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Properties

Label 80.12
Level 80
Weight 12
Dimension 1076
Nonzero newspaces 7
Newform subspaces 24
Sturm bound 4608
Trace bound 3

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Defining parameters

Level: \( N \) = \( 80 = 2^{4} \cdot 5 \)
Weight: \( k \) = \( 12 \)
Nonzero newspaces: \( 7 \)
Newform subspaces: \( 24 \)
Sturm bound: \(4608\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{12}(\Gamma_1(80))\).

Total New Old
Modular forms 2168 1102 1066
Cusp forms 2056 1076 980
Eisenstein series 112 26 86

Trace form

\( 1076 q - 4 q^{2} - 490 q^{3} - 6168 q^{4} + 1314 q^{5} - 60720 q^{6} + 136298 q^{7} - 149680 q^{8} - 679638 q^{9} + O(q^{10}) \) \( 1076 q - 4 q^{2} - 490 q^{3} - 6168 q^{4} + 1314 q^{5} - 60720 q^{6} + 136298 q^{7} - 149680 q^{8} - 679638 q^{9} + 988940 q^{10} + 656216 q^{11} - 4600528 q^{12} - 738142 q^{13} + 3659904 q^{14} + 12476754 q^{15} + 7442880 q^{16} - 15331542 q^{17} + 64438204 q^{18} + 24391500 q^{19} - 68655172 q^{20} - 75750572 q^{21} + 170022768 q^{22} + 31878302 q^{23} + 132361880 q^{24} + 250721396 q^{25} - 611370784 q^{26} - 48682252 q^{27} + 677706184 q^{28} + 19827976 q^{29} + 227370148 q^{30} - 210241060 q^{31} - 1652007664 q^{32} - 830147456 q^{33} + 1246520528 q^{34} + 468822922 q^{35} + 28790232 q^{36} + 1036033462 q^{37} - 238453536 q^{38} + 1696880804 q^{39} - 4812403712 q^{40} + 451135896 q^{41} + 4290562232 q^{42} - 8854563298 q^{43} + 9755249928 q^{44} - 3966720956 q^{45} - 12548953384 q^{46} + 14325614266 q^{47} + 456958568 q^{48} + 18754554758 q^{49} + 14213088896 q^{50} - 25475970292 q^{51} + 373123184 q^{52} + 6776692654 q^{53} - 5868866632 q^{54} + 3648536788 q^{55} - 25821691968 q^{56} + 10336328328 q^{57} + 42982306248 q^{58} - 22708013220 q^{59} - 25649307208 q^{60} - 4675022044 q^{61} + 31629039512 q^{62} + 14936034202 q^{63} + 32098868448 q^{64} - 27541382590 q^{65} - 117112465144 q^{66} + 79827436154 q^{67} - 46935011008 q^{68} + 55339179564 q^{69} + 170652026400 q^{70} - 34247335204 q^{71} + 32505143608 q^{72} - 37283309762 q^{73} - 231302691912 q^{74} + 217989333570 q^{75} - 30017907640 q^{76} + 40925455112 q^{77} + 282892621304 q^{78} - 204600447496 q^{79} + 223363907840 q^{80} + 132740043388 q^{81} + 85864043720 q^{82} + 42653930286 q^{83} - 779621708880 q^{84} - 29803403374 q^{85} - 163075652440 q^{86} + 131238934292 q^{87} + 702083668592 q^{88} + 76346563996 q^{89} + 594798277336 q^{90} - 59039456468 q^{91} + 126476184416 q^{92} + 77277245992 q^{93} - 939406376720 q^{94} - 185800160148 q^{95} + 92862255696 q^{96} + 76550026990 q^{97} + 229011965012 q^{98} + 1341415094208 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{12}^{\mathrm{new}}(\Gamma_1(80))\)

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
80.12.a \(\chi_{80}(1, \cdot)\) 80.12.a.a 1 1
80.12.a.b 1
80.12.a.c 1
80.12.a.d 1
80.12.a.e 1
80.12.a.f 1
80.12.a.g 2
80.12.a.h 2
80.12.a.i 2
80.12.a.j 2
80.12.a.k 2
80.12.a.l 3
80.12.a.m 3
80.12.c \(\chi_{80}(49, \cdot)\) 80.12.c.a 4 1
80.12.c.b 6
80.12.c.c 6
80.12.c.d 16
80.12.d \(\chi_{80}(41, \cdot)\) None 0 1
80.12.f \(\chi_{80}(9, \cdot)\) None 0 1
80.12.j \(\chi_{80}(43, \cdot)\) 80.12.j.a 260 2
80.12.l \(\chi_{80}(21, \cdot)\) 80.12.l.a 176 2
80.12.n \(\chi_{80}(47, \cdot)\) 80.12.n.a 2 2
80.12.n.b 20
80.12.n.c 44
80.12.o \(\chi_{80}(7, \cdot)\) None 0 2
80.12.q \(\chi_{80}(29, \cdot)\) 80.12.q.a 260 2
80.12.s \(\chi_{80}(3, \cdot)\) 80.12.s.a 260 2

Decomposition of \(S_{12}^{\mathrm{old}}(\Gamma_1(80))\) into lower level spaces

\( S_{12}^{\mathrm{old}}(\Gamma_1(80)) \cong \) \(S_{12}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 10}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 5}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 4}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 2}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 3}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 2}\)