Properties

Label 4.39.b
Level 4
Weight 39
Character orbit b
Rep. character \(\chi_{4}(3,\cdot)\)
Character field \(\Q\)
Dimension 18
Newforms 1
Sturm bound 19
Trace bound 0

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Defining parameters

Level: \( N \) = \( 4 = 2^{2} \)
Weight: \( k \) = \( 39 \)
Character orbit: \([\chi]\) = 4.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 4 \)
Character field: \(\Q\)
Newforms: \( 1 \)
Sturm bound: \(19\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{39}(4, [\chi])\).

Total New Old
Modular forms 20 20 0
Cusp forms 18 18 0
Eisenstein series 2 2 0

Trace form

\(18q \) \(\mathstrut +\mathstrut 364228q^{2} \) \(\mathstrut +\mathstrut 200567335824q^{4} \) \(\mathstrut -\mathstrut 8991287507020q^{5} \) \(\mathstrut +\mathstrut 817599417526752q^{6} \) \(\mathstrut +\mathstrut 90410803724813632q^{8} \) \(\mathstrut -\mathstrut 7529771892957713214q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(18q \) \(\mathstrut +\mathstrut 364228q^{2} \) \(\mathstrut +\mathstrut 200567335824q^{4} \) \(\mathstrut -\mathstrut 8991287507020q^{5} \) \(\mathstrut +\mathstrut 817599417526752q^{6} \) \(\mathstrut +\mathstrut 90410803724813632q^{8} \) \(\mathstrut -\mathstrut 7529771892957713214q^{9} \) \(\mathstrut -\mathstrut 3330064307292995160q^{10} \) \(\mathstrut +\mathstrut 214196660016355524480q^{12} \) \(\mathstrut -\mathstrut 1351697142828804018156q^{13} \) \(\mathstrut -\mathstrut 7517302305589491995328q^{14} \) \(\mathstrut +\mathstrut 146524491404032531730688q^{16} \) \(\mathstrut -\mathstrut 108377436655642595433244q^{17} \) \(\mathstrut -\mathstrut 2269182475834354952235228q^{18} \) \(\mathstrut +\mathstrut 14024643346150499263916960q^{20} \) \(\mathstrut -\mathstrut 3613555902040956758482176q^{21} \) \(\mathstrut -\mathstrut 48893102429006434191867360q^{22} \) \(\mathstrut -\mathstrut 507867326842846671102786048q^{24} \) \(\mathstrut +\mathstrut 441821122409714044642015590q^{25} \) \(\mathstrut +\mathstrut 1408725703649472883667066984q^{26} \) \(\mathstrut -\mathstrut 248593478439946838208756480q^{28} \) \(\mathstrut +\mathstrut 12039386014829706600024980948q^{29} \) \(\mathstrut -\mathstrut 36685926266894937628070825280q^{30} \) \(\mathstrut +\mathstrut 40815302174771571873068643328q^{32} \) \(\mathstrut -\mathstrut 25787267222238191864238656640q^{33} \) \(\mathstrut +\mathstrut 36261374450642004292958003976q^{34} \) \(\mathstrut -\mathstrut 580544496119856571348909156080q^{36} \) \(\mathstrut -\mathstrut 1267140929573154455938088740044q^{37} \) \(\mathstrut +\mathstrut 1030706182877614317326332452960q^{38} \) \(\mathstrut +\mathstrut 3677775331309955303335927125120q^{40} \) \(\mathstrut -\mathstrut 4228447688719256876424323554684q^{41} \) \(\mathstrut -\mathstrut 14054054841750269128772739402240q^{42} \) \(\mathstrut -\mathstrut 10408853597054255998042527960960q^{44} \) \(\mathstrut +\mathstrut 5968962977750993515218889928340q^{45} \) \(\mathstrut +\mathstrut 22407092921477343211835072559552q^{46} \) \(\mathstrut -\mathstrut 235299721005018637688575231641600q^{48} \) \(\mathstrut -\mathstrut 31615512188019323981649417734094q^{49} \) \(\mathstrut +\mathstrut 24292124186551164152560477361580q^{50} \) \(\mathstrut +\mathstrut 1002079305454954374889708255510176q^{52} \) \(\mathstrut +\mathstrut 9170251390510729272958214802164q^{53} \) \(\mathstrut -\mathstrut 787051683509089599494415837112896q^{54} \) \(\mathstrut +\mathstrut 1152829073224199082248229376115712q^{56} \) \(\mathstrut +\mathstrut 1668394969897754054685444684739200q^{57} \) \(\mathstrut +\mathstrut 6129531800884682398669731348277224q^{58} \) \(\mathstrut -\mathstrut 11636557112389656620532244922123520q^{60} \) \(\mathstrut -\mathstrut 3962895304807674280127771339766444q^{61} \) \(\mathstrut -\mathstrut 8994819235653434082008553861768960q^{62} \) \(\mathstrut +\mathstrut 24667562443996411690757328278360064q^{64} \) \(\mathstrut +\mathstrut 95108472178397576493345013351708360q^{65} \) \(\mathstrut -\mathstrut 59643686483535838768039195759223040q^{66} \) \(\mathstrut -\mathstrut 37428614071533769215405413189346016q^{68} \) \(\mathstrut -\mathstrut 378107798255717180855219732084825856q^{69} \) \(\mathstrut +\mathstrut 185830274294359588352082139216848000q^{70} \) \(\mathstrut -\mathstrut 260290846480495236441760743958748352q^{72} \) \(\mathstrut +\mathstrut 769773517671824524924524644742901764q^{73} \) \(\mathstrut -\mathstrut 250034850108007402381953386687905624q^{74} \) \(\mathstrut +\mathstrut 347277300516185248422743813412796800q^{76} \) \(\mathstrut -\mathstrut 1122048032159971455828617866562814720q^{77} \) \(\mathstrut -\mathstrut 1450998872578214468135780206011466560q^{78} \) \(\mathstrut +\mathstrut 391473453760426152176293685484792320q^{80} \) \(\mathstrut +\mathstrut 8894227269421968655762303906241837682q^{81} \) \(\mathstrut +\mathstrut 344096947623408239895482884304277576q^{82} \) \(\mathstrut -\mathstrut 6791395692770555756905407625225660416q^{84} \) \(\mathstrut -\mathstrut 3198312652592605820819998423888978200q^{85} \) \(\mathstrut +\mathstrut 8678996853442312035283130731028012832q^{86} \) \(\mathstrut -\mathstrut 815671442380761053869289210355156480q^{88} \) \(\mathstrut -\mathstrut 6268329434682461663886854261019826492q^{89} \) \(\mathstrut -\mathstrut 23166185157487343623484458734705269400q^{90} \) \(\mathstrut +\mathstrut 11421593562829281515681866911017506560q^{92} \) \(\mathstrut +\mathstrut 41748150138354461655386813609302195200q^{93} \) \(\mathstrut -\mathstrut 33742046901195882761657274622561154688q^{94} \) \(\mathstrut -\mathstrut 31638035665740952392118263378397667328q^{96} \) \(\mathstrut -\mathstrut 62817319233285161836922640968633412444q^{97} \) \(\mathstrut +\mathstrut 79415378721147757612981391241727219972q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{39}^{\mathrm{new}}(4, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
4.39.b.a \(18\) \(36.585\) \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(364228\) \(0\) \(-8\!\cdots\!20\) \(0\) \(q+(20235-\beta _{1})q^{2}+(-18+165\beta _{1}+\cdots)q^{3}+\cdots\)