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Properties

Label 72.17
Level 72
Weight 17
Dimension 1015
Nonzero newspaces 6
Sturm bound 4896
Trace bound 2

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Defining parameters

Level: \( N \) = \( 72 = 2^{3} \cdot 3^{2} \)
Weight: \( k \) = \( 17 \)
Nonzero newspaces: \( 6 \)
Sturm bound: \(4896\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{17}(\Gamma_1(72))\).

Total New Old
Modular forms 2352 1033 1319
Cusp forms 2256 1015 1241
Eisenstein series 96 18 78

Trace form

\( 1015 q - 96 q^{2} - 1908 q^{3} + 11314 q^{4} + 131068 q^{6} - 11366594 q^{7} - 11164134 q^{8} + 64111464 q^{9} + O(q^{10}) \) \( 1015 q - 96 q^{2} - 1908 q^{3} + 11314 q^{4} + 131068 q^{6} - 11366594 q^{7} - 11164134 q^{8} + 64111464 q^{9} - 202642152 q^{10} + 575041776 q^{11} + 920636866 q^{12} - 910969856 q^{13} + 5825490 q^{14} + 7938278718 q^{15} - 24854697850 q^{16} + 2448153114 q^{17} - 14548127328 q^{18} - 31274753386 q^{19} - 108517274742 q^{20} + 45829626720 q^{21} + 307393314338 q^{22} - 246990640326 q^{23} - 360799599096 q^{24} + 670488192427 q^{25} + 327624648240 q^{26} + 1441311454332 q^{27} - 1199398591576 q^{28} - 58756379616 q^{29} + 6322006015366 q^{30} + 58388856062 q^{31} - 7854678325386 q^{32} - 334284046612 q^{33} - 7452776088578 q^{34} - 4278356531724 q^{35} - 20394131955646 q^{36} + 2122774810464 q^{37} + 26520713317050 q^{38} + 4222615658778 q^{39} + 2532303796762 q^{40} - 37349371920246 q^{41} - 19029216420862 q^{42} - 72236692649588 q^{43} - 3174964015998 q^{44} + 2207607764384 q^{45} + 48217305096904 q^{46} + 68857513293018 q^{47} - 260394403338052 q^{48} - 63522529290133 q^{49} + 351918663495606 q^{50} + 79031547709608 q^{51} - 254851440546026 q^{52} - 63990193636488 q^{54} + 22002823814204 q^{55} + 747874850297808 q^{56} - 401553953844824 q^{57} - 865693101522250 q^{58} + 337790485199856 q^{59} + 601635150980766 q^{60} - 49335532860896 q^{61} - 362444154823812 q^{62} + 277258548430526 q^{63} - 551045646941684 q^{64} + 750409095111156 q^{65} + 3708531093250660 q^{66} - 963623665094836 q^{67} + 1365883195729356 q^{68} + 2881308909723328 q^{69} - 5814322985711794 q^{70} + 8831032572949314 q^{72} + 23376291981678 q^{73} - 6237990637030290 q^{74} + 1467729352620460 q^{75} + 514525148329910 q^{76} + 5778235023300288 q^{77} + 9810867072390106 q^{78} - 3562976421081058 q^{79} + 3367176764162160 q^{80} - 372698513842264 q^{81} + 8477669001856832 q^{82} + 4249838415026400 q^{83} + 1021717352363144 q^{84} - 225334253329888 q^{85} + 29833209714327138 q^{86} + 11968167642959262 q^{87} - 7612206108580594 q^{88} - 11742619827259494 q^{89} - 52279855454549786 q^{90} - 7505234688235020 q^{91} + 65641192299411222 q^{92} + 9019478510719232 q^{93} - 12904711525927716 q^{94} - 63759565956574368 q^{95} - 45991465663093896 q^{96} - 453038689508790 q^{97} + 92666152668964662 q^{98} + 57302715033931998 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{17}^{\mathrm{new}}(\Gamma_1(72))\)

We only show spaces with odd 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
72.17.b \(\chi_{72}(19, \cdot)\) 72.17.b.a 1 1
72.17.b.b 14
72.17.b.c 32
72.17.b.d 32
72.17.e \(\chi_{72}(17, \cdot)\) 72.17.e.a 8 1
72.17.e.b 8
72.17.g \(\chi_{72}(55, \cdot)\) None 0 1
72.17.h \(\chi_{72}(53, \cdot)\) 72.17.h.a 64 1
72.17.j \(\chi_{72}(5, \cdot)\) n/a 380 2
72.17.k \(\chi_{72}(7, \cdot)\) None 0 2
72.17.m \(\chi_{72}(41, \cdot)\) 72.17.m.a 96 2
72.17.p \(\chi_{72}(43, \cdot)\) n/a 380 2

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

Decomposition of \(S_{17}^{\mathrm{old}}(\Gamma_1(72))\) into lower level spaces

\( S_{17}^{\mathrm{old}}(\Gamma_1(72)) \cong \) \(S_{17}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 8}\)\(\oplus\)\(S_{17}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{17}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 6}\)\(\oplus\)\(S_{17}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 3}\)\(\oplus\)\(S_{17}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 4}\)\(\oplus\)\(S_{17}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 4}\)\(\oplus\)\(S_{17}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 3}\)\(\oplus\)\(S_{17}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 2}\)\(\oplus\)\(S_{17}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 2}\)