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Properties

Label 20.11
Level 20
Weight 11
Dimension 58
Nonzero newspaces 3
Newform subspaces 6
Sturm bound 264
Trace bound 1

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Defining parameters

Level: \( N \) = \( 20 = 2^{2} \cdot 5 \)
Weight: \( k \) = \( 11 \)
Nonzero newspaces: \( 3 \)
Newform subspaces: \( 6 \)
Sturm bound: \(264\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{11}(\Gamma_1(20))\).

Total New Old
Modular forms 130 62 68
Cusp forms 110 58 52
Eisenstein series 20 4 16

Trace form

\( 58 q + 22 q^{2} + 62 q^{3} - 36 q^{4} + 2450 q^{5} - 19264 q^{6} + 22286 q^{7} + 3448 q^{8} + 57520 q^{9} + O(q^{10}) \) \( 58 q + 22 q^{2} + 62 q^{3} - 36 q^{4} + 2450 q^{5} - 19264 q^{6} + 22286 q^{7} + 3448 q^{8} + 57520 q^{9} - 7074 q^{10} - 201700 q^{11} + 1329640 q^{12} - 39566 q^{13} - 1811224 q^{14} + 213662 q^{15} + 3722288 q^{16} - 876214 q^{17} - 3556082 q^{18} - 5470604 q^{20} + 11453812 q^{21} - 5811280 q^{22} - 4097986 q^{23} + 6545136 q^{24} + 43879442 q^{25} + 34258020 q^{26} - 4817488 q^{27} - 87415400 q^{28} - 85357072 q^{29} + 96291160 q^{30} + 23221660 q^{31} - 33171328 q^{32} + 117796780 q^{33} - 246528948 q^{34} - 55388242 q^{35} + 192889724 q^{36} - 241432630 q^{37} + 250352720 q^{38} - 467212824 q^{40} + 563589476 q^{41} - 570662040 q^{42} + 156325470 q^{43} + 1105470640 q^{44} - 483476800 q^{45} - 539220184 q^{46} - 450750018 q^{47} - 479727360 q^{48} + 692082000 q^{49} + 902891726 q^{50} + 1632585820 q^{51} - 110465096 q^{52} - 968097958 q^{53} - 96992048 q^{54} - 1301185140 q^{55} - 1804779504 q^{56} + 1408702544 q^{57} + 2075027916 q^{58} - 381215000 q^{60} - 486118204 q^{61} + 1664032240 q^{62} + 3352397678 q^{63} - 1534825536 q^{64} - 2830908830 q^{65} + 443772560 q^{66} - 6990333394 q^{67} + 3042411896 q^{68} - 6817126568 q^{69} - 5500157760 q^{70} + 9915200380 q^{71} + 1632326712 q^{72} + 10876202674 q^{73} + 12387003012 q^{74} - 10170758642 q^{75} + 3151593600 q^{76} - 19414930100 q^{77} - 19914223760 q^{78} + 8290924656 q^{80} + 30810309210 q^{81} - 3197757116 q^{82} + 16998617454 q^{83} - 9560718688 q^{84} - 26311581502 q^{85} + 13497422576 q^{86} - 36065578576 q^{87} + 2774318240 q^{88} + 12755289408 q^{89} - 7828582074 q^{90} + 52347612540 q^{91} - 27349072440 q^{92} + 14416571932 q^{93} + 21948902856 q^{94} - 23431125296 q^{95} + 8230267136 q^{96} - 88930013310 q^{97} + 38416891998 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{11}^{\mathrm{new}}(\Gamma_1(20))\)

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
20.11.b \(\chi_{20}(11, \cdot)\) 20.11.b.a 20 1
20.11.d \(\chi_{20}(19, \cdot)\) 20.11.d.a 1 1
20.11.d.b 1
20.11.d.c 2
20.11.d.d 24
20.11.f \(\chi_{20}(13, \cdot)\) 20.11.f.a 10 2

Decomposition of \(S_{11}^{\mathrm{old}}(\Gamma_1(20))\) into lower level spaces

\( S_{11}^{\mathrm{old}}(\Gamma_1(20)) \cong \) \(S_{11}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 2}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 3}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 2}\)