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

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

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

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