Properties

Label 1.32.a
Level 1
Weight 32
Character orbit a
Rep. character \(\chi_{1}(1,\cdot)\)
Character field \(\Q\)
Dimension 2
Newforms 1
Sturm bound 2
Trace bound 0

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Defining parameters

Level: \( N \) = \( 1 \)
Weight: \( k \) = \( 32 \)
Character orbit: \([\chi]\) = 1.a (trivial)
Character field: \(\Q\)
Newforms: \( 1 \)
Sturm bound: \(2\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{32}(\Gamma_0(1))\).

Total New Old
Modular forms 3 3 0
Cusp forms 2 2 0
Eisenstein series 1 1 0

Trace form

\(2q \) \(\mathstrut +\mathstrut 39960q^{2} \) \(\mathstrut +\mathstrut 17363160q^{3} \) \(\mathstrut +\mathstrut 1772534336q^{4} \) \(\mathstrut -\mathstrut 19391218020q^{5} \) \(\mathstrut +\mathstrut 2623167496224q^{6} \) \(\mathstrut +\mathstrut 30257527577200q^{7} \) \(\mathstrut +\mathstrut 160155058705920q^{8} \) \(\mathstrut -\mathstrut 101266456303926q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(2q \) \(\mathstrut +\mathstrut 39960q^{2} \) \(\mathstrut +\mathstrut 17363160q^{3} \) \(\mathstrut +\mathstrut 1772534336q^{4} \) \(\mathstrut -\mathstrut 19391218020q^{5} \) \(\mathstrut +\mathstrut 2623167496224q^{6} \) \(\mathstrut +\mathstrut 30257527577200q^{7} \) \(\mathstrut +\mathstrut 160155058705920q^{8} \) \(\mathstrut -\mathstrut 101266456303926q^{9} \) \(\mathstrut -\mathstrut 7861972212281520q^{10} \) \(\mathstrut -\mathstrut 7782353745118776q^{11} \) \(\mathstrut +\mathstrut 106347410955313920q^{12} \) \(\mathstrut +\mathstrut 74708953050260620q^{13} \) \(\mathstrut +\mathstrut 225544963845241152q^{14} \) \(\mathstrut -\mathstrut 3397345822674581040q^{15} \) \(\mathstrut -\mathstrut 3045212913684901888q^{16} \) \(\mathstrut +\mathstrut 17224607828987089380q^{17} \) \(\mathstrut +\mathstrut 37499616229575978360q^{18} \) \(\mathstrut -\mathstrut 12370563328022164040q^{19} \) \(\mathstrut -\mathstrut 315868245501283090560q^{20} \) \(\mathstrut +\mathstrut 98954957416071161664q^{21} \) \(\mathstrut -\mathstrut 2682713032996690080q^{22} \) \(\mathstrut +\mathstrut 1897344841989911219280q^{23} \) \(\mathstrut +\mathstrut 336914041234261985280q^{24} \) \(\mathstrut +\mathstrut 1477861250884539239150q^{25} \) \(\mathstrut -\mathstrut 23066680666744323279216q^{26} \) \(\mathstrut +\mathstrut 5469986602319662295280q^{27} \) \(\mathstrut +\mathstrut 11671395808124240043520q^{28} \) \(\mathstrut +\mathstrut 128576144217217055807340q^{29} \) \(\mathstrut -\mathstrut 154839394101764341823040q^{30} \) \(\mathstrut +\mathstrut 125733527517961838793664q^{31} \) \(\mathstrut -\mathstrut 483720527174276002775040q^{32} \) \(\mathstrut -\mathstrut 1549761835334435045280q^{33} \) \(\mathstrut +\mathstrut 581706909571293028834992q^{34} \) \(\mathstrut +\mathstrut 244269703121729304206880q^{35} \) \(\mathstrut +\mathstrut 1489586748818199413504832q^{36} \) \(\mathstrut -\mathstrut 833815207054016911025060q^{37} \) \(\mathstrut -\mathstrut 1078658489244045513633120q^{38} \) \(\mathstrut -\mathstrut 9961054164411363568284912q^{39} \) \(\mathstrut +\mathstrut 1906531481497967156966400q^{40} \) \(\mathstrut +\mathstrut 8724924335662925840671284q^{41} \) \(\mathstrut +\mathstrut 33123669600002676603713280q^{42} \) \(\mathstrut -\mathstrut 18397105293779438708372600q^{43} \) \(\mathstrut -\mathstrut 791008370873332311322368q^{44} \) \(\mathstrut -\mathstrut 55083793466681039024257140q^{45} \) \(\mathstrut -\mathstrut 59873011445275600509089856q^{46} \) \(\mathstrut +\mathstrut 95450963964856190793148320q^{47} \) \(\mathstrut -\mathstrut 60542278614741008947691520q^{48} \) \(\mathstrut +\mathstrut 169469294372320202530407186q^{49} \) \(\mathstrut +\mathstrut 174468018688948298981615400q^{50} \) \(\mathstrut +\mathstrut 252162404739970320085380144q^{51} \) \(\mathstrut -\mathstrut 915180155081494236104643200q^{52} \) \(\mathstrut +\mathstrut 194822508473721098983660860q^{53} \) \(\mathstrut -\mathstrut 1068822271687374190070274240q^{54} \) \(\mathstrut -\mathstrut 141313671368671671047892240q^{55} \) \(\mathstrut +\mathstrut 2598355397749815172431728640q^{56} \) \(\mathstrut -\mathstrut 466601717043760934967596640q^{57} \) \(\mathstrut +\mathstrut 3802934506602438134028187920q^{58} \) \(\mathstrut -\mathstrut 198723263547765513990746520q^{59} \) \(\mathstrut -\mathstrut 6485894626584890581155141120q^{60} \) \(\mathstrut -\mathstrut 12056218201113004361157656276q^{61} \) \(\mathstrut +\mathstrut 15224500099333079134598257920q^{62} \) \(\mathstrut -\mathstrut 4374875036601718967620305360q^{63} \) \(\mathstrut -\mathstrut 7488413368264058547677691904q^{64} \) \(\mathstrut +\mathstrut 34114584794425827928886318760q^{65} \) \(\mathstrut -\mathstrut 7561640583442461364265814912q^{66} \) \(\mathstrut -\mathstrut 9688140802872256994032247720q^{67} \) \(\mathstrut +\mathstrut 24758471836626330094958252160q^{68} \) \(\mathstrut -\mathstrut 25769856286394326078494576192q^{69} \) \(\mathstrut -\mathstrut 104525335953756946154610069120q^{70} \) \(\mathstrut +\mathstrut 55784576625034657512878287344q^{71} \) \(\mathstrut -\mathstrut 26400994734811244163462812160q^{72} \) \(\mathstrut +\mathstrut 62234095932086098750552955380q^{73} \) \(\mathstrut +\mathstrut 153133163632488378484794299472q^{74} \) \(\mathstrut +\mathstrut 75444402265645086720647965800q^{75} \) \(\mathstrut -\mathstrut 44190149699939358902474481920q^{76} \) \(\mathstrut -\mathstrut 128728748793695217194494555200q^{77} \) \(\mathstrut -\mathstrut 327207773523327347562124449600q^{78} \) \(\mathstrut -\mathstrut 119164191093299704964212710560q^{79} \) \(\mathstrut +\mathstrut 141515971255973138522638049280q^{80} \) \(\mathstrut -\mathstrut 398906922646891269649062634158q^{81} \) \(\mathstrut +\mathstrut 1145184549692595779551104209520q^{82} \) \(\mathstrut -\mathstrut 264863373681569145625357596360q^{83} \) \(\mathstrut +\mathstrut 1332316649919851794889339185152q^{84} \) \(\mathstrut -\mathstrut 503995105657776450242931421320q^{85} \) \(\mathstrut -\mathstrut 2173142482222838422832927019936q^{86} \) \(\mathstrut +\mathstrut 1649324800814841914442821796240q^{87} \) \(\mathstrut -\mathstrut 693913929707398651948752168960q^{88} \) \(\mathstrut -\mathstrut 2154414614246670291602721895980q^{89} \) \(\mathstrut -\mathstrut 1105313102749861362639913526640q^{90} \) \(\mathstrut +\mathstrut 2896781368068903069956049509024q^{91} \) \(\mathstrut -\mathstrut 2225812737244025604862645470720q^{92} \) \(\mathstrut +\mathstrut 6583298380663842229690665227520q^{93} \) \(\mathstrut +\mathstrut 4613808251402558431525114250112q^{94} \) \(\mathstrut +\mathstrut 1299465173198290044974084355600q^{95} \) \(\mathstrut -\mathstrut 6084370432669606716368714858496q^{96} \) \(\mathstrut -\mathstrut 9060767994874032615529957205180q^{97} \) \(\mathstrut -\mathstrut 8081619677193750912975770689320q^{98} \) \(\mathstrut +\mathstrut 1540246307744094989457731085288q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{32}^{\mathrm{new}}(\Gamma_0(1))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1.32.a.a \(2\) \(6.088\) \(\mathbb{Q}[x]/(x^{2} - \cdots)\) None \(39960\) \(17363160\) \(-19391218020\) \(30\!\cdots\!00\) \(+\) \(q+(19980-\beta )q^{2}+(8681580-432\beta )q^{3}+\cdots\)