Properties

Label 20.5
Level 20
Weight 5
Dimension 22
Nonzero newspaces 3
Newform subspaces 5
Sturm bound 120
Trace bound 1

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Defining parameters

Level: \( N \) = \( 20 = 2^{2} \cdot 5 \)
Weight: \( k \) = \( 5 \)
Nonzero newspaces: \( 3 \)
Newform subspaces: \( 5 \)
Sturm bound: \(120\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(\Gamma_1(20))\).

Total New Old
Modular forms 58 26 32
Cusp forms 38 22 16
Eisenstein series 20 4 16

Trace form

\( 22 q + 6 q^{2} - 10 q^{3} - 36 q^{4} + 4 q^{5} + 32 q^{6} + 110 q^{7} + 216 q^{8} - 170 q^{9} + O(q^{10}) \) \( 22 q + 6 q^{2} - 10 q^{3} - 36 q^{4} + 4 q^{5} + 32 q^{6} + 110 q^{7} + 216 q^{8} - 170 q^{9} - 210 q^{10} - 300 q^{11} - 200 q^{12} - 8 q^{13} - 184 q^{14} + 542 q^{15} - 592 q^{16} + 912 q^{17} + 286 q^{18} + 100 q^{20} - 2612 q^{21} + 800 q^{22} - 810 q^{23} + 3216 q^{24} + 2066 q^{25} + 324 q^{26} + 2120 q^{27} + 40 q^{28} + 1508 q^{29} - 920 q^{30} - 836 q^{31} - 2304 q^{32} - 2780 q^{33} - 4308 q^{34} - 2562 q^{35} - 9220 q^{36} - 6388 q^{37} - 3360 q^{38} + 4200 q^{40} + 10280 q^{41} + 12120 q^{42} + 3270 q^{43} + 9840 q^{44} + 3344 q^{45} + 14792 q^{46} - 2250 q^{47} + 8640 q^{48} - 5130 q^{49} - 11730 q^{50} + 1948 q^{51} - 12488 q^{52} + 4572 q^{53} - 26768 q^{54} - 6780 q^{55} - 25168 q^{56} - 10000 q^{57} - 7428 q^{58} + 11320 q^{60} + 22184 q^{61} + 25680 q^{62} + 12950 q^{63} + 33984 q^{64} - 3852 q^{65} + 38000 q^{66} - 4810 q^{67} + 2712 q^{68} - 18248 q^{69} - 10800 q^{70} - 5988 q^{71} - 36264 q^{72} - 28508 q^{73} - 42108 q^{74} - 11282 q^{75} - 36000 q^{76} + 1380 q^{77} - 14480 q^{78} + 19120 q^{80} - 1062 q^{81} + 27412 q^{82} + 19950 q^{83} + 80672 q^{84} + 36536 q^{85} + 46352 q^{86} + 24800 q^{87} + 18080 q^{88} + 60068 q^{89} - 29130 q^{90} - 11124 q^{91} - 52680 q^{92} - 22700 q^{93} - 67704 q^{94} - 15576 q^{95} - 78208 q^{96} - 7548 q^{97} - 21474 q^{98} + O(q^{100}) \)

Decomposition of \(S_{5}^{\mathrm{new}}(\Gamma_1(20))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
20.5.b \(\chi_{20}(11, \cdot)\) 20.5.b.a 8 1
20.5.d \(\chi_{20}(19, \cdot)\) 20.5.d.a 1 1
20.5.d.b 1
20.5.d.c 8
20.5.f \(\chi_{20}(13, \cdot)\) 20.5.f.a 4 2

Decomposition of \(S_{5}^{\mathrm{old}}(\Gamma_1(20))\) into lower level spaces

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