Properties

Label 6.18.a
Level 6
Weight 18
Character orbit a
Rep. character \(\chi_{6}(1,\cdot)\)
Character field \(\Q\)
Dimension 3
Newforms 3
Sturm bound 18
Trace bound 3

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Defining parameters

Level: \( N \) = \( 6 = 2 \cdot 3 \)
Weight: \( k \) = \( 18 \)
Character orbit: \([\chi]\) = 6.a (trivial)
Character field: \(\Q\)
Newforms: \( 3 \)
Sturm bound: \(18\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{18}(\Gamma_0(6))\).

Total New Old
Modular forms 19 3 16
Cusp forms 15 3 12
Eisenstein series 4 0 4

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

\(2\)\(3\)FrickeDim.
\(+\)\(+\)\(+\)\(1\)
\(+\)\(-\)\(-\)\(1\)
\(-\)\(+\)\(-\)\(1\)
Plus space\(+\)\(1\)
Minus space\(-\)\(2\)

Trace form

\(3q \) \(\mathstrut -\mathstrut 256q^{2} \) \(\mathstrut -\mathstrut 6561q^{3} \) \(\mathstrut +\mathstrut 196608q^{4} \) \(\mathstrut +\mathstrut 373314q^{5} \) \(\mathstrut -\mathstrut 1679616q^{6} \) \(\mathstrut +\mathstrut 20293512q^{7} \) \(\mathstrut -\mathstrut 16777216q^{8} \) \(\mathstrut +\mathstrut 129140163q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(3q \) \(\mathstrut -\mathstrut 256q^{2} \) \(\mathstrut -\mathstrut 6561q^{3} \) \(\mathstrut +\mathstrut 196608q^{4} \) \(\mathstrut +\mathstrut 373314q^{5} \) \(\mathstrut -\mathstrut 1679616q^{6} \) \(\mathstrut +\mathstrut 20293512q^{7} \) \(\mathstrut -\mathstrut 16777216q^{8} \) \(\mathstrut +\mathstrut 129140163q^{9} \) \(\mathstrut -\mathstrut 197789184q^{10} \) \(\mathstrut +\mathstrut 784792212q^{11} \) \(\mathstrut -\mathstrut 429981696q^{12} \) \(\mathstrut +\mathstrut 1602597066q^{13} \) \(\mathstrut +\mathstrut 7584004096q^{14} \) \(\mathstrut -\mathstrut 3396537846q^{15} \) \(\mathstrut +\mathstrut 12884901888q^{16} \) \(\mathstrut +\mathstrut 63064451862q^{17} \) \(\mathstrut -\mathstrut 11019960576q^{18} \) \(\mathstrut -\mathstrut 112465967988q^{19} \) \(\mathstrut +\mathstrut 24465506304q^{20} \) \(\mathstrut -\mathstrut 246522226680q^{21} \) \(\mathstrut -\mathstrut 136621919232q^{22} \) \(\mathstrut +\mathstrut 502204534536q^{23} \) \(\mathstrut -\mathstrut 110075314176q^{24} \) \(\mathstrut -\mathstrut 1827528895779q^{25} \) \(\mathstrut +\mathstrut 1754059256320q^{26} \) \(\mathstrut -\mathstrut 282429536481q^{27} \) \(\mathstrut +\mathstrut 1329955602432q^{28} \) \(\mathstrut -\mathstrut 3268241365782q^{29} \) \(\mathstrut +\mathstrut 1540184357376q^{30} \) \(\mathstrut +\mathstrut 4428127804848q^{31} \) \(\mathstrut -\mathstrut 1099511627776q^{32} \) \(\mathstrut +\mathstrut 10063371421188q^{33} \) \(\mathstrut +\mathstrut 2058013011456q^{34} \) \(\mathstrut -\mathstrut 1795311930576q^{35} \) \(\mathstrut +\mathstrut 8463329722368q^{36} \) \(\mathstrut -\mathstrut 34265998294158q^{37} \) \(\mathstrut -\mathstrut 4158262154240q^{38} \) \(\mathstrut +\mathstrut 26240907525138q^{39} \) \(\mathstrut -\mathstrut 12962311962624q^{40} \) \(\mathstrut -\mathstrut 49334969807970q^{41} \) \(\mathstrut -\mathstrut 20734268295168q^{42} \) \(\mathstrut -\mathstrut 78330110674764q^{43} \) \(\mathstrut +\mathstrut 51432142405632q^{44} \) \(\mathstrut +\mathstrut 16069943603394q^{45} \) \(\mathstrut -\mathstrut 254423840495616q^{46} \) \(\mathstrut +\mathstrut 609853163061552q^{47} \) \(\mathstrut -\mathstrut 28179280429056q^{48} \) \(\mathstrut +\mathstrut 15522206736555q^{49} \) \(\mathstrut +\mathstrut 