Properties

Label 21.9
Level 21
Weight 9
Dimension 86
Nonzero newspaces 4
Newform subspaces 6
Sturm bound 288
Trace bound 1

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 21 = 3 \cdot 7 \)
Weight: \( k \) = \( 9 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 6 \)
Sturm bound: \(288\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(\Gamma_1(21))\).

Total New Old
Modular forms 140 94 46
Cusp forms 116 86 30
Eisenstein series 24 8 16

Trace form

\( 86 q - 102 q^{3} - 38 q^{4} + 1674 q^{5} - 6054 q^{6} - 3890 q^{7} + 8082 q^{8} + 4644 q^{9} + O(q^{10}) \) \( 86 q - 102 q^{3} - 38 q^{4} + 1674 q^{5} - 6054 q^{6} - 3890 q^{7} + 8082 q^{8} + 4644 q^{9} - 31764 q^{10} + 14454 q^{11} + 87078 q^{12} - 41430 q^{13} - 218376 q^{14} - 16800 q^{15} + 243458 q^{16} + 219456 q^{17} - 398316 q^{18} + 104178 q^{19} - 272520 q^{21} - 303804 q^{22} - 455040 q^{23} + 256890 q^{24} + 1991072 q^{25} + 3302586 q^{26} + 1182144 q^{27} - 8078326 q^{28} - 4372668 q^{29} - 1764984 q^{30} + 1956030 q^{31} + 9787590 q^{32} + 4679070 q^{33} + 16066752 q^{34} - 89334 q^{35} - 16601514 q^{36} - 19094512 q^{37} - 5131890 q^{38} - 5473098 q^{39} + 631104 q^{40} + 14237424 q^{42} + 19073996 q^{43} + 27111672 q^{44} + 16864398 q^{45} - 43646604 q^{46} - 18612774 q^{47} - 25124970 q^{48} - 5296852 q^{49} - 29010906 q^{50} - 20051808 q^{51} + 49792920 q^{52} + 30565404 q^{53} + 65731092 q^{54} + 22038564 q^{55} + 80414226 q^{56} - 8701524 q^{57} - 26826912 q^{58} - 98837676 q^{59} - 203012364 q^{60} - 165305898 q^{61} + 106233786 q^{63} + 267327526 q^{64} + 141253578 q^{65} + 143356464 q^{66} + 54097918 q^{67} - 109292364 q^{68} - 83191464 q^{69} - 245516604 q^{70} + 55059624 q^{71} + 70430646 q^{72} - 303753420 q^{73} - 116681454 q^{74} + 130526304 q^{75} + 399453036 q^{76} + 106427736 q^{77} - 202996200 q^{78} + 96497386 q^{79} - 429558480 q^{80} - 55687032 q^{81} + 196555068 q^{82} + 45533394 q^{84} - 209363496 q^{85} + 52073154 q^{86} + 228935712 q^{87} + 289642728 q^{88} + 25623972 q^{89} - 20347116 q^{90} - 91636140 q^{91} - 284980500 q^{92} - 8630412 q^{93} + 44471628 q^{94} + 852528834 q^{95} + 538940406 q^{96} - 646548984 q^{97} - 535426182 q^{98} - 616551336 q^{99} + O(q^{100}) \)

Decomposition of \(S_{9}^{\mathrm{new}}(\Gamma_1(21))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
21.9.b \(\chi_{21}(8, \cdot)\) 21.9.b.a 16 1
21.9.d \(\chi_{21}(13, \cdot)\) 21.9.d.a 10 1
21.9.f \(\chi_{21}(10, \cdot)\) 21.9.f.a 10 2
21.9.f.b 12
21.9.h \(\chi_{21}(2, \cdot)\) 21.9.h.a 2 2
21.9.h.b 36

Decomposition of \(S_{9}^{\mathrm{old}}(\Gamma_1(21))\) into lower level spaces

\( S_{9}^{\mathrm{old}}(\Gamma_1(21)) \cong \) \(S_{9}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 2}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 2}\)