Properties

Label 2.28.a
Level 2
Weight 28
Character orbit a
Rep. character \(\chi_{2}(1,\cdot)\)
Character field \(\Q\)
Dimension 2
Newforms 2
Sturm bound 7
Trace bound 2

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Defining parameters

Level: \( N \) = \( 2 \)
Weight: \( k \) = \( 28 \)
Character orbit: \([\chi]\) = 2.a (trivial)
Character field: \(\Q\)
Newforms: \( 2 \)
Sturm bound: \(7\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{28}(\Gamma_0(2))\).

Total New Old
Modular forms 8 2 6
Cusp forms 6 2 4
Eisenstein series 2 0 2

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

\(2\)Dim.
\(+\)\(1\)
\(-\)\(1\)

Trace form

\( 2q + 2968440q^{3} + 134217728q^{4} - 6193086660q^{5} - 40969961472q^{6} + 317699702320q^{7} + 1660703786154q^{9} + O(q^{10}) \) \( 2q + 2968440q^{3} + 134217728q^{4} - 6193086660q^{5} - 40969961472q^{6} + 317699702320q^{7} + 1660703786154q^{9} - 4008412446720q^{10} - 117516933181656q^{11} + 199208636252160q^{12} + 1638224482617580q^{13} - 3438529946320896q^{14} - 7968335183143920q^{15} + 9007199254740992q^{16} + 73362024414183780q^{17} - 121616872431943680q^{18} + 10723011419801560q^{19} - 415611010406154240q^{20} + 1521147518291843904q^{21} - 1944049721404293120q^{22} + 2326506445206257040q^{23} - 2749447572509687808q^{24} + 4395711233008614350q^{25} - 17752045726960975872q^{26} + 16952271485001487920q^{27} + 21320466115833364480q^{28} - 22324461097024443060q^{29} + 120915895004807823360q^{30} - 367654080718117933376q^{31} + 419000194891783006560q^{33} + 657504278353903878144q^{34} - 881079197315107966560q^{35} + 111447944529293869056q^{36} - 1362897261694124886020q^{37} - 2508814875767372513280q^{38} + 7850297499745502472528q^{39} - 269000005742839726080q^{40} + 341149695749618405364q^{41} - 11611607198786534768640q^{42} + 7079373897890013650920q^{43} - 7886427886584839798784q^{44} - 1510353336940917049620q^{45} + 39655433734134146531328q^{46} - 39610669729640610624480q^{47} + 13368665277871675146240q^{48} + 7133677409417392315986q^{49} + 24824445651559592755200q^{50} - 91817797091509308851856q^{51} + 109939384005453540229120q^{52} - 277054655000983544064420q^{53} + 97894755692391086161920q^{54} + 421955320535451779183280q^{55} - 230755838527576310022144q^{56} + 781731048837488331061920q^{57} - 1049337015594916994088960q^{58} - 475035541633656110356920q^{59} - 534745922112020419706880q^{60} + 228388165269370282220044q^{61} + 864349001881323999068160q^{62} + 3379510616036199728252400q^{63} + 604462909807314587353088q^{64} - 4542668249056478745324120q^{65} - 478065365122657585987584q^{66} - 4874211806367053755583240q^{67} + 4923242119176138963025920q^{68} - 8651773751240417404779072q^{69} + 10010821249735865118228480q^{70} + 23885423832732540666942384q^{71} - 8161570152140657676779520q^{72} - 27814846608180566811276620q^{73} + 313924776717665408385024q^{74} - 1053459508882520097967800q^{75} + 719609115041909797027840q^{76} + 31137148978183467090002880q^{77} - 59906938276534712763678720q^{78} + 84440229400331850089878240q^{79} - 27891182774249189655183360q^{80} - 17385332406637801723773678q^{81} + 7669442327286373196759040q^{82} - 10301363055151996255698600q^{83} + 102082481928984864862765056q^{84} - 246805052648077280673957960q^{85} + 55335789369651410950422528q^{86} + 287175712360922793567141840q^{87} - 130462968362958596006215680q^{88} - 585639962549428184278515180q^{89} + 373263522281228719840296960q^{90} + 715022164675518680827587104q^{91} + 156129204626470155646402560q^{92} - 809522072507719149790882560q^{93} - 181920956461264041186164736q^{94} + 41721486775292229567512400q^{95} - 184512303218682777789530112q^{96} + 155974514949756369858194500q^{97} - 1092419940364554238395678720q^{98} + 1663954752079394723722991688q^{99} + O(q^{100}) \)

Decomposition of \(S_{28}^{\mathrm{new}}(\Gamma_0(2))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2
2.28.a.a \(1\) \(9.237\) \(\Q\) None \(-8192\) \(3984828\) \(-2851889250\) \(368721063704\) \(+\) \(q-2^{13}q^{2}+3984828q^{3}+2^{26}q^{4}+\cdots\)
2.28.a.b \(1\) \(9.237\) \(\Q\) None \(8192\) \(-1016388\) \(-3341197410\) \(-51021361384\) \(-\) \(q+2^{13}q^{2}-1016388q^{3}+2^{26}q^{4}+\cdots\)

Decomposition of \(S_{28}^{\mathrm{old}}(\Gamma_0(2))\) into lower level spaces

\( S_{28}^{\mathrm{old}}(\Gamma_0(2)) \cong \) \(S_{28}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 2}\)