Properties

Label 6.26.a
Level $6$
Weight $26$
Character orbit 6.a
Rep. character $\chi_{6}(1,\cdot)$
Character field $\Q$
Dimension $3$
Newform subspaces $3$
Sturm bound $26$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 6 = 2 \cdot 3 \)
Weight: \( k \) \(=\) \( 26 \)
Character orbit: \([\chi]\) \(=\) 6.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(26\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{26}(\Gamma_0(6))\).

Total New Old
Modular forms 27 3 24
Cusp forms 23 3 20
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

\( 3 q - 4096 q^{2} - 531441 q^{3} + 50331648 q^{4} - 501656766 q^{5} - 2176782336 q^{6} + 69400471272 q^{7} - 68719476736 q^{8} + 847288609443 q^{9} + O(q^{10}) \) \( 3 q - 4096 q^{2} - 531441 q^{3} + 50331648 q^{4} - 501656766 q^{5} - 2176782336 q^{6} + 69400471272 q^{7} - 68719476736 q^{8} + 847288609443 q^{9} - 4493305995264 q^{10} + 22845670039572 q^{11} - 8916100448256 q^{12} + 30450821742186 q^{13} - 219036270362624 q^{14} + 894153858385194 q^{15} + 844424930131968 q^{16} - 2385348946098858 q^{17} - 1156831381426176 q^{18} + 14104520876259852 q^{19} - 8416403921043456 q^{20} + 24613351854751080 q^{21} - 107995172524572672 q^{22} + 90333258211231176 q^{23} - 36520347436056576 q^{24} + 179162969991624381 q^{25} + 1220381575178690560 q^{26} - 150094635296999121 q^{27} + 1164346697032138752 q^{28} + 1409962486011973098 q^{29} - 182529585552973824 q^{30} + 5011711128039266448 q^{31} - 1152921504606846976 q^{32} - 2049841041647699772 q^{33} - 9705974252413722624 q^{34} + 26747683128100335984 q^{35} + 14215144014964850688 q^{36} - 17841936187683837678 q^{37} + 29296189221128028160 q^{38} - 159637895319333671982 q^{39} - 75385165236639105024 q^{40} + 373095228756349618590 q^{41} - 135481154614242213888 q^{42} - 807705677121179694924 q^{43} + 383286740918627991552 q^{44} - 141682687893937480446 q^{45} + 257799298522010517504 q^{46} - 955354718093634799248 q^{47} - 149587343098087735296 q^{48} - 599504111087003176725 q^{49} + 2058813302224954855424 q^{50} - 1417288889144960813970 q^{51} + 510880013746150834176 q^{52} + 8438280139556134306866 q^{53} - 614787626176508399616 q^{54} + 2588624858111147701560 q^{55} - 3674818819708141174784 q^{56} + 4694216688665844852060 q^{57} + 13961667263690936033280 q^{58} - 12476240604677288704380 q^{59} + 15001412419361810939904 q^{60} - 47676504789072080640678 q^{61} + 22892029317353709764608 q^{62} + 19600742932913916473832 q^{63} + 14167099448608935641088 q^{64} - 211293886085125475007972 q^{65} + 16059160391995653046272 q^{66} + 155812398195160308831612 q^{67} - 40019514504072898019328 q^{68} + 72463045035057094324584 q^{69} - 161697101980570235633664 q^{70} + 231460549503115767437592 q^{71} - 19408409961765342806016 q^{72} - 509887093613858387320674 q^{73} + 142075886430112696213504 q^{74} - 41454695422978740214479 q^{75} + 236634593317520809132032 q^{76} + 589407700813414856481504 q^{77} - 60968796351623000285184 q^{78} - 414060540359766911069664 q^{79} - 141203826526593006698496 q^{80} + 239299329230617529590083 q^{81} - 733984197974512175849472 q^{82} + 3022601781066725328158796 q^{83} + 412943520551159495393280 q^{84} - 328322749563918279410076 q^{85} + 308926951133286289457152 q^{86} + 400034407310802067532850 q^{87} - 1811858336402021025841152 q^{88} - 517117566735674597176434 q^{89} - 1269042329509709901225984 q^{90} - 6497119011338798607107664 q^{91} + 1515540584993599065686016 q^{92} + 2278005800496963545970288 q^{93} - 5066286344303250936102912 q^{94} + 615731847672906532122504 q^{95} - 612709757329767363772416 q^{96} + 7242920934093037399808742 q^{97} - 8011092758225737478541312 q^{98} + 6452291999874188887626132 q^{99} + O(q^{100}) \)

Decomposition of \(S_{26}^{\mathrm{new}}(\Gamma_0(6))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 3
6.26.a.a \(1\) \(23.760\) \(\Q\) None \(-4096\) \(-531441\) \(-292754850\) \(3580644032\) \(+\) \(+\) \(q-2^{12}q^{2}-3^{12}q^{3}+2^{24}q^{4}-292754850q^{5}+\cdots\)
6.26.a.b \(1\) \(23.760\) \(\Q\) None \(-4096\) \(531441\) \(590425734\) \(57857417576\) \(+\) \(-\) \(q-2^{12}q^{2}+3^{12}q^{3}+2^{24}q^{4}+590425734q^{5}+\cdots\)
6.26.a.c \(1\) \(23.760\) \(\Q\) None \(4096\) \(-531441\) \(-799327650\) \(7962409664\) \(-\) \(+\) \(q+2^{12}q^{2}-3^{12}q^{3}+2^{24}q^{4}-799327650q^{5}+\cdots\)

Decomposition of \(S_{26}^{\mathrm{old}}(\Gamma_0(6))\) into lower level spaces

\( S_{26}^{\mathrm{old}}(\Gamma_0(6)) \cong \) \(S_{26}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{26}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 2}\)\(\oplus\)\(S_{26}^{\mathrm{new}}(\Gamma_0(3))\)\(^{\oplus 2}\)