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Properties

Label 80.10
Level 80
Weight 10
Dimension 878
Nonzero newspaces 7
Newform subspaces 22
Sturm bound 3840
Trace bound 3

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Defining parameters

Level: \( N \) = \( 80 = 2^{4} \cdot 5 \)
Weight: \( k \) = \( 10 \)
Nonzero newspaces: \( 7 \)
Newform subspaces: \( 22 \)
Sturm bound: \(3840\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_1(80))\).

Total New Old
Modular forms 1784 904 880
Cusp forms 1672 878 794
Eisenstein series 112 26 86

Trace form

\( 878 q - 4 q^{2} + 158 q^{3} - 344 q^{4} + 352 q^{5} + 4368 q^{6} - 2758 q^{7} + 1424 q^{8} - 11628 q^{9} + O(q^{10}) \) \( 878 q - 4 q^{2} + 158 q^{3} - 344 q^{4} + 352 q^{5} + 4368 q^{6} - 2758 q^{7} + 1424 q^{8} - 11628 q^{9} - 4692 q^{10} - 109744 q^{11} - 434320 q^{12} + 258470 q^{13} + 267072 q^{14} - 586422 q^{15} + 1634496 q^{16} + 63774 q^{17} - 4359812 q^{18} - 9404 q^{19} + 3277980 q^{20} + 1863124 q^{21} + 68592 q^{22} + 53934 q^{23} - 3727720 q^{24} + 4399438 q^{25} + 12695520 q^{26} - 2152252 q^{27} - 5161912 q^{28} - 4307876 q^{29} - 28678652 q^{30} + 1005852 q^{31} + 54633616 q^{32} + 17285584 q^{33} - 53682096 q^{34} - 14276726 q^{35} - 118931880 q^{36} + 6023202 q^{37} + 117230112 q^{38} - 55844140 q^{39} + 167248960 q^{40} + 4940236 q^{41} - 340456648 q^{42} + 173446230 q^{43} - 25460920 q^{44} - 95141798 q^{45} + 24967448 q^{46} - 298361894 q^{47} + 429751400 q^{48} + 331049448 q^{49} - 126115488 q^{50} + 253264412 q^{51} - 362935120 q^{52} + 467993418 q^{53} - 130000456 q^{54} - 36232116 q^{55} - 53022528 q^{56} - 176735592 q^{57} + 356543560 q^{58} - 176837116 q^{59} - 231131272 q^{60} + 110282384 q^{61} + 273577880 q^{62} + 511442458 q^{63} + 764733664 q^{64} + 447916894 q^{65} + 573711560 q^{66} + 535990418 q^{67} - 969283648 q^{68} - 1007670132 q^{69} - 1401948640 q^{70} - 1090988692 q^{71} + 977392504 q^{72} + 713861754 q^{73} + 2188462584 q^{74} - 1303824246 q^{75} + 875120008 q^{76} + 25935928 q^{77} - 1448704456 q^{78} + 750500312 q^{79} - 2174562432 q^{80} + 1375360318 q^{81} + 1080832776 q^{82} + 928974710 q^{83} + 3673592496 q^{84} - 2162681882 q^{85} + 3074251816 q^{86} - 4838564236 q^{87} - 2311113872 q^{88} - 1605217032 q^{89} - 10365321320 q^{90} + 2129646988 q^{91} - 144567840 q^{92} + 3624143176 q^{93} + 4867285360 q^{94} + 1612367188 q^{95} + 18717655632 q^{96} - 787562518 q^{97} + 2236117908 q^{98} - 11854403736 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_1(80))\)

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
80.10.a \(\chi_{80}(1, \cdot)\) 80.10.a.a 1 1
80.10.a.b 1
80.10.a.c 1
80.10.a.d 1
80.10.a.e 1
80.10.a.f 2
80.10.a.g 2
80.10.a.h 2
80.10.a.i 2
80.10.a.j 2
80.10.a.k 3
80.10.c \(\chi_{80}(49, \cdot)\) 80.10.c.a 4 1
80.10.c.b 4
80.10.c.c 4
80.10.c.d 14
80.10.d \(\chi_{80}(41, \cdot)\) None 0 1
80.10.f \(\chi_{80}(9, \cdot)\) None 0 1
80.10.j \(\chi_{80}(43, \cdot)\) 80.10.j.a 212 2
80.10.l \(\chi_{80}(21, \cdot)\) 80.10.l.a 144 2
80.10.n \(\chi_{80}(47, \cdot)\) 80.10.n.a 2 2
80.10.n.b 16
80.10.n.c 36
80.10.o \(\chi_{80}(7, \cdot)\) None 0 2
80.10.q \(\chi_{80}(29, \cdot)\) 80.10.q.a 212 2
80.10.s \(\chi_{80}(3, \cdot)\) 80.10.s.a 212 2

Decomposition of \(S_{10}^{\mathrm{old}}(\Gamma_1(80))\) into lower level spaces

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