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Properties

Label 72.5
Level 72
Weight 5
Dimension 247
Nonzero newspaces 6
Newform subspaces 11
Sturm bound 1440
Trace bound 2

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Defining parameters

Level: \( N \) = \( 72 = 2^{3} \cdot 3^{2} \)
Weight: \( k \) = \( 5 \)
Nonzero newspaces: \( 6 \)
Newform subspaces: \( 11 \)
Sturm bound: \(1440\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(\Gamma_1(72))\).

Total New Old
Modular forms 624 265 359
Cusp forms 528 247 281
Eisenstein series 96 18 78

Trace form

\( 247 q - 14 q^{4} + 28 q^{6} - 50 q^{7} - 102 q^{8} - 108 q^{9} + O(q^{10}) \) \( 247 q - 14 q^{4} + 28 q^{6} - 50 q^{7} - 102 q^{8} - 108 q^{9} - 72 q^{10} + 156 q^{11} + 226 q^{12} + 256 q^{13} + 594 q^{14} + 78 q^{15} + 134 q^{16} - 126 q^{17} - 1954 q^{19} + 1098 q^{20} + 24 q^{21} + 962 q^{22} + 714 q^{23} - 1080 q^{24} + 3367 q^{25} - 6000 q^{26} + 540 q^{27} - 3160 q^{28} + 2376 q^{29} + 4486 q^{30} - 4546 q^{31} + 5430 q^{32} - 1096 q^{33} + 574 q^{34} - 1164 q^{35} - 5566 q^{36} + 3096 q^{37} - 3750 q^{38} - 3006 q^{39} + 9562 q^{40} - 1698 q^{41} - 3742 q^{42} + 2560 q^{43} + 10434 q^{44} - 4696 q^{45} + 10696 q^{46} + 4530 q^{47} + 12764 q^{48} - 361 q^{49} - 16554 q^{50} - 15036 q^{51} - 28586 q^{52} - 19848 q^{54} - 10996 q^{55} - 17904 q^{56} - 92 q^{57} - 6634 q^{58} + 3804 q^{59} + 13086 q^{60} + 712 q^{61} + 20700 q^{62} + 33710 q^{63} + 48268 q^{64} + 14196 q^{65} - 13244 q^{66} + 20528 q^{67} + 28044 q^{68} + 5680 q^{69} + 19886 q^{70} - 4062 q^{72} + 4686 q^{73} - 40722 q^{74} - 46520 q^{75} - 65290 q^{76} - 28368 q^{77} + 4090 q^{78} - 21370 q^{79} - 33360 q^{80} - 30364 q^{81} - 34432 q^{82} - 11400 q^{83} + 19400 q^{84} - 10168 q^{85} + 51714 q^{86} + 53094 q^{87} + 73742 q^{88} + 12642 q^{89} - 15386 q^{90} + 47220 q^{91} + 73686 q^{92} + 39488 q^{93} + 65052 q^{94} + 61272 q^{95} + 42648 q^{96} - 8562 q^{97} - 15018 q^{98} + 40566 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{5}^{\mathrm{new}}(\Gamma_1(72))\)

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
72.5.b \(\chi_{72}(19, \cdot)\) 72.5.b.a 1 1
72.5.b.b 2
72.5.b.c 8
72.5.b.d 8
72.5.e \(\chi_{72}(17, \cdot)\) 72.5.e.a 2 1
72.5.e.b 2
72.5.g \(\chi_{72}(55, \cdot)\) None 0 1
72.5.h \(\chi_{72}(53, \cdot)\) 72.5.h.a 16 1
72.5.j \(\chi_{72}(5, \cdot)\) 72.5.j.a 92 2
72.5.k \(\chi_{72}(7, \cdot)\) None 0 2
72.5.m \(\chi_{72}(41, \cdot)\) 72.5.m.a 24 2
72.5.p \(\chi_{72}(43, \cdot)\) 72.5.p.a 4 2
72.5.p.b 88

Decomposition of \(S_{5}^{\mathrm{old}}(\Gamma_1(72))\) into lower level spaces

\( S_{5}^{\mathrm{old}}(\Gamma_1(72)) \cong \) \(S_{5}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 9}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 8}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 6}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 1}\)