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Properties

Label 21.8
Level 21
Weight 8
Dimension 76
Nonzero newspaces 4
Newform subspaces 9
Sturm bound 256
Trace bound 1

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Defining parameters

Level: \( N \) = \( 21 = 3 \cdot 7 \)
Weight: \( k \) = \( 8 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 9 \)
Sturm bound: \(256\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_1(21))\).

Total New Old
Modular forms 124 88 36
Cusp forms 100 76 24
Eisenstein series 24 12 12

Trace form

\( 76 q - 12 q^{2} + 24 q^{3} + 690 q^{4} - 774 q^{5} - 972 q^{6} - 606 q^{7} + 6294 q^{8} - 2994 q^{9} + O(q^{10}) \) \( 76 q - 12 q^{2} + 24 q^{3} + 690 q^{4} - 774 q^{5} - 972 q^{6} - 606 q^{7} + 6294 q^{8} - 2994 q^{9} + 13488 q^{10} - 606 q^{11} - 26112 q^{12} + 1978 q^{13} - 38904 q^{14} + 36972 q^{15} + 88498 q^{16} + 5232 q^{17} + 16578 q^{18} - 8618 q^{19} - 390876 q^{20} - 22668 q^{21} + 482016 q^{22} + 349128 q^{23} - 133632 q^{24} - 243506 q^{25} - 688230 q^{26} - 39366 q^{27} - 537878 q^{28} + 93048 q^{29} + 510390 q^{30} + 1537126 q^{31} + 324750 q^{32} + 460638 q^{33} - 922524 q^{34} - 1268766 q^{35} - 924438 q^{36} - 1910076 q^{37} - 318858 q^{38} + 1448346 q^{39} + 3743976 q^{40} + 2477124 q^{41} + 4004046 q^{42} + 671520 q^{43} - 4494888 q^{44} - 5321754 q^{45} - 3647964 q^{46} + 834846 q^{47} - 2224800 q^{48} + 2965030 q^{49} + 397122 q^{50} + 7116084 q^{51} + 3677944 q^{52} - 757140 q^{53} - 6507702 q^{54} - 808440 q^{55} - 5485998 q^{56} - 9009756 q^{57} - 16780824 q^{58} - 4170036 q^{59} + 6846660 q^{60} + 20004946 q^{61} + 29624580 q^{62} + 10650138 q^{63} + 19885062 q^{64} + 2724594 q^{65} - 10102230 q^{66} - 24006694 q^{67} - 17104800 q^{68} - 8709768 q^{69} - 31565424 q^{70} - 1570548 q^{71} + 6811614 q^{72} + 3188920 q^{73} + 9720006 q^{74} - 7245654 q^{75} - 204728 q^{76} - 497568 q^{77} - 5336928 q^{78} + 16708382 q^{79} + 39324216 q^{80} + 17986770 q^{81} - 15181704 q^{82} - 12957732 q^{83} + 22358892 q^{84} - 22609392 q^{85} + 27742854 q^{86} + 26620524 q^{87} + 17131884 q^{88} + 13223256 q^{89} - 12159720 q^{90} - 23810888 q^{91} - 10696896 q^{92} - 51166212 q^{93} - 44319000 q^{94} - 44732166 q^{95} - 68479020 q^{96} - 17004164 q^{97} - 55932810 q^{98} + 18079740 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_1(21))\)

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
21.8.a \(\chi_{21}(1, \cdot)\) 21.8.a.a 1 1
21.8.a.b 2
21.8.a.c 2
21.8.a.d 3
21.8.c \(\chi_{21}(20, \cdot)\) 21.8.c.a 16 1
21.8.e \(\chi_{21}(4, \cdot)\) 21.8.e.a 8 2
21.8.e.b 10
21.8.g \(\chi_{21}(5, \cdot)\) 21.8.g.a 2 2
21.8.g.b 32

Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_1(21))\) into lower level spaces

\( S_{8}^{\mathrm{old}}(\Gamma_1(21)) \cong \) \(S_{8}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 1}\)