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Properties

Label 20.8
Level 20
Weight 8
Dimension 45
Nonzero newspaces 3
Newform subspaces 5
Sturm bound 192
Trace bound 1

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Defining parameters

Level: \( N \) = \( 20 = 2^{2} \cdot 5 \)
Weight: \( k \) = \( 8 \)
Nonzero newspaces: \( 3 \)
Newform subspaces: \( 5 \)
Sturm bound: \(192\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_1(20))\).

Total New Old
Modular forms 94 53 41
Cusp forms 74 45 29
Eisenstein series 20 8 12

Trace form

\( 45 q - 2 q^{2} - 26 q^{3} - 35 q^{5} + 104 q^{6} + 954 q^{7} - 1004 q^{8} + 671 q^{9} + O(q^{10}) \) \( 45 q - 2 q^{2} - 26 q^{3} - 35 q^{5} + 104 q^{6} + 954 q^{7} - 1004 q^{8} + 671 q^{9} - 3594 q^{10} - 2880 q^{11} + 10960 q^{12} + 2568 q^{13} + 3802 q^{15} - 44872 q^{16} + 13584 q^{17} + 60306 q^{18} - 55764 q^{19} + 89756 q^{20} - 32900 q^{21} - 191320 q^{22} + 43518 q^{23} + 249217 q^{25} + 252532 q^{26} - 159452 q^{27} - 142800 q^{28} - 446334 q^{29} - 252760 q^{30} - 100148 q^{31} + 188168 q^{32} + 551840 q^{33} + 986998 q^{35} + 231292 q^{36} + 14980 q^{37} - 406560 q^{38} - 2799124 q^{39} - 51924 q^{40} + 341138 q^{41} + 1616840 q^{42} + 2083230 q^{43} + 2566555 q^{45} - 2690616 q^{46} - 1832862 q^{47} + 549280 q^{48} - 4175253 q^{49} + 378586 q^{50} - 2308036 q^{51} - 3208564 q^{52} + 6094284 q^{53} + 5656640 q^{55} + 4064064 q^{56} - 3143464 q^{57} + 1530232 q^{58} - 9110148 q^{59} + 3280240 q^{60} - 4601290 q^{61} + 2750760 q^{62} + 7176506 q^{63} + 12375600 q^{65} - 2175120 q^{66} + 290634 q^{67} - 10060668 q^{68} - 10020092 q^{69} - 11417280 q^{70} - 2011164 q^{71} - 150012 q^{72} - 10208892 q^{73} + 2859638 q^{75} - 4045600 q^{76} + 9365280 q^{77} + 27127080 q^{78} + 11651688 q^{79} + 25379056 q^{80} + 12367749 q^{81} + 831896 q^{82} - 5962722 q^{83} - 27444652 q^{85} - 2245656 q^{86} - 3939564 q^{87} - 38612320 q^{88} + 4610214 q^{89} - 49385514 q^{90} + 8863668 q^{91} - 22809360 q^{92} + 4924984 q^{93} - 20143436 q^{95} + 49033664 q^{96} - 14554460 q^{97} + 58272326 q^{98} + 48327200 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_1(20))\)

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 available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
20.8.a \(\chi_{20}(1, \cdot)\) 20.8.a.a 1 1
20.8.a.b 2
20.8.c \(\chi_{20}(9, \cdot)\) 20.8.c.a 4 1
20.8.e \(\chi_{20}(3, \cdot)\) 20.8.e.a 2 2
20.8.e.b 36

Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_1(20))\) into lower level spaces

\( S_{8}^{\mathrm{old}}(\Gamma_1(20)) \cong \) \(S_{8}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 3}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 2}\)