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Properties

Label 72.18
Level 72
Weight 18
Dimension 1083
Nonzero newspaces 6
Sturm bound 5184
Trace bound 2

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Defining parameters

Level: \( N \) = \( 72 = 2^{3} \cdot 3^{2} \)
Weight: \( k \) = \( 18 \)
Nonzero newspaces: \( 6 \)
Sturm bound: \(5184\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{18}(\Gamma_1(72))\).

Total New Old
Modular forms 2496 1101 1395
Cusp forms 2400 1083 1317
Eisenstein series 96 18 78

Trace form

\( 1083 q + 268 q^{2} - 4083 q^{3} - 27438 q^{4} + 716956 q^{5} - 262148 q^{6} + 30795358 q^{7} + 261083866 q^{8} - 5799801 q^{9} + O(q^{10}) \) \( 1083 q + 268 q^{2} - 4083 q^{3} - 27438 q^{4} + 716956 q^{5} - 262148 q^{6} + 30795358 q^{7} + 261083866 q^{8} - 5799801 q^{9} + 1595435488 q^{10} - 2142557969 q^{11} + 3380840986 q^{12} - 1706724042 q^{13} - 7662070766 q^{14} + 23057201256 q^{15} + 38267447430 q^{16} - 57484643180 q^{17} + 44701838040 q^{18} - 7056828262 q^{19} + 400725503194 q^{20} + 239917989780 q^{21} - 97976080446 q^{22} - 720766600818 q^{23} - 294274429800 q^{24} - 5027450626844 q^{25} + 7331191864528 q^{26} - 6765907296960 q^{27} - 5686412179352 q^{28} + 3693316073310 q^{29} + 3699398262454 q^{30} - 9384870003152 q^{31} - 38151420050362 q^{32} + 1726966685993 q^{33} - 30117551802298 q^{34} + 25446306992100 q^{35} + 44718445414658 q^{36} + 27199835784126 q^{37} + 18338266287098 q^{38} + 95795340631044 q^{39} - 270421205196278 q^{40} + 81773178987859 q^{41} - 253968904068070 q^{42} + 270581983845785 q^{43} + 27508400573010 q^{44} + 128906148733730 q^{45} + 810014465720952 q^{46} + 682521251687562 q^{47} + 625950071738900 q^{48} - 375131622231392 q^{49} - 2708058980372510 q^{50} + 1351034813567001 q^{51} + 3175215291770694 q^{52} - 2719329676449014 q^{53} - 2854543789598256 q^{54} - 780846830665648 q^{55} + 4537047084594592 q^{56} - 1126851714663149 q^{57} - 705890323860050 q^{58} - 13611905865620831 q^{59} - 10040282873557026 q^{60} + 2814055686999504 q^{61} + 10167764155733756 q^{62} - 9548216215966048 q^{63} - 6196432613404884 q^{64} + 8518624645623278 q^{65} - 16062971151014252 q^{66} + 7544466491983175 q^{67} + 25757882028527196 q^{68} - 1261349620780010 q^{69} - 6794941198267474 q^{70} + 23883209532308648 q^{71} - 24847277840904822 q^{72} + 14264155429566096 q^{73} + 61237902632390854 q^{74} - 27939123911949503 q^{75} - 5923598658159610 q^{76} + 6867396296750412 q^{77} - 98975814857396294 q^{78} + 20305854793864732 q^{79} + 142136662181180352 q^{80} - 50456962076222725 q^{81} + 25955190123910760 q^{82} + 170762733725235152 q^{83} - 161976341611563784 q^{84} - 5521290923601960 q^{85} + 163056400038542530 q^{86} + 98659249456447218 q^{87} + 173418182903896014 q^{88} - 150956586598214018 q^{89} + 1710748548398350 q^{90} - 302087591454499752 q^{91} - 302026962680951706 q^{92} + 225757051834668470 q^{93} + 382344232633476612 q^{94} + 546505929748140160 q^{95} - 448285889050222992 q^{96} - 128021756082716949 q^{97} + 45898395140869146 q^{98} + 375316241108167902 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{18}^{\mathrm{new}}(\Gamma_1(72))\)

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
72.18.a \(\chi_{72}(1, \cdot)\) 72.18.a.a 2 1
72.18.a.b 2
72.18.a.c 2
72.18.a.d 2
72.18.a.e 2
72.18.a.f 3
72.18.a.g 4
72.18.a.h 4
72.18.c \(\chi_{72}(71, \cdot)\) None 0 1
72.18.d \(\chi_{72}(37, \cdot)\) 72.18.d.a 2 1
72.18.d.b 16
72.18.d.c 32
72.18.d.d 34
72.18.f \(\chi_{72}(35, \cdot)\) 72.18.f.a 68 1
72.18.i \(\chi_{72}(25, \cdot)\) n/a 102 2
72.18.l \(\chi_{72}(11, \cdot)\) n/a 404 2
72.18.n \(\chi_{72}(13, \cdot)\) n/a 404 2
72.18.o \(\chi_{72}(23, \cdot)\) None 0 2

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

Decomposition of \(S_{18}^{\mathrm{old}}(\Gamma_1(72))\) into lower level spaces

\( S_{18}^{\mathrm{old}}(\Gamma_1(72)) \cong \) \(S_{18}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{18}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 9}\)\(\oplus\)\(S_{18}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 8}\)\(\oplus\)\(S_{18}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{18}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 6}\)\(\oplus\)\(S_{18}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 3}\)\(\oplus\)\(S_{18}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 4}\)\(\oplus\)\(S_{18}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 4}\)\(\oplus\)\(S_{18}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 3}\)\(\oplus\)\(S_{18}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 2}\)\(\oplus\)\(S_{18}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 2}\)