97630780039424q^{50} \) \(\mathstrut +\mathstrut 18993259062990q^{51} \) \(\mathstrut +\mathstrut 105027801317376q^{52} \) \(\mathstrut -\mathstrut 201393768300174q^{53} \) \(\mathstrut -\mathstrut 72301961339136q^{54} \) \(\mathstrut -\mathstrut 431372192162760q^{55} \) \(\mathstrut +\mathstrut 497025292435456q^{56} \) \(\mathstrut +\mathstrut 813714677695260q^{57} \) \(\mathstrut -\mathstrut 330891509767680q^{58} \) \(\mathstrut -\mathstrut 3978739340006460q^{59} \) \(\mathstrut -\mathstrut 222595504275456q^{60} \) \(\mathstrut +\mathstrut 2545999496260602q^{61} \) \(\mathstrut +\mathstrut 1093581265543168q^{62} \) \(\mathstrut +\mathstrut 873569149174152q^{63} \) \(\mathstrut +\mathstrut 844424930131968q^{64} \) \(\mathstrut -\mathstrut 4546522505652132q^{65} \) \(\mathstrut -\mathstrut 2997996227693568q^{66} \) \(\mathstrut +\mathstrut 3306215142940092q^{67} \) \(\mathstrut +\mathstrut 4132991917228032q^{68} \) \(\mathstrut -\mathstrut 1075810753198296q^{69} \) \(\mathstrut -\mathstrut 2091756079263744q^{70} \) \(\mathstrut -\mathstrut 718407280036008q^{71} \) \(\mathstrut -\mathstrut 722204136308736q^{72} \) \(\mathstrut +\mathstrut 5920503858987486q^{73} \) \(\mathstrut +\mathstrut 19406546444491264q^{74} \) \(\mathstrut +\mathstrut 2047501942916481q^{75} \) \(\mathstrut -\mathstrut 7370569678061568q^{76} \) \(\mathstrut -\mathstrut 8870296929042336q^{77} \) \(\mathstrut -\mathstrut 20917802780757504q^{78} \) \(\mathstrut +\mathstrut 24057256930293696q^{79} \) \(\mathstrut +\mathstrut 1603371421138944q^{80} \) \(\mathstrut +\mathstrut 5559060566555523q^{81} \) \(\mathstrut -\mathstrut 37354157530163712q^{82} \) \(\mathstrut -\mathstrut 33050904413718324q^{83} \) \(\mathstrut -\mathstrut 16156080647700480q^{84} \) \(\mathstrut -\mathstrut 13005613799191836q^{85} \) \(\mathstrut +\mathstrut 59034957775885312q^{86} \) \(\mathstrut +\mathstrut 69098564553893010q^{87} \) \(\mathstrut -\mathstrut 8953654098788352q^{88} \) \(\mathstrut -\mathstrut 114944772828400434q^{89} \) \(\mathstrut -\mathstrut 8514175820465664q^{90} \) \(\mathstrut +\mathstrut 59742068442608496q^{91} \) \(\mathstrut +\mathstrut 32912476375351296q^{92} \) \(\mathstrut +\mathstrut 61239254144690448q^{93} \) \(\mathstrut -\mathstrut 4534883594514432q^{94} \) \(\mathstrut -\mathstrut 22335787055851896q^{95} \) \(\mathstrut -\mathstrut 7213895789838336q^{96} \) \(\mathstrut -\mathstrut 3753776454789018q^{97} \) \(\mathstrut +\mathstrut 195877499937900288q^{98} \) \(\mathstrut +\mathstrut 33782731392936852q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{18}^{\mathrm{new}}(\Gamma_0(6))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 3
6.18.a.a \(1\) \(10.993\) \(\Q\) None \(-256\) \(-6561\) \(645150\) \(3974432\) \(+\) \(+\) \(q-2^{8}q^{2}-3^{8}q^{3}+2^{16}q^{4}+645150q^{5}+\cdots\)
6.18.a.b \(1\) \(10.993\) \(\Q\) None \(-256\) \(6561\) \(-72186\) \(-8640184\) \(+\) \(-\) \(q-2^{8}q^{2}+3^{8}q^{3}+2^{16}q^{4}-72186q^{5}+\cdots\)
6.18.a.c \(1\) \(10.993\) \(\Q\) None \(256\) \(-6561\) \(-199650\) \(24959264\) \(-\) \(+\) \(q+2^{8}q^{2}-3^{8}q^{3}+2^{16}q^{4}-199650q^{5}+\cdots\)

Decomposition of \(S_{18}^{\mathrm{old}}(\Gamma_0(6))\) into lower level spaces

\( S_{18}^{\mathrm{old}}(\Gamma_0(6)) \cong \) \(S_{18}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{18}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 2}\)\(\oplus\)\(S_{18}^{\mathrm{new}}(\Gamma_0(3))\)\(^{\oplus 2}\)