Properties

Label 3.20.a
Level 3
Weight 20
Character orbit a
Rep. character \(\chi_{3}(1,\cdot)\)
Character field \(\Q\)
Dimension 3
Newforms 2
Sturm bound 6
Trace bound 1

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Defining parameters

Level: \( N \) = \( 3 \)
Weight: \( k \) = \( 20 \)
Character orbit: \([\chi]\) = 3.a (trivial)
Character field: \(\Q\)
Newforms: \( 2 \)
Sturm bound: \(6\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{20}(\Gamma_0(3))\).

Total New Old
Modular forms 7 3 4
Cusp forms 5 3 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.
\(+\)\(2\)
\(-\)\(1\)

Trace form

\( 3q - 402q^{2} - 19683q^{3} + 1467012q^{4} + 9532410q^{5} - 35547498q^{6} - 81698520q^{7} + 820556664q^{8} + 1162261467q^{9} + O(q^{10}) \) \( 3q - 402q^{2} - 19683q^{3} + 1467012q^{4} + 9532410q^{5} - 35547498q^{6} - 81698520q^{7} + 820556664q^{8} + 1162261467q^{9} + 4780280340q^{10} - 9396929220q^{11} - 1534407948q^{12} - 88472801406q^{13} + 155230785312q^{14} - 49204941210q^{15} - 37037839344q^{16} - 449701045866q^{17} - 155743036578q^{18} + 917529390276q^{19} + 9364339167000q^{20} - 6091546960584q^{21} - 16615928152152q^{22} + 7268812701720q^{23} - 23549658112872q^{24} + 491067463125q^{25} + 96507401354196q^{26} - 7625597484987q^{27} - 162528726930240q^{28} + 293165772642642q^{29} - 246907577173500q^{30} - 1103509347456q^{31} + 59063350272480q^{32} + 76826947856292q^{33} + 68377350274524q^{34} - 763971710819280q^{35} + 568350506408868q^{36} + 214541768601690q^{37} - 1772527797374952q^{38} - 6457777952130q^{39} + 3082572607358160q^{40} + 36117739384494q^{41} + 5444971751141280q^{42} + 3956619191676252q^{43} - 16630934170959312q^{44} + 3693050943548490q^{45} - 11390312842270416q^{46} - 4071719279051664q^{47} - 5437331931370032q^{48} + 16981598133894843q^{49} + 49343632177008450q^{50} - 22089522102612246q^{51} - 3662935255751016q^{52} + 9478548542794410q^{53} - 13771829057886522q^{54} - 101689996818710520q^{55} + 83281437047844480q^{56} - 5643282616526628q^{57} + 61636794482767716q^{58} + 37546964215826604q^{59} - 88180690814996040q^{60} - 65839606734261198q^{61} + 28961995987437360q^{62} - 31651680568976280q^{63} - 253827091361167296q^{64} - 26788465728644100q^{65} + 446429936037796488q^{66} + 767364718585772724q^{67} - 1060003104102450936q^{68} + 49843425642458472q^{69} + 802706080735753920q^{70} - 28358482901250744q^{71} + 317900464019088696q^{72} - 787389978479424690q^{73} - 1150804422931511388q^{74} - 273785229241636725q^{75} - 696607169913035184q^{76} + 1265570460418319520q^{77} + 30091011686536644q^{78} - 676018458956583120q^{79} + 950313005686646880q^{80} + 450283905890997363q^{81} + 3675019929537285900q^{82} + 3077702007691905156q^{83} - 2148548003869326912q^{84} - 5568478266829874220q^{85} + 1640978749090426920q^{86} - 5290568598145265586q^{87} - 4713152322325163616q^{88} + 7296838195168516446q^{89} + 1851978546879886260q^{90} + 2149235336559905904q^{91} - 463273104918015840q^{92} - 1659745510007603040q^{93} + 3793350947439764160q^{94} - 3884054656531697160q^{95} + 9524122810436974176q^{96} + 976515183972078054q^{97} - 44582425294272288354q^{98} - 3640562913510788580q^{99} + O(q^{100}) \)

Decomposition of \(S_{20}^{\mathrm{new}}(\Gamma_0(3))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 3
3.20.a.a \(1\) \(6.865\) \(\Q\) None \(-1104\) \(19683\) \(3516270\) \(-195590584\) \(-\) \(q-1104q^{2}+3^{9}q^{3}+694528q^{4}+\cdots\)
3.20.a.b \(2\) \(6.865\) \(\Q(\sqrt{87481}) \) None \(702\) \(-39366\) \(6016140\) \(113892064\) \(+\) \(q+(351-\beta )q^{2}-3^{9}q^{3}+(386242-702\beta )q^{4}+\cdots\)

Decomposition of \(S_{20}^{\mathrm{old}}(\Gamma_0(3))\) into lower level spaces

\( S_{20}^{\mathrm{old}}(\Gamma_0(3)) \cong \) \(S_{20}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 2}\)