Properties

Label 2.28.a
Level $2$
Weight $28$
Character orbit 2.a
Rep. character $\chi_{2}(1,\cdot)$
Character field $\Q$
Dimension $2$
Newform subspaces $2$
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: \(\Q\)
Newform subspaces: \( 2 \)
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 and the Fricke involution.

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

Trace form

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

Decomposition of \(S_{28}^{\mathrm{new}}(\Gamma_0(2))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2
2.28.a.a 2.a 1.a $1$ $9.237$ \(\Q\) None \(-8192\) \(3984828\) \(-2851889250\) \(368721063704\) $+$ $\mathrm{SU}(2)$ \(q-2^{13}q^{2}+3984828q^{3}+2^{26}q^{4}+\cdots\)
2.28.a.b 2.a 1.a $1$ $9.237$ \(\Q\) None \(8192\) \(-1016388\) \(-3341197410\) \(-51021361384\) $-$ $\mathrm{SU}(2)$ \(q+2^{13}q^{2}-1016388q^{3}+2^{26}q^{4}+\cdots\)

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

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