↑

Properties

Label 21.23
Level 21
Weight 23
Dimension 246
Nonzero newspaces 4
Newform subspaces 6
Sturm bound 736
Trace bound 1

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 21 = 3 \cdot 7 \)
Weight: \( k \) = \( 23 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 6 \)
Sturm bound: \(736\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{23}(\Gamma_1(21))\).

Total New Old
Modular forms 364 254 110
Cusp forms 340 246 94
Eisenstein series 24 8 16

Trace form

\( 246 q + 3804 q^{3} + 39294586 q^{4} + 130280694 q^{5} - 587150214 q^{6} - 1807364858 q^{7} + 76133034114 q^{8} - 96579390186 q^{9} + O(q^{10}) \) \( 246 q + 3804 q^{3} + 39294586 q^{4} + 130280694 q^{5} - 587150214 q^{6} - 1807364858 q^{7} + 76133034114 q^{8} - 96579390186 q^{9} + 1309636985868 q^{10} - 527604434934 q^{11} + 1312087935918 q^{12} - 7409073691298 q^{13} + 5024582838264 q^{14} - 14765516914812 q^{15} + 113204527718082 q^{16} - 112846780131312 q^{17} + 24370020535236 q^{18} - 797532884590502 q^{19} - 599331234013074 q^{21} - 1199174323094988 q^{22} + 204794022734304 q^{23} + 703866863206002 q^{24} + 17166599015410188 q^{25} - 29681041591819926 q^{26} + 35099655894432588 q^{27} - 7905078777078102 q^{28} - 17002321390703508 q^{29} + 158522296876569024 q^{30} - 60011702855249594 q^{31} + 33615635882404278 q^{32} + 656890899102096 q^{33} - 96424920681267360 q^{34} - 29367169066504290 q^{35} - 850762258413964890 q^{36} - 894283992911172340 q^{37} - 1107235263913722786 q^{38} + 2408601995956985994 q^{39} - 8091994070823280464 q^{40} + 681801281074115928 q^{42} - 6756109777229262868 q^{43} - 7032462630173645448 q^{44} - 2434081163907168648 q^{45} + 13753376844437203860 q^{46} - 13813392469568656962 q^{47} + 4796355170486088150 q^{48} + 60051807280065049728 q^{49} - 30197028192818376954 q^{50} - 11289073197986656134 q^{51} + 66077843272108769272 q^{52} + 11020148813338062348 q^{53} - 111304233930161086500 q^{54} - 80317278458205674004 q^{55} + 180527645928716898354 q^{56} - 39614940643827313872 q^{57} + 148219297751468845440 q^{58} - 170481159547472969076 q^{59} + 234586704053331935916 q^{60} + 251453481488254084054 q^{61} - 311023000559620611072 q^{63} - 1200620364125872016954 q^{64} + 890145156783594161358 q^{65} + 691095515113099394856 q^{66} - 1247036749306561310538 q^{67} + 356162314619252511396 q^{68} + 483047355155367203460 q^{69} + 224211238647340845540 q^{70} + 809163638863309117896 q^{71} + 1246838337965966143854 q^{72} - 1880209194341967617120 q^{73} - 1225709624270085820974 q^{74} - 221721786319327801680 q^{75} - 2330052468952038157844 q^{76} - 247562524115111454408 q^{77} - 1311956296685498674776 q^{78} - 1573240434560843242374 q^{79} - 5839753034330262291072 q^{80} - 928136740544037942210 q^{81} + 3758368554132835014828 q^{82} - 9296377091516765085678 q^{84} + 1053976684786794227952 q^{85} - 1347680264574119418894 q^{86} + 3381862765356189994692 q^{87} + 12652965180753293499816 q^{88} - 9025688779465016553348 q^{89} - 41777514613068392629212 q^{90} + 14591492341576272935812 q^{91} + 36443838356959948323276 q^{92} + 8811168675512477619666 q^{93} + 13392149467151359082076 q^{94} - 71425180972083851932458 q^{95} + 17899112458936639387974 q^{96} + 69708106484149104999784 q^{97} + 69004591644762678015450 q^{98} - 23235675685801236864396 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{23}^{\mathrm{new}}(\Gamma_1(21))\)

We only show spaces with odd 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
21.23.b \(\chi_{21}(8, \cdot)\) 21.23.b.a 44 1
21.23.d \(\chi_{21}(13, \cdot)\) 21.23.d.a 30 1
21.23.f \(\chi_{21}(10, \cdot)\) 21.23.f.a 28 2
21.23.f.b 30
21.23.h \(\chi_{21}(2, \cdot)\) 21.23.h.a 2 2
21.23.h.b 112

Decomposition of \(S_{23}^{\mathrm{old}}(\Gamma_1(21))\) into lower level spaces

\( S_{23}^{\mathrm{old}}(\Gamma_1(21)) \cong \) \(S_{23}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 2}\)\(\oplus\)\(S_{23}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 2}\)