Properties

Label 20.12
Level 20
Weight 12
Dimension 71
Nonzero newspaces 3
Newforms 5
Sturm bound 288
Trace bound 1

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Defining parameters

Level: \( N \) = \( 20 = 2^{2} \cdot 5 \)
Weight: \( k \) = \( 12 \)
Nonzero newspaces: \( 3 \)
Newforms: \( 5 \)
Sturm bound: \(288\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{12}(\Gamma_1(20))\).

Total New Old
Modular forms 142 79 63
Cusp forms 122 71 51
Eisenstein series 20 8 12

Trace form

\( 71q - 2q^{2} + 526q^{3} - 1005q^{5} - 22360q^{6} - 28734q^{7} + 74836q^{8} - 541267q^{9} + O(q^{10}) \) \( 71q - 2q^{2} + 526q^{3} - 1005q^{5} - 22360q^{6} - 28734q^{7} + 74836q^{8} - 541267q^{9} + 141686q^{10} + 1591240q^{11} - 822800q^{12} + 1683696q^{13} - 3579398q^{15} - 9951048q^{16} + 17157688q^{17} + 7500306q^{18} + 2915508q^{19} + 19078396q^{20} + 12662164q^{21} + 11921800q^{22} + 22871382q^{23} - 21444893q^{25} + 137924084q^{26} - 31679468q^{27} - 111299120q^{28} - 99211842q^{29} - 488561080q^{30} + 368018364q^{31} + 894200968q^{32} + 242796800q^{33} - 198176602q^{35} - 1921753988q^{36} - 1009458468q^{37} + 1225929280q^{38} - 434288212q^{39} + 1481289516q^{40} + 556160998q^{41} - 4639041880q^{42} - 16928250q^{43} + 4684258285q^{45} + 7692828040q^{46} - 1145164758q^{47} - 8859314720q^{48} - 4798597599q^{49} - 6505828614q^{50} - 1872185332q^{51} + 18163869196q^{52} + 4023859300q^{53} - 792966600q^{55} - 23336652160q^{56} + 1769435864q^{57} + 15872923352q^{58} - 8259115724q^{59} + 17596714000q^{60} + 4224748082q^{61} - 15717288920q^{62} + 11880551714q^{63} + 47691466040q^{65} - 1233051600q^{66} + 2526990306q^{67} + 15025583492q^{68} - 59350995716q^{69} - 5648378720q^{70} - 54542711388q^{71} - 22275369852q^{72} + 23952274556q^{73} + 103111464398q^{75} + 29079600800q^{76} + 12621147840q^{77} - 28110803160q^{78} - 190446554136q^{79} - 87469704784q^{80} - 4477542297q^{81} + 165949305656q^{82} + 56064195942q^{83} + 123468971548q^{85} - 192079958360q^{86} - 121965495516q^{87} + 98741644960q^{88} - 298514754598q^{89} + 197558381526q^{90} + 92641274196q^{91} - 212561751280q^{92} + 152834305816q^{93} + 460054091404q^{95} + 334276984640q^{96} - 30346976548q^{97} - 201918342874q^{98} - 1031718518440q^{99} + O(q^{100}) \)

Decomposition of \(S_{12}^{\mathrm{new}}(\Gamma_1(20))\)

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
20.12.a \(\chi_{20}(1, \cdot)\) 20.12.a.a 1 1
20.12.a.b 2
20.12.c \(\chi_{20}(9, \cdot)\) 20.12.c.a 6 1
20.12.e \(\chi_{20}(3, \cdot)\) 20.12.e.a 2 2
20.12.e.b 60

Decomposition of \(S_{12}^{\mathrm{old}}(\Gamma_1(20))\) into lower level spaces

\( S_{12}^{\mathrm{old}}(\Gamma_1(20)) \cong \) \(S_{12}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 2}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 3}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 2}\)