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Properties

Label 8.20
Level 8
Weight 20
Dimension 23
Nonzero newspaces 2
Newform subspaces 3
Sturm bound 80
Trace bound 1

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Defining parameters

Level: \( N \) = \( 8 = 2^{3} \)
Weight: \( k \) = \( 20 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 3 \)
Sturm bound: \(80\)
Trace bound: \(1\)

Dimensions

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

Total New Old
Modular forms 41 25 16
Cusp forms 35 23 12
Eisenstein series 6 2 4

Trace form

\( 23 q - 458 q^{2} - 4180 q^{3} - 412108 q^{4} + 3366838 q^{5} - 47240948 q^{6} + 63655016 q^{7} - 173313752 q^{8} - 4808787337 q^{9} + O(q^{10}) \) \( 23 q - 458 q^{2} - 4180 q^{3} - 412108 q^{4} + 3366838 q^{5} - 47240948 q^{6} + 63655016 q^{7} - 173313752 q^{8} - 4808787337 q^{9} + 758800104 q^{10} - 7461180572 q^{11} - 9351642296 q^{12} - 24989324626 q^{13} - 122453668784 q^{14} + 313775442840 q^{15} - 696212072432 q^{16} + 745408812286 q^{17} + 1813497117770 q^{18} + 91789194652 q^{19} + 6517087595632 q^{20} + 1413706100256 q^{21} - 11074654117412 q^{22} + 12366423799224 q^{23} - 36473014189168 q^{24} - 4283851921075 q^{25} + 26782030269304 q^{26} + 11408404421240 q^{27} - 97002327802784 q^{28} + 47417600266014 q^{29} + 327847200544208 q^{30} + 56684472288928 q^{31} + 122449430282912 q^{32} + 261008379402584 q^{33} - 478448330325748 q^{34} - 954185847061488 q^{35} - 1053851053424436 q^{36} + 1600526867615382 q^{37} - 486194587539796 q^{38} - 4629801688702440 q^{39} - 1697818250610976 q^{40} + 6559782861515446 q^{41} + 4964410757677984 q^{42} - 12296885808859324 q^{43} + 7031781193616424 q^{44} + 26569910848304302 q^{45} - 14917443628457488 q^{46} - 21582002902394640 q^{47} - 3197964747991392 q^{48} + 79583802656715631 q^{49} - 34734151321861826 q^{50} - 46515035377714280 q^{51} - 26877456911772208 q^{52} + 46649219708073478 q^{53} + 32102189624395064 q^{54} - 139301757145687448 q^{55} + 52858270161183424 q^{56} + 99401193783928920 q^{57} - 20470056808312424 q^{58} - 55774821261089228 q^{59} - 25825294995349152 q^{60} - 124702231193815042 q^{61} + 93766686763697984 q^{62} + 623085861964036072 q^{63} - 253721318369185216 q^{64} - 745666944375540604 q^{65} + 479551889901302712 q^{66} + 226785809908434796 q^{67} + 201388986348307752 q^{68} - 441174309724134304 q^{69} - 340698473416023872 q^{70} - 371529087787501144 q^{71} - 115475454880420648 q^{72} - 1032388677649304106 q^{73} - 93558253821761240 q^{74} + 3003253016266453684 q^{75} - 1090379619519933176 q^{76} - 2128959489278385312 q^{77} + 2029949680340770544 q^{78} + 3026712362616316816 q^{79} + 3057120301750869696 q^{80} + 280284797908382295 q^{81} - 2418785089528546244 q^{82} - 215922401337864868 q^{83} + 141493317659087296 q^{84} + 380436178852939660 q^{85} + 1332333723895598620 q^{86} - 14591356949907369192 q^{87} - 3097741184498130608 q^{88} + 9250198136648847142 q^{89} - 288100905697646824 q^{90} - 11324095727937747120 q^{91} - 2965990502259463392 q^{92} + 7763117681805520000 q^{93} - 3533635112749329696 q^{94} + 7889689928181619768 q^{95} - 2990158800543707584 q^{96} + 23827823451554462862 q^{97} + 8841667592735478822 q^{98} - 30782609165566913612 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

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
8.20.a \(\chi_{8}(1, \cdot)\) 8.20.a.a 2 1
8.20.a.b 3
8.20.b \(\chi_{8}(5, \cdot)\) 8.20.b.a 18 1

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

\( S_{20}^{\mathrm{old}}(\Gamma_1(8)) \cong \) \(S_{20}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{20}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 3}\)\(\oplus\)\(S_{20}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 2}\)