Properties

Label 3.18.a
Level 3
Weight 18
Character orbit a
Rep. character \(\chi_{3}(1,\cdot)\)
Character field \(\Q\)
Dimension 3
Newforms 2
Sturm bound 6
Trace bound 1

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 3 \)
Weight: \( k \) = \( 18 \)
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 \(M_{18}(\Gamma_0(3))\).

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.
\(+\)\(1\)
\(-\)\(2\)

Trace form

\(3q \) \(\mathstrut +\mathstrut 798q^{2} \) \(\mathstrut +\mathstrut 6561q^{3} \) \(\mathstrut +\mathstrut 87060q^{4} \) \(\mathstrut +\mathstrut 219306q^{5} \) \(\mathstrut +\mathstrut 2558790q^{6} \) \(\mathstrut +\mathstrut 3625008q^{7} \) \(\mathstrut +\mathstrut 85352520q^{8} \) \(\mathstrut +\mathstrut 129140163q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(3q \) \(\mathstrut +\mathstrut 798q^{2} \) \(\mathstrut +\mathstrut 6561q^{3} \) \(\mathstrut +\mathstrut 87060q^{4} \) \(\mathstrut +\mathstrut 219306q^{5} \) \(\mathstrut +\mathstrut 2558790q^{6} \) \(\mathstrut +\mathstrut 3625008q^{7} \) \(\mathstrut +\mathstrut 85352520q^{8} \) \(\mathstrut +\mathstrut 129140163q^{9} \) \(\mathstrut -\mathstrut 842747436q^{10} \) \(\mathstrut -\mathstrut 170181156q^{11} \) \(\mathstrut +\mathstrut 1745042292q^{12} \) \(\mathstrut -\mathstrut 2219808486q^{13} \) \(\mathstrut -\mathstrut 4688263536q^{14} \) \(\mathstrut +\mathstrut 3585022254q^{15} \) \(\mathstrut +\mathstrut 53159007504q^{16} \) \(\mathstrut -\mathstrut 79088732442q^{17} \) \(\mathstrut +\mathstrut 34351283358q^{18} \) \(\mathstrut +\mathstrut 158802194148q^{19} \) \(\mathstrut -\mathstrut 499895208456q^{20} \) \(\mathstrut +\mathstrut 297332237808q^{21} \) \(\mathstrut -\mathstrut 92958889464q^{22} \) \(\mathstrut -\mathstrut 407443266456q^{23} \) \(\mathstrut +\mathstrut 1150326640584q^{24} \) \(\mathstrut +\mathstrut 1060505718141q^{25} \) \(\mathstrut -\mathstrut 1574420844444q^{26} \) \(\mathstrut +\mathstrut 282429536481q^{27} \) \(\mathstrut -\mathstrut 551289349344q^{28} \) \(\mathstrut -\mathstrut 634167854814q^{29} \) \(\mathstrut -\mathstrut 5091450187644q^{30} \) \(\mathstrut +\mathstrut 4450615285992q^{31} \) \(\mathstrut +\mathstrut 11442856470048q^{32} \) \(\mathstrut -\mathstrut 11842118619948q^{33} \) \(\mathstrut -\mathstrut 24914627178660q^{34} \) \(\mathstrut +\mathstrut 35210876428320q^{35} \) \(\mathstrut +\mathstrut 3747647530260q^{36} \) \(\mathstrut -\mathstrut 9153723676782q^{37} \) \(\mathstrut +\mathstrut 70458442084920q^{38} \) \(\mathstrut -\mathstrut 18495380281122q^{39} \) \(\mathstrut -\mathstrut 91019811331152q^{40} \) \(\mathstrut -\mathstrut 98716763516658q^{41} \) \(\mathstrut +\mathstrut 25044209245584q^{42} \) \(\mathstrut +\mathstrut 177675896172444q^{43} \) \(\mathstrut -\mathstrut 140319636812688q^{44} \) \(\mathstrut +\mathstrut 9440404195626q^{45} \) \(\mathstrut +\mathstrut 302624033519952q^{46} \) \(\mathstrut -\mathstrut 456252236520672q^{47} \) \(\mathstrut +\mathstrut 315345544244496q^{48} \) \(\mathstrut +\mathstrut 262417912322283q^{49} \) \(\mathstrut +\mathstrut 30020883850914q^{50} \) \(\mathstrut +\mathstrut 