Properties

Label 1.32.a
Level $1$
Weight $32$
Character orbit 1.a
Rep. character $\chi_{1}(1,\cdot)$
Character field $\Q$
Dimension $2$
Newform subspaces $1$
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: \(\Q\)
Newform subspaces: \( 1 \)
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

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

Decomposition of \(S_{32}^{\mathrm{new}}(\Gamma_0(1))\) into newform subspaces

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 \(39960\) \(17363160\) \(-19391218020\) \(30\!\cdots\!00\) \(+\) \(q+(19980-\beta )q^{2}+(8681580-432\beta )q^{3}+\cdots\)