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Properties

Label 9.62.a
Level $9$
Weight $62$
Character orbit 9.a
Rep. character $\chi_{9}(1,\cdot)$
Character field $\Q$
Dimension $25$
Newform subspaces $4$
Sturm bound $62$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 9 = 3^{2} \)
Weight: \( k \) \(=\) \( 62 \)
Character orbit: \([\chi]\) \(=\) 9.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(62\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{62}(\Gamma_0(9))\).

Total New Old
Modular forms 63 26 37
Cusp forms 59 25 34
Eisenstein series 4 1 3

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

\(3\)Dim
\(+\)\(10\)
\(-\)\(15\)

Trace form

\( 25 q + 2220053826 q^{2} + 26362275301432841620 q^{4} + 2954438736455271796494 q^{5} - 40514538566448777257398600 q^{7} + 5627871120786495521762101272 q^{8} + O(q^{10}) \) \( 25 q + 2220053826 q^{2} + 26362275301432841620 q^{4} + 2954438736455271796494 q^{5} - 40514538566448777257398600 q^{7} + 5627871120786495521762101272 q^{8} - 7016097535496937050552029672236 q^{10} + 35515991560426068580878106960500 q^{11} + 3935000735407164442169262050626598 q^{13} + 308530478393090516574178950340905360 q^{14} + 18463386833389825454742289719714683920 q^{16} + 12939138341270055795651069066829091298 q^{17} - 42665863094840835369549133621666362940 q^{19} + 1977469026523456479938535772719770406216 q^{20} + 316618256903943082358640156094627328437704 q^{22} - 98188589293405608859018051363017888239400 q^{23} + 20817993588526648363164775724390708510117551 q^{25} - 8586663220324527286905011602722062122136580 q^{26} - 63703149588309318046583952938598285724746400 q^{28} - 95636510970024524373838781706991350340532490 q^{29} + 4134465195052492142030777655353859830771766800 q^{31} + 19415293359087138322620248707876469753699242080 q^{32} + 51204606209486592769007255414279377674263298780 q^{34} + 48033399834996205146199949975420418912237538560 q^{35} - 287519175577641388114147130131064324796960942010 q^{37} + 1093882802387957225487862532018364589996715840904 q^{38} - 20337364482249383490265110356059407915128771209872 q^{40} + 13879153620262342580579758237830651040022413815930 q^{41} + 116383353017472116213273254742378219207692720264604 q^{43} + 426450103020437224410873204485044527944828097799440 q^{44} - 116044574564558313043545744200680568562761956871280 q^{46} - 1600668811475768532904972094046793055656327499591808 q^{47} + 7316264528159168286792161317490689203221256879970065 q^{49} + 23858359044446890054010490046089876620243333288450526 q^{50} + 18730174894393762379700530807843117407624082557089752 q^{52} + 114655380556716233832116284395535647011928329630116110 q^{53} - 467403228254445797133643424235848398961360915226438744 q^{55} + 1316312354071583366501997407518119917484696754071355200 q^{56} - 1408524477602902965107215230506808283189636343804385948 q^{58} + 3435841849058215968013924417917760474628407251387455220 q^{59} - 3872470581172775950274012082859961660294775311152052770 q^{61} + 27820771730267232016875572470816176386860702735507728000 q^{62} + 15558196339756662976885685504261223021700021236159438400 q^{64} + 15355662526544412048534266619734296659201630571444003332 q^{65} - 67284167086504020380543350804982375017229568644198462188 q^{67} - 104767588304629631572302225762571736258878554437394353448 q^{68} + 489750847899260642214160530698711694346185939789805353120 q^{70} - 703540403125553993133759700761412604797422915287497131480 q^{71} + 6876898315673147183394372777152034558482682718273256210 q^{73} - 3919651440524455327935376244015571422466403842136876501140 q^{74} + 817637723486749065316197205876167556462036480747007085200 q^{76} - 12065725644479231814177954949654109699601912756953635574400 q^{77} + 16448813334913401874676483768189980142731806742049368734560 q^{79} - 5132024212060985339938523294957630062424570959672825156704 q^{80} - 36859022647164241018327990665288315196047367910747029479060 q^{82} + 121966101950298541306667137277676778267523561231236597229388 q^{83} - 172254005386744594207216501056954403008045132120592150158108 q^{85} + 484537213553067099572426453016274507805651744749694030734200 q^{86} + 615364686955908213961856824817346096196574853144607720113888 q^{88} + 297831582868120299844719697105839823448517676666089274628730 q^{89} - 181958878756200976439948029221350057666627606270886145233680 q^{91} - 978721775783841511449906569840381549529960150460472928597600 q^{92} - 1612259953644011182482068857053890368661282015803971980008800 q^{94} - 9329441725570367362336624148657581021052106395775169120601304 q^{95} - 1503861018296984940301351175397473059842764211516209537693398 q^{97} - 9217571149541664337965561835699064038363269835216360589728782 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{62}^{\mathrm{new}}(\Gamma_0(9))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 3
9.62.a.a 9.a 1.a $4$ $212.091$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(-1146312000\) \(0\) \(52\!\cdots\!00\) \(-63\!\cdots\!00\) $-$ $\mathrm{SU}(2)$ \(q+(-286578000+\beta _{1})q^{2}+\cdots\)
9.62.a.b 9.a 1.a $5$ $212.091$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(1129169964\) \(0\) \(16\!\cdots\!70\) \(-85\!\cdots\!76\) $-$ $\mathrm{SU}(2)$ \(q+(225833993+\beta _{1})q^{2}+(1256252067797850262+\cdots)q^{4}+\cdots\)
9.62.a.c 9.a 1.a $6$ $212.091$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(2237195862\) \(0\) \(81\!\cdots\!24\) \(97\!\cdots\!76\) $-$ $\mathrm{SU}(2)$ \(q+(372865977-\beta _{1})q^{2}+(1131894729745867078+\cdots)q^{4}+\cdots\)
9.62.a.d 9.a 1.a $10$ $212.091$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(0\) \(0\) \(0\) \(-66\!\cdots\!00\) $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(888664890876842608+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{62}^{\mathrm{old}}(\Gamma_0(9))\) into lower level spaces

\( S_{62}^{\mathrm{old}}(\Gamma_0(9)) \cong \) \(S_{62}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 3}\)\(\oplus\)\(S_{62}^{\mathrm{new}}(\Gamma_0(3))\)\(^{\oplus 2}\)