Properties

Label 3.37.b
Level 3
Weight 37
Character orbit b
Rep. character \(\chi_{3}(2,\cdot)\)
Character field \(\Q\)
Dimension 11
Newforms 2
Sturm bound 12
Trace bound 1

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Defining parameters

Level: \( N \) = \( 3 \)
Weight: \( k \) = \( 37 \)
Character orbit: \([\chi]\) = 3.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 3 \)
Character field: \(\Q\)
Newforms: \( 2 \)
Sturm bound: \(12\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{37}(3, [\chi])\).

Total New Old
Modular forms 13 13 0
Cusp forms 11 11 0
Eisenstein series 2 2 0

Trace form

\(11q \) \(\mathstrut -\mathstrut 164736261q^{3} \) \(\mathstrut -\mathstrut 366480813328q^{4} \) \(\mathstrut +\mathstrut 77238909590832q^{6} \) \(\mathstrut +\mathstrut 1529656139588998q^{7} \) \(\mathstrut +\mathstrut 219422675471657499q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(11q \) \(\mathstrut -\mathstrut 164736261q^{3} \) \(\mathstrut -\mathstrut 366480813328q^{4} \) \(\mathstrut +\mathstrut 77238909590832q^{6} \) \(\mathstrut +\mathstrut 1529656139588998q^{7} \) \(\mathstrut +\mathstrut 219422675471657499q^{9} \) \(\mathstrut +\mathstrut 976353968400999840q^{10} \) \(\mathstrut +\mathstrut 12713663984972326704q^{12} \) \(\mathstrut -\mathstrut 26664183895525067642q^{13} \) \(\mathstrut +\mathstrut 7346306914204243680q^{15} \) \(\mathstrut +\mathstrut 12912742276961748775040q^{16} \) \(\mathstrut -\mathstrut 116380061882656121268000q^{18} \) \(\mathstrut +\mathstrut 138821577295896839366518q^{19} \) \(\mathstrut -\mathstrut 2247956081834234679653850q^{21} \) \(\mathstrut +\mathstrut 6375713195756021276887200q^{22} \) \(\mathstrut -\mathstrut 18479722715707703137259904q^{24} \) \(\mathstrut +\mathstrut 7279508127194401821131675q^{25} \) \(\mathstrut +\mathstrut 95231216966669978862527019q^{27} \) \(\mathstrut -\mathstrut 391577988767589793638714272q^{28} \) \(\mathstrut +\mathstrut 832077359475776822335514400q^{30} \) \(\mathstrut -\mathstrut 1733608557857573255379602138q^{31} \) \(\mathstrut -\mathstrut 1833168501223628340439879200q^{33} \) \(\mathstrut +\mathstrut 11044532239488942328340194176q^{34} \) \(\mathstrut -\mathstrut 21948402658393775440817520912q^{36} \) \(\mathstrut +\mathstrut 12786450877411433164392216358q^{37} \) \(\mathstrut -\mathstrut 9936827303902532409454966170q^{39} \) \(\mathstrut +\mathstrut 14850499435375431475622142720q^{40} \) \(\mathstrut +\mathstrut 551003488989169331884355647200q^{42} \) \(\mathstrut -\mathstrut 515487319179727929010406869802q^{43} \) \(\mathstrut -\mathstrut 75992211973807694886478996800q^{45} \) \(\mathstrut -\mathstrut 887182867438274648036289139776q^{46} \) \(\mathstrut -\mathstrut 4346257047411219928317289501056q^{48} \) \(\mathstrut +\mathstrut 9110404204240350847814031518529q^{49} \) \(\mathstrut -\mathstrut 2349347159740543712848217109888q^{51} \) \(\mathstrut -\mathstrut 13203626071464804773830678836512q^{52} \) \(\mathstrut +\mathstrut 35390782846752825865826083751568q^{54} \) \(\mathstrut -\mathstrut 30568574550133842572339360395200q^{55} \) \(\mathstrut +\mathstrut 96963716675033228271210975522198q^{57} \) \(\mathstrut -\mathstrut 112605799975805654976196455444000q^{58} \) \(\mathstrut +\mathstrut 19469866547367779716225803605760q^{60} \) \(\mathstrut +\mathstrut 66999347224237022458014520403782q^{61} \) \(\mathstrut -\mathstrut 20218845986102637586445162314842q^{63} \) \(\mathstrut -\mathstrut 304236018528391125615295992251392q^{64} \) \(\mathstrut +\mathstrut 1808913396822349027193824888380960q^{66} \) \(\mathstrut -\mathstrut 3004194906649294236056896403510282q^{67} \) \(\mathstrut +\mathstrut 5226032060124551681525948207907648q^{69} \) \(\mathstrut -\mathstrut 11529100185846942980259125797809600q^{70} \) \(\mathstrut +\mathstrut 19879821238248816464160255047788800q^{72} \) \(\mathstrut -\mathstrut 10390545366461872145216469125969162q^{73} \) \(\mathstrut +\mathstrut 21376990929305061495027761443252875q^{75} \) \(\mathstrut -\mathstrut 39862084315848733842646101136440224q^{76} \) \(\mathstrut +\mathstrut 66756441224105756984056960627624800q^{78} \) \(\mathstrut -\mathstrut 71385979381146382550075928433902362q^{79} \) \(\mathstrut +\mathstrut 124901631937240804827635146103482731q^{81} \) \(\mathstrut -\mathstrut 295731520386077266321378186874491200q^{82} \) \(\mathstrut +\mathstrut 565465498335095720662452392509252320q^{84} \) \(\mathstrut -\mathstrut 416995278796335191384264774379644160q^{85} \) \(\mathstrut +\mathstrut 502161755301600073278417594406864800q^{87} \) \(\mathstrut -\mathstrut 1043368725545479380062123692743456000q^{88} \) \(\mathstrut +\mathstrut 1148239664725140620121403824942828960q^{90} \) \(\mathstrut -\mathstrut 676075249402808126607982688855079700q^{91} \) \(\mathstrut +\mathstrut 1136822552118204808049516782296691398q^{93} \) \(\mathstrut -\mathstrut 1775468098694354855547362712124166784q^{94} \) \(\mathstrut +\mathstrut 2402404280227868861578148783194622976q^{96} \) \(\mathstrut -\mathstrut 1638469121614694224091416117067972522q^{97} \) \(\mathstrut +\mathstrut 2995711137935834844910948248309577920q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{37}^{\mathrm{new}}(3, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
3.37.b.a \(1\) \(24.627\) \(\Q\) \(\Q(\sqrt{-3}) \) \(0\) \(387420489\) \(0\) \(27\!\cdots\!98\) \(q+3^{18}q^{3}+2^{36}q^{4}+2757049053441698q^{7}+\cdots\)
3.37.b.b \(10\) \(24.627\) \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None \(0\) \(-552156750\) \(0\) \(-1\!\cdots\!00\) \(q+\beta _{1}q^{2}+(-55215675-69\beta _{1}-\beta _{2}+\cdots)q^{3}+\cdots\)