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Properties

Label 80.20
Level 80
Weight 20
Dimension 1868
Nonzero newspaces 7
Sturm bound 7680
Trace bound 3

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Defining parameters

Level: \( N \) = \( 80 = 2^{4} \cdot 5 \)
Weight: \( k \) = \( 20 \)
Nonzero newspaces: \( 7 \)
Sturm bound: \(7680\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{20}(\Gamma_1(80))\).

Total New Old
Modular forms 3704 1894 1810
Cusp forms 3592 1868 1724
Eisenstein series 112 26 86

Trace form

\( 1868 q - 4 q^{2} - 39370 q^{3} - 1456920 q^{4} - 1782966 q^{5} - 89181744 q^{6} + 287433898 q^{7} - 1591441840 q^{8} - 4579780542 q^{9} + O(q^{10}) \) \( 1868 q - 4 q^{2} - 39370 q^{3} - 1456920 q^{4} - 1782966 q^{5} - 89181744 q^{6} + 287433898 q^{7} - 1591441840 q^{8} - 4579780542 q^{9} - 7100508020 q^{10} + 20056632632 q^{11} - 26969936848 q^{12} + 112923669458 q^{13} + 147596129664 q^{14} + 212768978994 q^{15} + 1203763340736 q^{16} - 716221450662 q^{17} + 528757293244 q^{18} - 2961679269076 q^{19} + 6090140162108 q^{20} - 9921227111084 q^{21} + 1980993746288 q^{22} + 23790953521502 q^{23} + 84977599803032 q^{24} + 164359835343436 q^{25} + 267613537729760 q^{26} - 94734853933132 q^{27} - 436279659479096 q^{28} - 13071362002184 q^{29} - 354835406697692 q^{30} - 823239562049828 q^{31} - 584009604481264 q^{32} + 1006015894663744 q^{33} + 646827547231952 q^{34} - 2002480140845558 q^{35} + 4119525082934232 q^{36} + 2840355204970822 q^{37} + 4710719748141024 q^{38} - 6761401576466332 q^{39} + 1136879608627968 q^{40} + 9576909913281096 q^{41} - 17734420867584328 q^{42} + 7458625079753982 q^{43} + 10460595672988680 q^{44} + 19746449484505804 q^{45} + 25570118336354776 q^{46} + 44852063226569146 q^{47} - 101172325692765592 q^{48} + 202188046481386110 q^{49} + 99459985728571136 q^{50} - 4671766155307444 q^{51} + 1232943414407024 q^{52} - 75501098591048066 q^{53} + 99858159147920312 q^{54} + 9588590765787828 q^{55} - 90133798479574080 q^{56} - 325977198070819512 q^{57} + 103623932538251208 q^{58} + 60675360701281020 q^{59} + 30073323674065592 q^{60} + 446737643600569396 q^{61} - 363376231923574888 q^{62} - 445282115432408678 q^{63} - 883840270105785120 q^{64} + 482399205143936210 q^{65} + 2923005091575108104 q^{66} + 400667951593839194 q^{67} - 1987192874941167808 q^{68} - 1211429623439289684 q^{69} - 147484237305293280 q^{70} + 4188780552897531164 q^{71} + 347471356873490488 q^{72} + 816604965424261838 q^{73} - 5034160076781649224 q^{74} + 2666487064308184290 q^{75} + 8242895664485406536 q^{76} + 2235009872878665032 q^{77} - 8434301452400722696 q^{78} - 2048071218894563976 q^{79} - 3883828422533628160 q^{80} + 17855850651571117300 q^{81} + 13118452423161435080 q^{82} - 165058534688337714 q^{83} - 25211125187689775184 q^{84} - 13042619563672638974 q^{85} + 23418335328612996776 q^{86} + 33386169362856479252 q^{87} - 22813573016927500688 q^{88} - 7572723978553197140 q^{89} + 6325446863668944856 q^{90} - 30878767199240466772 q^{91} + 54844754561985962336 q^{92} + 32056555466735114152 q^{93} - 28170242590921556240 q^{94} - 64322798020871577588 q^{95} + 34667963548471145040 q^{96} + 9100489939273530110 q^{97} + 80043719204665687892 q^{98} + 97160541048057787488 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{20}^{\mathrm{new}}(\Gamma_1(80))\)

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
80.20.a \(\chi_{80}(1, \cdot)\) 80.20.a.a 1 1
80.20.a.b 1
80.20.a.c 1
80.20.a.d 2
80.20.a.e 3
80.20.a.f 3
80.20.a.g 4
80.20.a.h 4
80.20.a.i 4
80.20.a.j 5
80.20.a.k 5
80.20.a.l 5
80.20.c \(\chi_{80}(49, \cdot)\) 80.20.c.a 8 1
80.20.c.b 10
80.20.c.c 10
80.20.c.d 28
80.20.d \(\chi_{80}(41, \cdot)\) None 0 1
80.20.f \(\chi_{80}(9, \cdot)\) None 0 1
80.20.j \(\chi_{80}(43, \cdot)\) n/a 452 2
80.20.l \(\chi_{80}(21, \cdot)\) n/a 304 2
80.20.n \(\chi_{80}(47, \cdot)\) n/a 114 2
80.20.o \(\chi_{80}(7, \cdot)\) None 0 2
80.20.q \(\chi_{80}(29, \cdot)\) n/a 452 2
80.20.s \(\chi_{80}(3, \cdot)\) n/a 452 2

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{20}^{\mathrm{old}}(\Gamma_1(80))\) into lower level spaces

\( S_{20}^{\mathrm{old}}(\Gamma_1(80)) \cong \) \(S_{20}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 10}\)\(\oplus\)\(S_{20}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 8}\)\(\oplus\)\(S_{20}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{20}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 5}\)\(\oplus\)\(S_{20}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{20}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 4}\)\(\oplus\)\(S_{20}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 2}\)\(\oplus\)\(S_{20}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 3}\)\(\oplus\)\(S_{20}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 2}\)