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Properties

Label 72.21
Level 72
Weight 21
Dimension 1271
Nonzero newspaces 6
Sturm bound 6048
Trace bound 2

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Defining parameters

Level: \( N \) = \( 72 = 2^{3} \cdot 3^{2} \)
Weight: \( k \) = \( 21 \)
Nonzero newspaces: \( 6 \)
Sturm bound: \(6048\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{21}(\Gamma_1(72))\).

Total New Old
Modular forms 2928 1289 1639
Cusp forms 2832 1271 1561
Eisenstein series 96 18 78

Trace form

\( 1271 q + 624 q^{2} - 10608 q^{3} + 1773554 q^{4} + 2097148 q^{6} + 187327246 q^{7} + 3250902426 q^{8} - 4614984444 q^{9} + O(q^{10}) \) \( 1271 q + 624 q^{2} - 10608 q^{3} + 1773554 q^{4} + 2097148 q^{6} + 187327246 q^{7} + 3250902426 q^{8} - 4614984444 q^{9} + 2485208888 q^{10} + 17204979084 q^{11} + 43764724066 q^{12} - 164244011776 q^{13} + 1125941212626 q^{14} + 49966873998 q^{15} + 7543044743302 q^{16} + 990389375394 q^{17} + 5071262884032 q^{18} - 3429516685570 q^{19} - 905372554422 q^{20} + 44046871197048 q^{21} + 5743863835618 q^{22} + 108084786051594 q^{23} - 185225102125368 q^{24} + 455553006559447 q^{25} + 565053227881968 q^{26} - 157950631156068 q^{27} - 344882591525976 q^{28} - 1152884208314520 q^{29} - 2102375501593274 q^{30} - 2324919620620482 q^{31} - 2106166601686986 q^{32} - 140308838709592 q^{33} - 7409565512195106 q^{34} + 2852923700343156 q^{35} - 32873664509438398 q^{36} - 8666443278779016 q^{37} + 6904548824630010 q^{38} + 13898455646458722 q^{39} - 758586945417638 q^{40} + 37751280038243310 q^{41} + 171651139491019298 q^{42} + 971087379441552 q^{43} - 258199768481253438 q^{44} + 71143601859337544 q^{45} + 100808029162326536 q^{46} - 233308649906321262 q^{47} + 92128808318770268 q^{48} - 400178081604025593 q^{49} + 130314145660259526 q^{50} + 307826743428510708 q^{51} + 64330922499280214 q^{52} - 139529007462744936 q^{54} + 2408694765810896204 q^{55} + 789918586953873168 q^{56} - 1283930417081838764 q^{57} - 1347733378972037610 q^{58} + 2432486205362121420 q^{59} + 867770889950704926 q^{60} - 2177987353783431448 q^{61} - 1658931466251292932 q^{62} - 4544240069481966994 q^{63} + 3939613611408944780 q^{64} + 3916119371583842676 q^{65} + 3296267112992954788 q^{66} - 6139921193646514816 q^{67} - 3309979436501218164 q^{68} + 6903773142328692976 q^{69} + 33859278816015114446 q^{70} - 3382928070097705566 q^{72} + 5104463845359100878 q^{73} + 49910247380625758286 q^{74} + 36079518413440432120 q^{75} - 10799967404630443018 q^{76} - 37102929004126862352 q^{77} + 80102902752137929306 q^{78} + 11283809945225014950 q^{79} + 22227068144200206000 q^{80} + 16501695225613878548 q^{81} - 139366377163736246368 q^{82} - 55952143194264537000 q^{83} + 74099554952922671816 q^{84} + 5967242750491732072 q^{85} - 75362390900074723806 q^{86} - 167474475407720941818 q^{87} + 30760182474201070606 q^{88} + 54107024905441330434 q^{89} - 67382245747501126586 q^{90} + 51808214286268572276 q^{91} - 210205889815171251498 q^{92} - 222625193756394443968 q^{93} + 80301958634910007740 q^{94} + 264973637837105927352 q^{95} - 216990945338284809960 q^{96} - 273717153426172203810 q^{97} - 379054721111273515098 q^{98} + 448906198071681035094 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{21}^{\mathrm{new}}(\Gamma_1(72))\)

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
72.21.b \(\chi_{72}(19, \cdot)\) 72.21.b.a 1 1
72.21.b.b 18
72.21.b.c 40
72.21.b.d 40
72.21.e \(\chi_{72}(17, \cdot)\) 72.21.e.a 10 1
72.21.e.b 10
72.21.g \(\chi_{72}(55, \cdot)\) None 0 1
72.21.h \(\chi_{72}(53, \cdot)\) 72.21.h.a 80 1
72.21.j \(\chi_{72}(5, \cdot)\) n/a 476 2
72.21.k \(\chi_{72}(7, \cdot)\) None 0 2
72.21.m \(\chi_{72}(41, \cdot)\) n/a 120 2
72.21.p \(\chi_{72}(43, \cdot)\) n/a 476 2

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

Decomposition of \(S_{21}^{\mathrm{old}}(\Gamma_1(72))\) into lower level spaces

\( S_{21}^{\mathrm{old}}(\Gamma_1(72)) \cong \) \(S_{21}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{21}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 9}\)\(\oplus\)\(S_{21}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 8}\)\(\oplus\)\(S_{21}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{21}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 6}\)\(\oplus\)\(S_{21}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 3}\)\(\oplus\)\(S_{21}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 4}\)\(\oplus\)\(S_{21}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 4}\)\(\oplus\)\(S_{21}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 3}\)\(\oplus\)\(S_{21}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 2}\)\(\oplus\)\(S_{21}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 2}\)\(\oplus\)\(S_{21}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 1}\)