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Properties

Label 8.21.d
Level $8$
Weight $21$
Character orbit 8.d
Rep. character $\chi_{8}(3,\cdot)$
Character field $\Q$
Dimension $19$
Newform subspaces $2$
Sturm bound $21$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 8 = 2^{3} \)
Weight: \( k \) \(=\) \( 21 \)
Character orbit: \([\chi]\) \(=\) 8.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 8 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(21\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{21}(8, [\chi])\).

Total New Old
Modular forms 21 21 0
Cusp forms 19 19 0
Eisenstein series 2 2 0

Trace form

\( 19 q + 626 q^{2} - 2 q^{3} + 1773556 q^{4} + 25323676 q^{6} - 2031549544 q^{8} + 19758444937 q^{9} + O(q^{10}) \) \( 19 q + 626 q^{2} - 2 q^{3} + 1773556 q^{4} + 25323676 q^{6} - 2031549544 q^{8} + 19758444937 q^{9} + 742754160 q^{10} - 14520628706 q^{11} - 92518091912 q^{12} - 431248136928 q^{14} + 140976757264 q^{16} + 990389375398 q^{17} + 5272759222774 q^{18} - 1375336086082 q^{19} - 32520172742880 q^{20} - 109675699217572 q^{22} + 144938556063376 q^{24} - 300360045368285 q^{25} + 154289718058128 q^{26} - 514588541331140 q^{27} - 394619539621440 q^{28} + 223250517248160 q^{30} - 1707914682142624 q^{32} - 379273727638900 q^{33} - 4373483391631324 q^{34} + 3615863153468160 q^{35} + 11585741011529500 q^{36} + 11866377694661788 q^{38} + 11813880412973760 q^{40} - 8427241614192506 q^{41} + 38127588900300480 q^{42} - 24717352370364898 q^{43} - 11262977142561032 q^{44} - 21739818881100192 q^{46} + 153956946591726688 q^{48} - 173173121721250637 q^{49} + 139361869584456530 q^{50} - 417243550710750724 q^{51} - 44583718369992480 q^{52} + 131060624290419256 q^{54} - 505574909383001472 q^{56} - 638353406270838580 q^{57} - 677523738697093680 q^{58} - 80800002484130978 q^{59} + 1631640690429240000 q^{60} + 1780090172849178240 q^{62} + 1328363317618417216 q^{64} + 1575343920200472960 q^{65} + 3043614561170466056 q^{66} - 1808783156240800642 q^{67} - 2362666796221870232 q^{68} - 6151558949299572480 q^{70} + 4959295908955144264 q^{72} + 3866104143546483398 q^{73} - 5642095430673385488 q^{74} + 24308156015351409310 q^{75} - 9480723535297927816 q^{76} - 14599907290310144160 q^{78} - 22104885212702947200 q^{80} + 13599596957313525631 q^{81} - 15707154812006670172 q^{82} - 77448386448570160322 q^{83} + 17095266896298568320 q^{84} + 36403346004507897820 q^{86} - 13164074256796170352 q^{88} + 33127276190960144518 q^{89} - 33204348719592139440 q^{90} + 161045136122144660736 q^{91} - 932896292396925120 q^{92} - 107259275077774974528 q^{94} + 197187886676221266496 q^{96} + 77267514659308382822 q^{97} + 236544665851892453426 q^{98} - 342412845288286744966 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{21}^{\mathrm{new}}(8, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
8.21.d.a 8.d 8.d $1$ $20.281$ \(\Q\) \(\Q(\sqrt{-2}) \) \(1024\) \(114226\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+2^{10}q^{2}+114226q^{3}+2^{20}q^{4}+\cdots\)
8.21.d.b 8.d 8.d $18$ $20.281$ \(\mathbb{Q}[x]/(x^{18} + \cdots)\) None \(-398\) \(-114228\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-22+\beta _{1})q^{2}+(-6347-5\beta _{1}+\cdots)q^{3}+\cdots\)