Properties

Label 20.9
Level 20
Weight 9
Dimension 46
Nonzero newspaces 3
Newform subspaces 5
Sturm bound 216
Trace bound 1

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Defining parameters

Level: \( N \) = \( 20 = 2^{2} \cdot 5 \)
Weight: \( k \) = \( 9 \)
Nonzero newspaces: \( 3 \)
Newform subspaces: \( 5 \)
Sturm bound: \(216\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(\Gamma_1(20))\).

Total New Old
Modular forms 106 50 56
Cusp forms 86 46 40
Eisenstein series 20 4 16

Trace form

\( 46 q + 6 q^{2} - 70 q^{3} - 292 q^{4} + 724 q^{5} + 2720 q^{6} - 2030 q^{7} - 14184 q^{8} + 562 q^{9} + O(q^{10}) \) \( 46 q + 6 q^{2} - 70 q^{3} - 292 q^{4} + 724 q^{5} + 2720 q^{6} - 2030 q^{7} - 14184 q^{8} + 562 q^{9} + 4590 q^{10} - 420 q^{11} - 64040 q^{12} + 84572 q^{13} + 138824 q^{14} - 48478 q^{15} - 9552 q^{16} + 71172 q^{17} - 616994 q^{18} + 488260 q^{20} + 326068 q^{21} - 389120 q^{22} - 663270 q^{23} - 1287216 q^{24} + 1537386 q^{25} + 596676 q^{26} + 1576040 q^{27} + 1288520 q^{28} + 3466316 q^{29} - 3297080 q^{30} - 3178492 q^{31} - 4379904 q^{32} - 6465620 q^{33} + 8136492 q^{34} + 2571618 q^{35} - 3237892 q^{36} + 14353552 q^{37} - 3087360 q^{38} - 560280 q^{40} - 22531576 q^{41} - 4067400 q^{42} - 10342710 q^{43} + 19588080 q^{44} + 26139524 q^{45} - 654520 q^{46} + 19232250 q^{47} - 2696640 q^{48} - 25225998 q^{49} + 4383630 q^{50} - 47126684 q^{51} + 6679352 q^{52} - 21868608 q^{53} - 13863632 q^{54} + 21483180 q^{55} + 14835440 q^{56} + 100176080 q^{57} + 52156572 q^{58} - 46919720 q^{60} - 113927608 q^{61} + 1290000 q^{62} - 77441350 q^{63} + 6212288 q^{64} + 36903528 q^{65} + 51260720 q^{66} + 100675930 q^{67} + 16095192 q^{68} + 52534648 q^{69} + 1774000 q^{70} - 99290076 q^{71} - 42242664 q^{72} - 31621288 q^{73} - 119096508 q^{74} + 76524178 q^{75} - 52428000 q^{76} - 22797780 q^{77} - 104032400 q^{78} + 127478320 q^{80} + 174217170 q^{81} + 83921012 q^{82} - 10450350 q^{83} + 15568928 q^{84} + 13516156 q^{85} - 87919600 q^{86} + 164801600 q^{87} + 44728480 q^{88} - 1955764 q^{89} - 198194250 q^{90} - 130681068 q^{91} - 13876200 q^{92} + 55380220 q^{93} + 170290504 q^{94} + 84367944 q^{95} - 755889280 q^{96} - 7719528 q^{97} - 285387714 q^{98} + O(q^{100}) \)

Decomposition of \(S_{9}^{\mathrm{new}}(\Gamma_1(20))\)

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
20.9.b \(\chi_{20}(11, \cdot)\) 20.9.b.a 16 1
20.9.d \(\chi_{20}(19, \cdot)\) 20.9.d.a 1 1
20.9.d.b 1
20.9.d.c 20
20.9.f \(\chi_{20}(13, \cdot)\) 20.9.f.a 8 2

Decomposition of \(S_{9}^{\mathrm{old}}(\Gamma_1(20))\) into lower level spaces

\( S_{9}^{\mathrm{old}}(\Gamma_1(20)) \cong \) \(S_{9}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 2}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 3}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 2}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 1}\)