Properties

Label 20.6
Level 20
Weight 6
Dimension 29
Nonzero newspaces 3
Newforms 4
Sturm bound 144
Trace bound 1

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Defining parameters

Level: \( N \) = \( 20 = 2^{2} \cdot 5 \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 3 \)
Newforms: \( 4 \)
Sturm bound: \(144\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(20))\).

Total New Old
Modular forms 70 37 33
Cusp forms 50 29 21
Eisenstein series 20 8 12

Trace form

\( 29q - 2q^{2} + 22q^{3} - 39q^{5} - 184q^{6} + 218q^{7} + 244q^{8} + 479q^{9} + O(q^{10}) \) \( 29q - 2q^{2} + 22q^{3} - 39q^{5} - 184q^{6} + 218q^{7} + 244q^{8} + 479q^{9} + 566q^{10} - 680q^{11} - 1280q^{12} - 504q^{13} - 1790q^{15} + 1976q^{16} + 1192q^{17} - 3246q^{18} + 3284q^{19} - 1364q^{20} + 3700q^{21} - 2440q^{22} - 3186q^{23} - 13319q^{25} + 6836q^{26} - 44q^{27} + 5920q^{28} + 21234q^{29} + 8600q^{30} + 5068q^{31} + 17608q^{32} - 160q^{33} - 19090q^{35} - 27908q^{36} - 3796q^{37} - 22160q^{38} + 2684q^{39} - 31444q^{40} - 38870q^{41} - 39400q^{42} - 370q^{43} + 20671q^{45} + 29416q^{46} + 16146q^{47} + 108160q^{48} + 34323q^{49} + 114186q^{50} + 25916q^{51} + 38476q^{52} - 63356q^{53} + 13000q^{55} - 85984q^{56} + 13832q^{57} - 183672q^{58} - 63692q^{59} - 263840q^{60} + 103238q^{61} - 109400q^{62} + 52538q^{63} + 29192q^{65} + 186000q^{66} - 11542q^{67} + 313988q^{68} - 146228q^{69} + 364240q^{70} + 45684q^{71} + 309828q^{72} + 72996q^{73} + 26150q^{75} - 297600q^{76} - 157920q^{77} - 586200q^{78} - 128248q^{79} - 467824q^{80} - 276315q^{81} - 458744q^{82} - 38466q^{83} + 76892q^{85} + 545416q^{86} + 121572q^{87} + 690080q^{88} + 121166q^{89} + 945366q^{90} + 44452q^{91} + 576800q^{92} + 388072q^{93} + 7660q^{95} - 841984q^{96} + 224084q^{97} - 1036906q^{98} - 139480q^{99} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(20))\)

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
20.6.a \(\chi_{20}(1, \cdot)\) 20.6.a.a 1 1
20.6.c \(\chi_{20}(9, \cdot)\) 20.6.c.a 2 1
20.6.e \(\chi_{20}(3, \cdot)\) 20.6.e.a 2 2
20.6.e.b 24

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(20))\) into lower level spaces

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