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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

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

Display 100 coefficients 10 coefficients

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 available 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

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