Properties

Label 21.30.g
Level $21$
Weight $30$
Character orbit 21.g
Rep. character $\chi_{21}(5,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $150$
Newform subspaces $2$
Sturm bound $80$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 21 = 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 30 \)
Character orbit: \([\chi]\) \(=\) 21.g (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 21 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(80\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{30}(21, [\chi])\).

Total New Old
Modular forms 158 158 0
Cusp forms 150 150 0
Eisenstein series 8 8 0

Trace form

\( 150q - 3q^{3} + 19327352830q^{4} + 1509655161365q^{7} - 34829554460625q^{9} + O(q^{10}) \) \( 150q - 3q^{3} + 19327352830q^{4} + 1509655161365q^{7} - 34829554460625q^{9} + 413746480644090q^{10} - 9533913671699904q^{12} + 200570198569375224q^{15} - 4243949196112829066q^{16} + 520580784857050698q^{18} + 247924957570133847q^{19} + 27385696394198154972q^{21} - 212672318498356979636q^{22} - 385716873401524913994q^{24} - 2346556740414147893385q^{25} - 3539845482433945149058q^{28} - 4558184762015670200718q^{30} - 8994755287899267198549q^{31} + 6219186156728304992514q^{33} - 94436420691907344433548q^{36} + 9851724110096484323965q^{37} - 120926983148202309840297q^{39} + 869560445336183215028970q^{40} + 1496793296190188459505210q^{42} - 1768840837234607272695434q^{43} + 3562065146267375340124962q^{45} - 1460642749357671389802872q^{46} + 4147192294605908692997301q^{49} - 1146131282310227498547792q^{51} + 3543226134477646914367392q^{52} - 65899892936090671485423858q^{54} - 80091143552076035106289446q^{57} - 44725223389891553641949222q^{58} + 52029657509386418096035914q^{60} - 462424824135841580035213104q^{61} - 273707080790362219125154329q^{63} - 1843608793719046437193195684q^{64} - 703225480506538357722730842q^{66} - 350120554727658692048983587q^{67} - 1150490913683451505581299310q^{70} - 1435334836486116836935587120q^{72} - 243912940788600754992156765q^{73} - 5502324460356865487296745295q^{75} + 5737497530456491653202307592q^{78} + 977015409556353156770551881q^{79} + 12519660413399813154042672339q^{81} + 4384869702835666156462439712q^{82} + 11631280126811603944353413376q^{84} + 32901924208372985551432429416q^{85} - 53058805585478911889161063776q^{87} - 46793001062184569953668924106q^{88} - 82315871502753111539312352207q^{91} + 94225130449507555700118850377q^{93} + 422182960303769206098070410420q^{94} - 32804189119893126887316885114q^{96} - 38558390545788825335174612976q^{99} + O(q^{100}) \)

Decomposition of \(S_{30}^{\mathrm{new}}(21, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
21.30.g.a \(2\) \(111.884\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(14348907\) \(0\) \(-2\!\cdots\!49\) \(q+(3^{14}+3^{14}\zeta_{6})q^{3}+(-2^{29}+2^{29}\zeta_{6})q^{4}+\cdots\)
21.30.g.b \(148\) \(111.884\) None \(0\) \(-14348910\) \(0\) \(40\!\cdots\!14\)