Properties

Label 21.6
Level 21
Weight 6
Dimension 52
Nonzero newspaces 4
Newform subspaces 11
Sturm bound 192
Trace bound 1

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Defining parameters

Level: \( N \) = \( 21 = 3 \cdot 7 \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 11 \)
Sturm bound: \(192\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(21))\).

Total New Old
Modular forms 92 64 28
Cusp forms 68 52 16
Eisenstein series 24 12 12

Trace form

\( 52q + 12q^{2} - 12q^{3} - 142q^{4} + 54q^{5} + 324q^{6} + 266q^{7} + 6q^{8} - 816q^{9} + O(q^{10}) \) \( 52q + 12q^{2} - 12q^{3} - 142q^{4} + 54q^{5} + 324q^{6} + 266q^{7} + 6q^{8} - 816q^{9} - 3024q^{10} + 714q^{11} + 2040q^{12} + 2070q^{13} + 3480q^{14} + 2268q^{15} + 178q^{16} - 5016q^{17} - 6534q^{18} + 2838q^{19} - 5052q^{20} - 5334q^{21} - 12816q^{22} - 5976q^{23} + 6696q^{24} + 25114q^{25} + 22986q^{26} + 1458q^{27} + 11146q^{28} - 5568q^{29} - 21042q^{30} - 15018q^{31} - 1794q^{32} + 17604q^{33} - 13548q^{34} - 13158q^{35} + 64410q^{36} + 38944q^{37} + 32118q^{38} - 29814q^{39} - 106152q^{40} - 32940q^{41} - 90306q^{42} - 16688q^{43} - 8424q^{44} - 22104q^{45} + 7524q^{46} + 5934q^{47} + 71136q^{48} - 8006q^{49} + 28650q^{50} + 72072q^{51} + 165528q^{52} + 4812q^{53} + 123282q^{54} + 229272q^{55} + 84018q^{56} + 43488q^{57} - 138552q^{58} - 61188q^{59} - 257796q^{60} - 263238q^{61} - 117756q^{62} - 188958q^{63} - 339994q^{64} - 233682q^{65} - 303534q^{66} + 24986q^{67} + 89904q^{68} + 129384q^{69} + 730224q^{70} + 310188q^{71} + 603126q^{72} + 412644q^{73} + 288102q^{74} + 431706q^{75} + 131400q^{76} - 173184q^{77} - 246816q^{78} - 641170q^{79} - 244056q^{80} - 109764q^{81} - 656424q^{82} - 437652q^{83} - 795156q^{84} - 363240q^{85} - 95322q^{86} - 437076q^{87} + 52140q^{88} + 146496q^{89} + 103032q^{90} + 283224q^{91} + 872928q^{92} + 1050546q^{93} + 1055448q^{94} + 722922q^{95} + 1080036q^{96} - 366516q^{97} - 16626q^{98} + 500868q^{99} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(21))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
21.6.a \(\chi_{21}(1, \cdot)\) 21.6.a.a 1 1
21.6.a.b 1
21.6.a.c 1
21.6.a.d 1
21.6.c \(\chi_{21}(20, \cdot)\) 21.6.c.a 12 1
21.6.e \(\chi_{21}(4, \cdot)\) 21.6.e.a 2 2
21.6.e.b 4
21.6.e.c 8
21.6.g \(\chi_{21}(5, \cdot)\) 21.6.g.a 2 2
21.6.g.b 4
21.6.g.c 16

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(21))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(21)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 2}\)