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Properties

Label 21.5
Level 21
Weight 5
Dimension 42
Nonzero newspaces 4
Newform subspaces 7
Sturm bound 160
Trace bound 1

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Defining parameters

Level: \( N \) = \( 21 = 3 \cdot 7 \)
Weight: \( k \) = \( 5 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 7 \)
Sturm bound: \(160\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(\Gamma_1(21))\).

Total New Old
Modular forms 76 50 26
Cusp forms 52 42 10
Eisenstein series 24 8 16

Trace form

\( 42 q - 12 q^{3} + 58 q^{4} + 54 q^{5} - 6 q^{6} - 110 q^{7} - 558 q^{8} + 18 q^{9} + O(q^{10}) \) \( 42 q - 12 q^{3} + 58 q^{4} + 54 q^{5} - 6 q^{6} - 110 q^{7} - 558 q^{8} + 18 q^{9} + 396 q^{10} + 522 q^{11} + 678 q^{12} + 310 q^{13} - 648 q^{14} - 780 q^{15} - 1566 q^{16} - 864 q^{17} - 1596 q^{18} - 1814 q^{19} + 1782 q^{21} + 4836 q^{22} + 2880 q^{23} + 3882 q^{24} + 1632 q^{25} + 378 q^{26} + 624 q^{27} + 234 q^{28} - 612 q^{29} - 984 q^{30} - 3986 q^{31} - 1530 q^{32} - 2460 q^{33} - 4800 q^{34} - 2394 q^{35} - 13290 q^{36} - 2452 q^{37} + 270 q^{38} - 3906 q^{39} - 1056 q^{40} - 576 q^{42} - 364 q^{43} + 4536 q^{44} + 9828 q^{45} + 16788 q^{46} + 15606 q^{47} + 27510 q^{48} + 16596 q^{49} + 6534 q^{50} + 9210 q^{51} - 2600 q^{52} + 2484 q^{53} - 13692 q^{54} - 34956 q^{55} - 36270 q^{56} - 21744 q^{57} - 34272 q^{58} - 14868 q^{59} - 17004 q^{60} - 5498 q^{61} - 12564 q^{63} + 40006 q^{64} + 7398 q^{65} + 32112 q^{66} + 35598 q^{67} + 42516 q^{68} + 47916 q^{69} + 62436 q^{70} + 29304 q^{71} + 28326 q^{72} - 17480 q^{73} - 54414 q^{74} - 47316 q^{75} - 86420 q^{76} - 32184 q^{77} - 84360 q^{78} - 39486 q^{79} - 68400 q^{80} - 47034 q^{81} - 3492 q^{82} + 25218 q^{84} + 54864 q^{85} + 60354 q^{86} + 74712 q^{87} + 90408 q^{88} + 24732 q^{89} + 115284 q^{90} + 13516 q^{91} + 61740 q^{92} + 24438 q^{93} - 44724 q^{94} - 20466 q^{95} - 60810 q^{96} - 37784 q^{97} - 26982 q^{98} - 72468 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{5}^{\mathrm{new}}(\Gamma_1(21))\)

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
21.5.b \(\chi_{21}(8, \cdot)\) 21.5.b.a 8 1
21.5.d \(\chi_{21}(13, \cdot)\) 21.5.d.a 6 1
21.5.f \(\chi_{21}(10, \cdot)\) 21.5.f.a 2 2
21.5.f.b 2
21.5.f.c 6
21.5.h \(\chi_{21}(2, \cdot)\) 21.5.h.a 2 2
21.5.h.b 16

Decomposition of \(S_{5}^{\mathrm{old}}(\Gamma_1(21))\) into lower level spaces

\( S_{5}^{\mathrm{old}}(\Gamma_1(21)) \cong \) \(S_{5}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 2}\)