Properties

Label 20.4
Level 20
Weight 4
Dimension 17
Nonzero newspaces 3
Newforms 4
Sturm bound 96
Trace bound 1

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Defining parameters

Level: \( N \) = \( 20 = 2^{2} \cdot 5 \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 3 \)
Newforms: \( 4 \)
Sturm bound: \(96\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(20))\).

Total New Old
Modular forms 46 25 21
Cusp forms 26 17 9
Eisenstein series 20 8 12

Trace form

\(17q \) \(\mathstrut -\mathstrut 2q^{2} \) \(\mathstrut +\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 15q^{5} \) \(\mathstrut +\mathstrut 8q^{6} \) \(\mathstrut -\mathstrut 16q^{7} \) \(\mathstrut -\mathstrut 44q^{8} \) \(\mathstrut -\mathstrut 109q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(17q \) \(\mathstrut -\mathstrut 2q^{2} \) \(\mathstrut +\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 15q^{5} \) \(\mathstrut +\mathstrut 8q^{6} \) \(\mathstrut -\mathstrut 16q^{7} \) \(\mathstrut -\mathstrut 44q^{8} \) \(\mathstrut -\mathstrut 109q^{9} \) \(\mathstrut -\mathstrut 74q^{10} \) \(\mathstrut -\mathstrut 20q^{11} \) \(\mathstrut -\mathstrut 80q^{12} \) \(\mathstrut +\mathstrut 128q^{13} \) \(\mathstrut +\mathstrut 172q^{15} \) \(\mathstrut +\mathstrut 184q^{16} \) \(\mathstrut -\mathstrut 116q^{17} \) \(\mathstrut +\mathstrut 306q^{18} \) \(\mathstrut -\mathstrut 124q^{19} \) \(\mathstrut +\mathstrut 316q^{20} \) \(\mathstrut -\mathstrut 56q^{21} \) \(\mathstrut +\mathstrut 360q^{22} \) \(\mathstrut +\mathstrut 48q^{23} \) \(\mathstrut +\mathstrut 77q^{25} \) \(\mathstrut -\mathstrut 460q^{26} \) \(\mathstrut -\mathstrut 152q^{27} \) \(\mathstrut -\mathstrut 880q^{28} \) \(\mathstrut -\mathstrut 174q^{29} \) \(\mathstrut -\mathstrut 1240q^{30} \) \(\mathstrut -\mathstrut 272q^{31} \) \(\mathstrut -\mathstrut 632q^{32} \) \(\mathstrut -\mathstrut 160q^{33} \) \(\mathstrut -\mathstrut 232q^{35} \) \(\mathstrut +\mathstrut 892q^{36} \) \(\mathstrut +\mathstrut 580q^{37} \) \(\mathstrut +\mathstrut 1600q^{38} \) \(\mathstrut +\mathstrut 1256q^{39} \) \(\mathstrut +\mathstrut 1836q^{40} \) \(\mathstrut +\mathstrut 1006q^{41} \) \(\mathstrut +\mathstrut 1160q^{42} \) \(\mathstrut -\mathstrut 100q^{43} \) \(\mathstrut -\mathstrut 155q^{45} \) \(\mathstrut -\mathstrut 1432q^{46} \) \(\mathstrut +\mathstrut 168q^{47} \) \(\mathstrut -\mathstrut 2720q^{48} \) \(\mathstrut +\mathstrut 447q^{49} \) \(\mathstrut -\mathstrut 2214q^{50} \) \(\mathstrut -\mathstrut 1144q^{51} \) \(\mathstrut -\mathstrut 1524q^{52} \) \(\mathstrut -\mathstrut 1196q^{53} \) \(\mathstrut -\mathstrut 20q^{55} \) \(\mathstrut +\mathstrut 2048q^{56} \) \(\mathstrut -\mathstrut 784q^{57} \) \(\mathstrut +\mathstrut 2712q^{58} \) \(\mathstrut -\mathstrut 308q^{59} \) \(\mathstrut +\mathstrut 3280q^{60} \) \(\mathstrut -\mathstrut 1526q^{61} \) \(\mathstrut +\mathstrut 2440q^{62} \) \(\mathstrut +\mathstrut 176q^{63} \) \(\mathstrut -\mathstrut 2260q^{65} \) \(\mathstrut -\mathstrut 1680q^{66} \) \(\mathstrut -\mathstrut 1036q^{67} \) \(\mathstrut -\mathstrut 2428q^{68} \) \(\mathstrut -\mathstrut 872q^{69} \) \(\mathstrut -\mathstrut 3040q^{70} \) \(\mathstrut +\mathstrut 984q^{71} \) \(\mathstrut -\mathstrut 2172q^{72} \) \(\mathstrut +\mathstrut 2448q^{73} \) \(\mathstrut +\mathstrut 2228q^{75} \) \(\mathstrut +\mathstrut 800q^{76} \) \(\mathstrut +\mathstrut 4080q^{77} \) \(\mathstrut +\mathstrut 3720q^{78} \) \(\mathstrut +\mathstrut 368q^{79} \) \(\mathstrut +\mathstrut 2096q^{80} \) \(\mathstrut +\mathstrut 4917q^{81} \) \(\mathstrut +\mathstrut 536q^{82} \) \(\mathstrut +\mathstrut 948q^{83} \) \(\mathstrut +\mathstrut 3588q^{85} \) \(\mathstrut -\mathstrut 2552q^{86} \) \(\mathstrut -\mathstrut 744q^{87} \) \(\mathstrut -\mathstrut 2400q^{88} \) \(\mathstrut -\mathstrut 4066q^{89} \) \(\mathstrut -\mathstrut 2154q^{90} \) \(\mathstrut -\mathstrut 2288q^{91} \) \(\mathstrut -\mathstrut 1840q^{92} \) \(\mathstrut -\mathstrut 2576q^{93} \) \(\mathstrut -\mathstrut 956q^{95} \) \(\mathstrut +\mathstrut 1088q^{96} \) \(\mathstrut -\mathstrut 6760q^{97} \) \(\mathstrut +\mathstrut 326q^{98} \) \(\mathstrut -\mathstrut 1300q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(20))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
20.4.a \(\chi_{20}(1, \cdot)\) 20.4.a.a 1 1
20.4.c \(\chi_{20}(9, \cdot)\) 20.4.c.a 2 1
20.4.e \(\chi_{20}(3, \cdot)\) 20.4.e.a 2 2
20.4.e.b 12

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(20))\) into lower level spaces

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