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Properties

Label 72.6
Level 72
Weight 6
Dimension 312
Nonzero newspaces 6
Newform subspaces 16
Sturm bound 1728
Trace bound 2

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Defining parameters

Level: \( N \) = \( 72 = 2^{3} \cdot 3^{2} \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 6 \)
Newform subspaces: \( 16 \)
Sturm bound: \(1728\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(72))\).

Total New Old
Modular forms 768 330 438
Cusp forms 672 312 360
Eisenstein series 96 18 78

Trace form

\( 312 q - 4 q^{2} - 15 q^{3} + 18 q^{4} + 26 q^{5} - 68 q^{6} + 118 q^{7} + 602 q^{8} - 165 q^{9} + O(q^{10}) \) \( 312 q - 4 q^{2} - 15 q^{3} + 18 q^{4} + 26 q^{5} - 68 q^{6} + 118 q^{7} + 602 q^{8} - 165 q^{9} - 512 q^{10} - 1105 q^{11} - 1094 q^{12} - 36 q^{13} - 238 q^{14} + 456 q^{15} + 4230 q^{16} + 854 q^{17} - 4488 q^{18} + 5414 q^{19} - 1126 q^{20} + 2268 q^{21} + 4290 q^{22} - 12810 q^{23} + 9048 q^{24} - 9149 q^{25} + 12752 q^{26} - 3312 q^{27} - 3992 q^{28} + 12780 q^{29} - 38666 q^{30} + 9856 q^{31} + 6406 q^{32} - 6331 q^{33} + 1766 q^{34} - 13740 q^{35} + 66818 q^{36} - 10716 q^{37} - 8582 q^{38} - 19524 q^{39} - 28598 q^{40} + 50417 q^{41} - 96070 q^{42} + 29177 q^{43} - 31854 q^{44} + 4490 q^{45} + 33336 q^{46} + 32034 q^{47} + 141236 q^{48} - 93791 q^{49} + 146450 q^{50} + 13053 q^{51} + 42630 q^{52} + 44072 q^{53} - 44496 q^{54} - 72088 q^{55} - 244768 q^{56} + 22255 q^{57} - 226802 q^{58} - 165367 q^{59} + 62814 q^{60} + 15678 q^{61} + 153532 q^{62} - 42880 q^{63} - 142932 q^{64} - 13022 q^{65} + 65044 q^{66} - 7777 q^{67} + 30492 q^{68} + 32854 q^{69} + 343406 q^{70} + 508240 q^{71} - 84246 q^{72} - 2766 q^{73} + 78566 q^{74} + 137317 q^{75} + 73286 q^{76} + 52188 q^{77} + 248314 q^{78} - 70556 q^{79} - 85248 q^{80} - 91321 q^{81} - 703864 q^{82} - 557540 q^{83} - 186568 q^{84} - 7140 q^{85} - 750142 q^{86} - 286422 q^{87} - 178482 q^{88} - 187504 q^{89} + 319150 q^{90} + 154344 q^{91} + 765990 q^{92} - 111322 q^{93} + 638244 q^{94} + 636560 q^{95} + 36624 q^{96} + 36129 q^{97} + 398826 q^{98} + 81678 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(72))\)

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
72.6.a \(\chi_{72}(1, \cdot)\) 72.6.a.a 1 1
72.6.a.b 1
72.6.a.c 1
72.6.a.d 1
72.6.a.e 1
72.6.a.f 1
72.6.c \(\chi_{72}(71, \cdot)\) None 0 1
72.6.d \(\chi_{72}(37, \cdot)\) 72.6.d.a 2 1
72.6.d.b 4
72.6.d.c 8
72.6.d.d 10
72.6.f \(\chi_{72}(35, \cdot)\) 72.6.f.a 20 1
72.6.i \(\chi_{72}(25, \cdot)\) 72.6.i.a 14 2
72.6.i.b 16
72.6.l \(\chi_{72}(11, \cdot)\) 72.6.l.a 4 2
72.6.l.b 112
72.6.n \(\chi_{72}(13, \cdot)\) 72.6.n.a 116 2
72.6.o \(\chi_{72}(23, \cdot)\) None 0 2

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(72))\) into lower level spaces

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