Properties

Label 72.22
Level 72
Weight 22
Dimension 1340
Nonzero newspaces 6
Sturm bound 6336
Trace bound 2

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Defining parameters

Level: \( N \) = \( 72 = 2^{3} \cdot 3^{2} \)
Weight: \( k \) = \( 22 \)
Nonzero newspaces: \( 6 \)
Sturm bound: \(6336\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{22}(\Gamma_1(72))\).

Total New Old
Modular forms 3072 1358 1714
Cusp forms 2976 1340 1636
Eisenstein series 96 18 78

Trace form

\( 1340 q + 284 q^{2} + 67713 q^{3} + 409874 q^{4} + 17058866 q^{5} - 4194308 q^{6} - 175809578 q^{7} - 6634270630 q^{8} - 15969907221 q^{9} + O(q^{10}) \) \( 1340 q + 284 q^{2} + 67713 q^{3} + 409874 q^{4} + 17058866 q^{5} - 4194308 q^{6} - 175809578 q^{7} - 6634270630 q^{8} - 15969907221 q^{9} + 107766898688 q^{10} - 287243704657 q^{11} + 622607444026 q^{12} - 565825160812 q^{13} + 2642026375442 q^{14} - 4924408866744 q^{15} - 8144598667130 q^{16} + 756319963646 q^{17} + 32927894321784 q^{18} + 106606046635862 q^{19} + 92674321185434 q^{20} + 92041381916796 q^{21} - 104192125409534 q^{22} - 886174674405738 q^{23} - 555615329734056 q^{24} - 5272515437040209 q^{25} + 592305198005264 q^{26} + 4673211288689232 q^{27} - 6517180804013976 q^{28} + 5249332956983748 q^{29} - 22719858879872906 q^{30} - 5852428388204352 q^{31} + 42688256350916614 q^{32} - 2792738033302411 q^{33} + 65222228955732390 q^{34} + 54254688994600980 q^{35} + 12582037897942274 q^{36} - 15332418658447524 q^{37} - 9790886180446022 q^{38} + 113080627906970268 q^{39} + 373758613795321162 q^{40} + 169989123366443849 q^{41} + 511238925015175610 q^{42} + 588008026879446393 q^{43} - 523800188661410670 q^{44} + 384635196894589610 q^{45} + 144400619467100600 q^{46} + 2812882996541568642 q^{47} + 764522082037242932 q^{48} - 382590607114479243 q^{49} - 1141333815014974030 q^{50} + 929331155700149133 q^{51} + 2654685020592664454 q^{52} - 831951046317824320 q^{53} - 5965734025708811664 q^{54} + 9314943583596095432 q^{55} + 11478805522199310560 q^{56} + 13130459171101825567 q^{57} - 13016342889510266610 q^{58} + 18966520664346871721 q^{59} + 10887323889375660894 q^{60} - 7393106861149785706 q^{61} + 4260552694704573820 q^{62} - 16246675993331981056 q^{63} - 108873001757860879444 q^{64} + 11095037175850243378 q^{65} - 46396692422480651564 q^{66} + 25149460654325884415 q^{67} - 76450093363623035364 q^{68} - 22691808718452795818 q^{69} + 17422622215062257966 q^{70} + 311552368154863354096 q^{71} - 102109684535951427990 q^{72} - 18826833132758788902 q^{73} + 176926973706553256870 q^{74} + 92119912693383157 q^{75} + 429897560458655249222 q^{76} + 129483366790878985500 q^{77} - 19946767810025244614 q^{78} - 192695686203800628348 q^{79} + 402196890286728471552 q^{80} + 643683978092397136439 q^{81} - 246031522103404007608 q^{82} - 1823909738545437747380 q^{83} + 818619207052593951800 q^{84} - 155711601422125658900 q^{85} + 125886063378444503042 q^{86} - 1161016603475333168886 q^{87} - 1314192199959965748530 q^{88} - 9913523356631823112 q^{89} + 167263110723000813550 q^{90} - 305969112712615233240 q^{91} + 777290240612251808550 q^{92} - 550135695050265243418 q^{93} - 3332880752971704135324 q^{94} + 3270958986704102321360 q^{95} + 7466484389201194952592 q^{96} - 573801660593644181031 q^{97} - 12407473676062102180278 q^{98} - 6730134831054413816370 q^{99} + O(q^{100}) \)

Decomposition of \(S_{22}^{\mathrm{new}}(\Gamma_1(72))\)

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
72.22.a \(\chi_{72}(1, \cdot)\) 72.22.a.a 2 1
72.22.a.b 2
72.22.a.c 3
72.22.a.d 3
72.22.a.e 3
72.22.a.f 3
72.22.a.g 5
72.22.a.h 5
72.22.c \(\chi_{72}(71, \cdot)\) None 0 1
72.22.d \(\chi_{72}(37, \cdot)\) n/a 104 1
72.22.f \(\chi_{72}(35, \cdot)\) 72.22.f.a 84 1
72.22.i \(\chi_{72}(25, \cdot)\) n/a 126 2
72.22.l \(\chi_{72}(11, \cdot)\) n/a 500 2
72.22.n \(\chi_{72}(13, \cdot)\) n/a 500 2
72.22.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 \(S_{22}^{\mathrm{old}}(\Gamma_1(72))\) into lower level spaces

\( S_{22}^{\mathrm{old}}(\Gamma_1(72)) \cong \) \(S_{22}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 9}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 8}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 6}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 3}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 4}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 4}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 3}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 2}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 2}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 1}\)