Properties

Label 20.6
Level 20
Weight 6
Dimension 29
Nonzero newspaces 3
Newform subspaces 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: \( 3 \)
Newform subspaces: \( 4 \)
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

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

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

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