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Properties

Label 72.20
Level 72
Weight 20
Dimension 1212
Nonzero newspaces 6
Sturm bound 5760
Trace bound 2

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Defining parameters

Level: \( N \) = \( 72 = 2^{3} \cdot 3^{2} \)
Weight: \( k \) = \( 20 \)
Nonzero newspaces: \( 6 \)
Sturm bound: \(5760\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{20}(\Gamma_1(72))\).

Total New Old
Modular forms 2784 1230 1554
Cusp forms 2688 1212 1476
Eisenstein series 96 18 78

Trace form

\( 1212 q - 460 q^{2} - 15507 q^{3} - 412110 q^{4} - 4445662 q^{5} - 1048580 q^{6} - 225069450 q^{7} - 868736998 q^{8} + 934582437 q^{9} + O(q^{10}) \) \( 1212 q - 460 q^{2} - 15507 q^{3} - 412110 q^{4} - 4445662 q^{5} - 1048580 q^{6} - 225069450 q^{7} - 868736998 q^{8} + 934582437 q^{9} - 15319069200 q^{10} + 25644838955 q^{11} - 48236893334 q^{12} - 3550940328 q^{13} - 114933461614 q^{14} - 94190808936 q^{15} + 464512430214 q^{16} - 801811193446 q^{17} - 109700159256 q^{18} - 7950440858154 q^{19} - 9447673106374 q^{20} - 8011676624124 q^{21} + 1822151745186 q^{22} + 46705015995990 q^{23} + 15439899719160 q^{24} - 190856100631851 q^{25} - 113764649309776 q^{26} + 201632026399200 q^{27} + 234722423101800 q^{28} - 102670174675080 q^{29} + 351907472301718 q^{30} + 107375803086240 q^{31} - 381133940019290 q^{32} + 235798562333531 q^{33} - 334982450234442 q^{34} - 192865939170684 q^{35} + 1582505411916290 q^{36} - 157800727724112 q^{37} + 6339772271220634 q^{38} - 7106682732983028 q^{39} - 2414892911910870 q^{40} - 4738921490637985 q^{41} + 148732353657002 q^{42} - 19295465543603235 q^{43} + 17733805842956658 q^{44} + 13552586782444766 q^{45} + 6343336925510808 q^{46} - 58905562475340942 q^{47} + 17226659662218596 q^{48} - 60788433863086125 q^{49} + 115146523943217962 q^{50} - 46031229782424375 q^{51} - 237085197833684250 q^{52} - 36373814711617204 q^{53} + 200409625253241312 q^{54} - 85871813982643800 q^{55} - 466529479444658368 q^{56} + 110570379925108273 q^{57} + 317081732349381342 q^{58} + 362530939040861981 q^{59} - 592291602615136482 q^{60} - 195918357471894306 q^{61} - 648130188575198276 q^{62} + 983116986801569312 q^{63} + 1120831140223244652 q^{64} - 743134069863586946 q^{65} + 989982043946684212 q^{66} + 55524183725275443 q^{67} - 2062298624865021252 q^{68} + 1947610783061768962 q^{69} - 456799587224786322 q^{70} - 5413203981255596336 q^{71} + 1241171905311974202 q^{72} + 462109515746653158 q^{73} - 3062144414016965962 q^{74} - 430418494097713799 q^{75} + 123880280509472934 q^{76} - 2333954660496281004 q^{77} + 720328613223344890 q^{78} + 3283151467807504308 q^{79} - 19011562035449790240 q^{80} - 1970411706792266623 q^{81} + 2570138530438528152 q^{82} - 1441882330066174628 q^{83} - 12751361433255427816 q^{84} - 1271436539952912276 q^{85} + 2660633982256898210 q^{86} - 7708202417124223062 q^{87} + 1333884742432947534 q^{88} - 2222201436473931856 q^{89} + 14862819089417946430 q^{90} + 1532407016204290968 q^{91} + 6619195397472697926 q^{92} - 8427453540762382366 q^{93} - 6322704029303027724 q^{94} + 202994354462657072 q^{95} - 18351499438377839424 q^{96} + 30667002615713766279 q^{97} + 50762227145823986706 q^{98} + 19412099446461511710 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{20}^{\mathrm{new}}(\Gamma_1(72))\)

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
72.20.a \(\chi_{72}(1, \cdot)\) 72.20.a.a 2 1
72.20.a.b 2
72.20.a.c 2
72.20.a.d 2
72.20.a.e 3
72.20.a.f 3
72.20.a.g 5
72.20.a.h 5
72.20.c \(\chi_{72}(71, \cdot)\) None 0 1
72.20.d \(\chi_{72}(37, \cdot)\) 72.20.d.a 2 1
72.20.d.b 18
72.20.d.c 36
72.20.d.d 38
72.20.f \(\chi_{72}(35, \cdot)\) 72.20.f.a 76 1
72.20.i \(\chi_{72}(25, \cdot)\) n/a 114 2
72.20.l \(\chi_{72}(11, \cdot)\) n/a 452 2
72.20.n \(\chi_{72}(13, \cdot)\) n/a 452 2
72.20.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 \(S_{20}^{\mathrm{old}}(\Gamma_1(72))\) into lower level spaces

\( S_{20}^{\mathrm{old}}(\Gamma_1(72)) \cong \) \(S_{20}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{20}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 9}\)\(\oplus\)\(S_{20}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 8}\)\(\oplus\)\(S_{20}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{20}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 6}\)\(\oplus\)\(S_{20}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 3}\)\(\oplus\)\(S_{20}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 4}\)\(\oplus\)\(S_{20}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 4}\)\(\oplus\)\(S_{20}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 3}\)\(\oplus\)\(S_{20}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 2}\)\(\oplus\)\(S_{20}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 2}\)