Properties

Label 3.26.a
Level 3
Weight 26
Character orbit a
Rep. character \(\chi_{3}(1,\cdot)\)
Character field \(\Q\)
Dimension 5
Newforms 2
Sturm bound 8
Trace bound 1

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Defining parameters

Level: \( N \) = \( 3 \)
Weight: \( k \) = \( 26 \)
Character orbit: \([\chi]\) = 3.a (trivial)
Character field: \(\Q\)
Newforms: \( 2 \)
Sturm bound: \(8\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{26}(\Gamma_0(3))\).

Total New Old
Modular forms 9 5 4
Cusp forms 7 5 2
Eisenstein series 2 0 2

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

\(3\)Dim.
\(+\)\(2\)
\(-\)\(3\)

Trace form

\(5q \) \(\mathstrut -\mathstrut 4002q^{2} \) \(\mathstrut +\mathstrut 531441q^{3} \) \(\mathstrut +\mathstrut 116355284q^{4} \) \(\mathstrut +\mathstrut 407709006q^{5} \) \(\mathstrut -\mathstrut 1782453114q^{6} \) \(\mathstrut -\mathstrut 39309958472q^{7} \) \(\mathstrut -\mathstrut 291312800760q^{8} \) \(\mathstrut +\mathstrut 1412147682405q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(5q \) \(\mathstrut -\mathstrut 4002q^{2} \) \(\mathstrut +\mathstrut 531441q^{3} \) \(\mathstrut +\mathstrut 116355284q^{4} \) \(\mathstrut +\mathstrut 407709006q^{5} \) \(\mathstrut -\mathstrut 1782453114q^{6} \) \(\mathstrut -\mathstrut 39309958472q^{7} \) \(\mathstrut -\mathstrut 291312800760q^{8} \) \(\mathstrut +\mathstrut 1412147682405q^{9} \) \(\mathstrut +\mathstrut 6147590052564q^{10} \) \(\mathstrut -\mathstrut 24134783749332q^{11} \) \(\mathstrut +\mathstrut 34618009344372q^{12} \) \(\mathstrut +\mathstrut 142994137728454q^{13} \) \(\mathstrut +\mathstrut 281682671800272q^{14} \) \(\mathstrut -\mathstrut 390085403083146q^{15} \) \(\mathstrut -\mathstrut 378809104605424q^{16} \) \(\mathstrut +\mathstrut 6183897836895738q^{17} \) \(\mathstrut -\mathstrut 1130283004996962q^{18} \) \(\mathstrut +\mathstrut 9614719536266548q^{19} \) \(\mathstrut -\mathstrut 77002472769731976q^{20} \) \(\mathstrut +\mathstrut 10663264277029944q^{21} \) \(\mathstrut +\mathstrut 26761044671198856q^{22} \) \(\mathstrut +\mathstrut 84783342948789624q^{23} \) \(\mathstrut -\mathstrut 130050447316112376q^{24} \) \(\mathstrut -\mathstrut 99189140617918789q^{25} \) \(\mathstrut +\mathstrut 147840851396154660q^{26} \) \(\mathstrut +\mathstrut 150094635296999121q^{27} \) \(\mathstrut +\mathstrut 2191353545749530016q^{28} \) \(\mathstrut -\mathstrut 2502539841117381594q^{29} \) \(\mathstrut +\mathstrut 5622001512394220676q^{30} \) \(\mathstrut +\mathstrut 954876643541101456q^{31} \) \(\mathstrut -\mathstrut 21954104161995916512q^{32} \) \(\mathstrut +\mathstrut 6505256343289039452q^{33} \) \(\mathstrut -\mathstrut 1854027316439415972q^{34} \) \(\mathstrut -\mathstrut 10429196484047083440q^{35} \) \(\mathstrut +\mathstrut 32862168927235115604q^{36} \) \(\mathstrut +\mathstrut 69152558317233520798q^{37} \) \(\mathstrut -\mathstrut 318832149907630898760q^{38} \) \(\mathstrut +\mathstrut 187748226389447040366q^{39} \) \(\mathstrut +\mathstrut 524570550230746268208q^{40} \) \(\mathstrut -\mathstrut 597401254139237025294q^{41} \) \(\mathstrut +\mathstrut 652099689206655819984q^{42} \) \(\mathstrut +\mathstrut 272662541690214829324q^{43} \) \(\mathstrut -\mathstrut 1971518245902562385040q^{44} \) \(\mathstrut +\mathstrut 115149065583709247886q^{45} \) \(\mathstrut +\mathstrut 1122026015545224939216q^{46} \) \(\mathstrut -\mathstrut 1317381085286900621232q^{47} \) \(\mathstrut +\mathstrut 2746532159144226606096q^{48} \) \(\mathstrut +\mathstrut 1759829504488690145757q^{49} \) \(\mathstrut -\mathstrut 8748160206152998259166q^{50} \) \(\mathstrut +\mathstrut 3772100494132165133010q^{51} \) \(\mathstrut +\mathstrut 456938492077599979288q^{52} \) \(\mathstrut +\mathstrut 562007823967323032094q^{53} \) \(\mathstrut -\mathstrut 503417406786135051834q^{54} \) \(\mathstrut +\mathstrut 9480212039078845571016q^{55} \) \(\mathstrut +\mathstrut 17341408417833155830080q^{56} \) \(\mathstrut -\mathstrut 9661681057738447542780q^{57} \) \(\mathstrut -\mathstrut 31236506660525159082780q^{58} \) \(\mathstrut +\mathstrut 32201402276983996948092q^{59} \) \(\mathstrut -\mathstrut 49422263670781084662984q^{60} \) \(\mathstrut -\mathstrut 35650844679114201340778q^{61} \) \(\mathstrut +\mathstrut 75489372062508933475296q^{62} \) \(\mathstrut -\mathstrut 11102293350334319017032q^{63} \) \(\mathstrut -\mathstrut 27045286271674562960320q^{64} \) \(\mathstrut +\mathstrut 77231798191654195817028q^{65} \) \(\mathstrut -\mathstrut 85732038362088400645080q^{66} \) \(\mathstrut -\mathstrut 83472346788757030801532q^{67} \) \(\mathstrut +\mathstrut 303643995600011618215656q^{68} \) \(\mathstrut -\mathstrut 103047076779758115574248q^{69} \) \(\mathstrut -\mathstrut 183924416222173820086560q^{70} \) \(\mathstrut +\mathstrut 383358431003395605774120q^{71} \) \(\mathstrut -\mathstrut 82275339289628704525560q^{72} \) \(\mathstrut +\mathstrut 73225288673685458167474q^{73} \) \(\mathstrut -\mathstrut 525224845214049550608588q^{74} \) \(\mathstrut +\mathstrut 355922403636181174181199q^{75} \) \(\mathstrut +\mathstrut 235955349730005758966032q^{76} \) \(\mathstrut -\mathstrut 1585949533175292431417184q^{77} \) \(\mathstrut +\mathstrut 893336260671388338546132q^{78} \) \(\mathstrut +\mathstrut 760218847521043733000320q^{79} \) \(\mathstrut -\mathstrut 2337439770619285359693216q^{80} \) \(\mathstrut +\mathstrut 398832215384362549316805q^{81} \) \(\mathstrut +\mathstrut 3692827177594097874372396q^{82} \) \(\mathstrut -\mathstrut 936536331267412457078796q^{83} \) \(\mathstrut +\mathstrut 1404155691579558819001248q^{84} \) \(\mathstrut -\mathstrut 3147845920523300761594308q^{85} \) \(\mathstrut -\mathstrut 2134843460602993978402872q^{86} \) \(\mathstrut +\mathstrut 1329414084492021374701230q^{87} \) \(\mathstrut +\mathstrut 2854164686565702215990880q^{88} \) \(\mathstrut -\mathstrut 1229086967010673719324222q^{89} \) \(\mathstrut +\mathstrut 1736261009020856945587284q^{90} \) \(\mathstrut +\mathstrut 6852388264039769311678736q^{91} \) \(\mathstrut -\mathstrut 727913052083093798383392q^{92} \) \(\mathstrut -\mathstrut 635639340921259388051088q^{93} \) \(\mathstrut -\mathstrut 16997751485168022275936544q^{94} \) \(\mathstrut +\mathstrut 2339560291274106904595064q^{95} \) \(\mathstrut -\mathstrut 13229430648783271528771296q^{96} \) \(\mathstrut -\mathstrut 17623548522544072790935382q^{97} \) \(\mathstrut +\mathstrut 38198701780426394919644526q^{98} \) \(\mathstrut -\mathstrut 6816375787393008053380692q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{26}^{\mathrm{new}}(\Gamma_0(3))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 3
3.26.a.a \(2\) \(11.880\) \(\Q(\sqrt{1287001}) \) None \(-324\) \(-1062882\) \(570861756\) \(-29687385728\) \(+\) \(q+(-162-\beta )q^{2}-3^{12}q^{3}+(12803848+\cdots)q^{4}+\cdots\)
3.26.a.b \(3\) \(11.880\) \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None \(-3678\) \(1594323\) \(-163152750\) \(-9622572744\) \(-\) \(q+(-1226+\beta _{1})q^{2}+3^{12}q^{3}+(30249196+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{26}^{\mathrm{old}}(\Gamma_0(3))\) into lower level spaces

\( S_{26}^{\mathrm{old}}(\Gamma_0(3)) \cong \) \(S_{26}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 2}\)