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Properties

Label 80.4
Level 80
Weight 4
Dimension 284
Nonzero newspaces 7
Newform subspaces 16
Sturm bound 1536
Trace bound 3

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Defining parameters

Level: \( N \) = \( 80 = 2^{4} \cdot 5 \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 7 \)
Newform subspaces: \( 16 \)
Sturm bound: \(1536\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(80))\).

Total New Old
Modular forms 632 310 322
Cusp forms 520 284 236
Eisenstein series 112 26 86

Trace form

\( 284 q - 4 q^{2} - 10 q^{3} - 24 q^{4} - 6 q^{5} + 48 q^{6} + 42 q^{7} + 80 q^{8} + 18 q^{9} + O(q^{10}) \) \( 284 q - 4 q^{2} - 10 q^{3} - 24 q^{4} - 6 q^{5} + 48 q^{6} + 42 q^{7} + 80 q^{8} + 18 q^{9} + 60 q^{10} - 136 q^{11} - 208 q^{12} - 142 q^{13} - 384 q^{14} + 114 q^{15} - 576 q^{16} - 6 q^{17} - 356 q^{18} + 364 q^{19} + 188 q^{20} + 340 q^{21} + 1168 q^{22} - 34 q^{23} + 1688 q^{24} + 156 q^{25} + 512 q^{26} - 460 q^{27} - 56 q^{28} + 280 q^{29} + 388 q^{30} - 804 q^{31} - 1264 q^{32} - 320 q^{33} - 1456 q^{34} - 758 q^{35} - 552 q^{36} - 986 q^{37} + 384 q^{38} - 796 q^{39} - 1792 q^{40} - 792 q^{41} - 1288 q^{42} + 1342 q^{43} - 2808 q^{44} - 836 q^{45} - 2088 q^{46} + 1978 q^{47} - 1432 q^{48} + 142 q^{49} + 1856 q^{50} + 3020 q^{51} + 4208 q^{52} + 2782 q^{53} + 4472 q^{54} + 1268 q^{55} + 960 q^{56} + 1992 q^{57} - 24 q^{58} - 2628 q^{59} - 328 q^{60} - 2028 q^{61} + 152 q^{62} - 614 q^{63} - 4896 q^{64} + 1970 q^{65} - 5752 q^{66} + 1178 q^{67} - 1216 q^{68} - 1620 q^{69} - 960 q^{70} - 868 q^{71} + 568 q^{72} - 2130 q^{73} + 5208 q^{74} - 6750 q^{75} + 6728 q^{76} + 200 q^{77} + 13304 q^{78} - 392 q^{79} + 8960 q^{80} - 3068 q^{81} + 7304 q^{82} - 3186 q^{83} + 5040 q^{84} - 3294 q^{85} - 5176 q^{86} - 6124 q^{87} - 2448 q^{88} - 1652 q^{89} - 5624 q^{90} - 84 q^{91} - 6304 q^{92} + 7336 q^{93} - 848 q^{94} + 4812 q^{95} - 3504 q^{96} + 4830 q^{97} - 4204 q^{98} + 3360 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(80))\)

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
80.4.a \(\chi_{80}(1, \cdot)\) 80.4.a.a 1 1
80.4.a.b 1
80.4.a.c 1
80.4.a.d 1
80.4.a.e 1
80.4.a.f 1
80.4.c \(\chi_{80}(49, \cdot)\) 80.4.c.a 2 1
80.4.c.b 2
80.4.c.c 4
80.4.d \(\chi_{80}(41, \cdot)\) None 0 1
80.4.f \(\chi_{80}(9, \cdot)\) None 0 1
80.4.j \(\chi_{80}(43, \cdot)\) 80.4.j.a 68 2
80.4.l \(\chi_{80}(21, \cdot)\) 80.4.l.a 48 2
80.4.n \(\chi_{80}(47, \cdot)\) 80.4.n.a 2 2
80.4.n.b 4
80.4.n.c 12
80.4.o \(\chi_{80}(7, \cdot)\) None 0 2
80.4.q \(\chi_{80}(29, \cdot)\) 80.4.q.a 68 2
80.4.s \(\chi_{80}(3, \cdot)\) 80.4.s.a 68 2

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(80))\) into lower level spaces

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