cdots)q^{4}+\cdots\)
21.30.a.d \(8\) \(111.884\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(-19461\) \(38263752\) \(-8498112672\) \(-5\!\cdots\!92\) \(-\) \(+\) \(q+(-2433+\beta _{1})q^{2}+3^{14}q^{3}+(183377628+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{30}^{\mathrm{old}}(\Gamma_0(21))\) into lower level spaces

\( S_{30}^{\mathrm{old}}(\Gamma_0(21)) \cong \) \(S_{30}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{30}^{\mathrm{new}}(\Gamma_0(3))\)\(^{\oplus 2}\)\(\oplus\)\(S_{30}^{\mathrm{new}}(\Gamma_0(7))\)\(^{\oplus 2}\)