Properties

Label 21.27.h
Level $21$
Weight $27$
Character orbit 21.h
Rep. character $\chi_{21}(2,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $134$
Newform subspaces $2$
Sturm bound $72$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 21 = 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 27 \)
Character orbit: \([\chi]\) \(=\) 21.h (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 21 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(72\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{27}(21, [\chi])\).

Total New Old
Modular forms 142 142 0
Cusp forms 134 134 0
Eisenstein series 8 8 0

Trace form

\( 134 q - q^{3} + 2147483646 q^{4} + 23185031164 q^{6} - 170398305279 q^{7} - 1888965480679 q^{9} + O(q^{10}) \) \( 134 q - q^{3} + 2147483646 q^{4} + 23185031164 q^{6} - 170398305279 q^{7} - 1888965480679 q^{9} - 7069944086530 q^{10} + 96313602199516 q^{12} + 986151663995718 q^{13} - 160542130108300 q^{15} - 64243065460481034 q^{16} - 16597497731878580 q^{18} + 92529012535920645 q^{19} + 37815168535618342 q^{21} - 497959263743674900 q^{22} + 3632954766065572782 q^{24} + 19812515265634585935 q^{25} + 2036831441791265138 q^{27} + 7982132707173499274 q^{28} + 30370018091633794780 q^{30} + 12965977460980649747 q^{31} - 57958060332265813390 q^{33} - 681405681947402082480 q^{34} - 632374220215102206092 q^{36} + 96251514233790940289 q^{37} - 797259492363987020083 q^{39} + 749507617849412080650 q^{40} - 5910218287172912165110 q^{42} - 6107199000241429959146 q^{43} + 641297025013460059400 q^{45} - 1093604647969819535268 q^{46} - 27670612390320322604408 q^{48} - 34193134037607343305499 q^{49} - 53709331751911258366296 q^{51} + 28190966548266121403344 q^{52} - 63358738410344291379290 q^{54} - 78611544455342540641340 q^{55} + 13078009079089863779582 q^{57} - 276968925637217172004030 q^{58} - 90268257660620471097650 q^{60} - 171627227573608168463382 q^{61} - 90314446122383320358513 q^{63} - 4761497514088671773828788 q^{64} - 1440731638813106361501008 q^{66} - 522346626446709743877291 q^{67} + 5089361868011274034708920 q^{69} + 3297011461077369102905950 q^{70} + 827002729616389131510120 q^{72} + 2699748914661919096548941 q^{73} - 3037973746358445948844565 q^{75} + 20914509519885393129924664 q^{76} + 47184215924861958049801240 q^{78} - 14230997890364151695437997 q^{79} + 10881651825389377760522045 q^{81} + 50850184487998228013805460 q^{82} - 83775655931975713416254872 q^{84} - 80542708263248362337966640 q^{85} - 34387245587617132086455110 q^{87} - 72157697352048937495690290 q^{88} + 112557118722369917694499780 q^{90} + 80368473717550030191686089 q^{91} + 58778935160178730874443173 q^{93} + 113734518405600867492660996 q^{94} - 374006181713495475173434846 q^{96} - 201470754609842947282515088 q^{97} + 556341080893615529737562768 q^{99} + O(q^{100}) \)

Decomposition of \(S_{27}^{\mathrm{new}}(21, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
21.27.h.a 21.h 21.h $2$ $89.942$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(1594323\) \(0\) \(-44342429053\) $\mathrm{U}(1)[D_{6}]$ \(q+3^{13}\zeta_{6}q^{3}-2^{26}\zeta_{6}q^{4}+(-76625836565+\cdots)q^{7}+\cdots\)
21.27.h.b 21.h 21.h $132$ $89.942$ None \(0\) \(-1594324\) \(0\) \(-126055876226\) $\mathrm{SU}(2)[C_{6}]$