68644329403554q^{51} \) \(\mathstrut -\mathstrut 776199022315752q^{52} \) \(\mathstrut -\mathstrut 378100541976246q^{53} \) \(\mathstrut +\mathstrut 110147519227590q^{54} \) \(\mathstrut -\mathstrut 441005798390904q^{55} \) \(\mathstrut +\mathstrut 1503419383717440q^{56} \) \(\mathstrut +\mathstrut 8561384733420q^{57} \) \(\mathstrut -\mathstrut 714120377553180q^{58} \) \(\mathstrut +\mathstrut 1464726939790332q^{59} \) \(\mathstrut -\mathstrut 3471798956959944q^{60} \) \(\mathstrut +\mathstrut 1425735374545338q^{61} \) \(\mathstrut +\mathstrut 2372754366104736q^{62} \) \(\mathstrut +\mathstrut 156044707998768q^{63} \) \(\mathstrut -\mathstrut 19526757111744q^{64} \) \(\mathstrut +\mathstrut 2591923576531308q^{65} \) \(\mathstrut -\mathstrut 2797917525081432q^{66} \) \(\mathstrut -\mathstrut 2884438056080892q^{67} \) \(\mathstrut -\mathstrut 2343067864452504q^{68} \) \(\mathstrut +\mathstrut 6573470832979704q^{69} \) \(\mathstrut -\mathstrut 2628913293194400q^{70} \) \(\mathstrut -\mathstrut 17492672971295784q^{71} \) \(\mathstrut +\mathstrut 3674146115086920q^{72} \) \(\mathstrut +\mathstrut 1361422453453854q^{73} \) \(\mathstrut +\mathstrut 14348572647202164q^{74} \) \(\mathstrut +\mathstrut 16618257189589599q^{75} \) \(\mathstrut +\mathstrut 18207808259019792q^{76} \) \(\mathstrut -\mathstrut 30109942873431744q^{77} \) \(\mathstrut -\mathstrut 11131743388510188q^{78} \) \(\mathstrut +\mathstrut 19123349308011960q^{79} \) \(\mathstrut -\mathstrut 15645855535606176q^{80} \) \(\mathstrut +\mathstrut 5559060566555523q^{81} \) \(\mathstrut -\mathstrut 13744587323604564q^{82} \) \(\mathstrut -\mathstrut 13463478996802716q^{83} \) \(\mathstrut -\mathstrut 28087569433031904q^{84} \) \(\mathstrut +\mathstrut 20429373327033492q^{85} \) \(\mathstrut +\mathstrut 90856812547402824q^{86} \) \(\mathstrut -\mathstrut 2011473245489130q^{87} \) \(\mathstrut -\mathstrut 96641522137971360q^{88} \) \(\mathstrut -\mathstrut 31911563984537682q^{89} \) \(\mathstrut -\mathstrut 36277513750957356q^{90} \) \(\mathstrut -\mathstrut 11007612437859168q^{91} \) \(\mathstrut +\mathstrut 301981464587455968q^{92} \) \(\mathstrut +\mathstrut 15424213061762712q^{93} \) \(\mathstrut -\mathstrut 135193059999506592q^{94} \) \(\mathstrut -\mathstrut 105329716438805256q^{95} \) \(\mathstrut -\mathstrut 9118853133499872q^{96} \) \(\mathstrut +\mathstrut 158195160856210758q^{97} \) \(\mathstrut -\mathstrut 129362780127951954q^{98} \) \(\mathstrut -\mathstrut 7325740741789476q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{18}^{\mathrm{new}}(\Gamma_0(3))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 3
3.18.a.a \(1\) \(5.497\) \(\Q\) None \(204\) \(-6561\) \(-163554\) \(-20846560\) \(+\) \(q+204q^{2}-3^{8}q^{3}-89456q^{4}-163554q^{5}+\cdots\)
3.18.a.b \(2\) \(5.497\) \(\Q(\sqrt{14569}) \) None \(594\) \(13122\) \(382860\) \(24471568\) \(-\) \(q+(297-\beta )q^{2}+3^{8}q^{3}+(88258-594\beta )q^{4}+\cdots\)

Decomposition of \(S_{18}^{\mathrm{old}}(\Gamma_0(3))\) into lower level spaces

\( S_{18}^{\mathrm{old}}(\Gamma_0(3)) \cong \) \(S_{18}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 2}\)