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Properties

Label 21.26
Level 21
Weight 26
Dimension 284
Nonzero newspaces 4
Newform subspaces 9
Sturm bound 832
Trace bound 1

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Defining parameters

Level: \( N \) = \( 21 = 3 \cdot 7 \)
Weight: \( k \) = \( 26 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 9 \)
Sturm bound: \(832\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{26}(\Gamma_1(21))\).

Total New Old
Modular forms 412 296 116
Cusp forms 388 284 104
Eisenstein series 24 12 12

Trace form

\( 284 q + 8004 q^{2} - 531444 q^{3} - 98492846 q^{4} + 385230954 q^{5} + 16625600244 q^{6} + 43903871434 q^{7} - 575030701722 q^{8} - 673662046182 q^{9} + O(q^{10}) \) \( 284 q + 8004 q^{2} - 531444 q^{3} - 98492846 q^{4} + 385230954 q^{5} + 16625600244 q^{6} + 43903871434 q^{7} - 575030701722 q^{8} - 673662046182 q^{9} + 5218042232976 q^{10} + 33126460788090 q^{11} - 153486630422904 q^{12} - 48574190104254 q^{13} - 1624717152921672 q^{14} + 2078273472509268 q^{15} - 6405028309933966 q^{16} - 4408605215269224 q^{17} - 32686463754763326 q^{18} - 14605352221414074 q^{19} - 56040588067742652 q^{20} + 118442698432217724 q^{21} + 192615163207817712 q^{22} - 307808546321753304 q^{23} + 648738164802742488 q^{24} + 102043178303904014 q^{25} - 4090970880826647990 q^{26} + 300189270593998242 q^{27} - 15618639286316421430 q^{28} + 8848108310374544664 q^{29} - 4919140419173805042 q^{30} - 19711348229827349946 q^{31} + 49393902391829951070 q^{32} - 39242580789107172726 q^{33} - 38478693619555102236 q^{34} + 84363843439517355642 q^{35} + 358790036560866794202 q^{36} - 16491437193223273396 q^{37} + 291240244647356211654 q^{38} - 203608835404033867710 q^{39} - 501315374856872143752 q^{40} + 991045249362993307188 q^{41} - 281107741019557491882 q^{42} - 1994698430072586905008 q^{43} + 4536443718117903049944 q^{44} - 950619233563327450854 q^{45} - 3276974925785163675708 q^{46} - 688222552452869749002 q^{47} - 2202142770130523035680 q^{48} + 4796429863656199852886 q^{49} - 3516115364684695942350 q^{50} - 1143543241594251034200 q^{51} + 10690847988565143878616 q^{52} - 23116892773124567899500 q^{53} + 9222668068208616541746 q^{54} + 51410719252161065667672 q^{55} - 2108541030097729972878 q^{56} - 47406618706906856266236 q^{57} + 78439668138827530649544 q^{58} + 57885724889369996253660 q^{59} + 3796472994581608867404 q^{60} + 147908571426764665610418 q^{61} - 63483290125334427667740 q^{62} + 132083330608179999832254 q^{63} - 345276820959243444119834 q^{64} + 58984595619820626885618 q^{65} + 119655532039095839364930 q^{66} - 358342264932427669705670 q^{67} - 533961070024063068620400 q^{68} + 485606071706171705049960 q^{69} - 1465612590969805074376176 q^{70} - 405034685431879159503444 q^{71} + 1293067940671317218028678 q^{72} + 927799536797706004030536 q^{73} + 1290502262131911888745446 q^{74} - 1641278436416718613900494 q^{75} - 176803901443092053548536 q^{76} + 2515270108390072246854696 q^{77} - 620532306942721744748976 q^{78} - 6586975626964049561980466 q^{79} + 6371997319331561950841544 q^{80} + 2595931175962483881922494 q^{81} + 234310569293328040866312 q^{82} - 9897685621550895362359764 q^{83} + 2744243484116246112042444 q^{84} + 21308852647203233690300160 q^{85} - 9626110625278100117101674 q^{86} - 7414081767269093430814356 q^{87} - 2485876743765258551514708 q^{88} + 7619012165027114309622840 q^{89} - 83367580269713891174568 q^{90} - 13472175016743755504966952 q^{91} + 28052959714540066231095072 q^{92} + 6059934246828588353232024 q^{93} + 26052644218596806836148664 q^{94} - 5625589303401510012474078 q^{95} - 3520150818935638816904508 q^{96} + 53213763085099518402953268 q^{97} - 9454724639946074055951450 q^{98} - 30306724770505817268811116 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{26}^{\mathrm{new}}(\Gamma_1(21))\)

We only show spaces with even parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
21.26.a \(\chi_{21}(1, \cdot)\) 21.26.a.a 5 1
21.26.a.b 6
21.26.a.c 6
21.26.a.d 7
21.26.c \(\chi_{21}(20, \cdot)\) 21.26.c.a 64 1
21.26.e \(\chi_{21}(4, \cdot)\) 21.26.e.a 32 2
21.26.e.b 34
21.26.g \(\chi_{21}(5, \cdot)\) 21.26.g.a 2 2
21.26.g.b 128

Decomposition of \(S_{26}^{\mathrm{old}}(\Gamma_1(21))\) into lower level spaces

\( S_{26}^{\mathrm{old}}(\Gamma_1(21)) \cong \) \(S_{26}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{26}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 2}\)\(\oplus\)\(S_{26}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 2}\)