↑

Properties

Label 72.10
Level 72
Weight 10
Dimension 569
Nonzero newspaces 6
Newform subspaces 18
Sturm bound 2880
Trace bound 2

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 72 = 2^{3} \cdot 3^{2} \)
Weight: \( k \) = \( 10 \)
Nonzero newspaces: \( 6 \)
Newform subspaces: \( 18 \)
Sturm bound: \(2880\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_1(72))\).

Total New Old
Modular forms 1344 587 757
Cusp forms 1248 569 679
Eisenstein series 96 18 78

Trace form

\( 569 q - 20 q^{2} + 69 q^{3} - 430 q^{4} + 1936 q^{5} - 1028 q^{6} - 1106 q^{7} - 21542 q^{8} + 37695 q^{9} + O(q^{10}) \) \( 569 q - 20 q^{2} + 69 q^{3} - 430 q^{4} + 1936 q^{5} - 1028 q^{6} - 1106 q^{7} - 21542 q^{8} + 37695 q^{9} + 3488 q^{10} - 103313 q^{11} - 55334 q^{12} - 53926 q^{13} + 635410 q^{14} + 194856 q^{15} - 2197370 q^{16} - 1333952 q^{17} + 1920408 q^{18} + 1184258 q^{19} - 4549286 q^{20} + 728004 q^{21} + 862018 q^{22} - 4500930 q^{23} + 3310872 q^{24} - 9135314 q^{25} - 14758832 q^{26} + 2844576 q^{27} - 3571608 q^{28} + 6733938 q^{29} + 2149174 q^{30} - 14444784 q^{31} - 44627770 q^{32} + 4784273 q^{33} + 11595654 q^{34} + 45575940 q^{35} + 36448514 q^{36} - 532446 q^{37} - 49250182 q^{38} - 26944620 q^{39} + 8130442 q^{40} + 46187047 q^{41} - 956710 q^{42} - 98011431 q^{43} + 108754386 q^{44} - 69029230 q^{45} - 45314056 q^{46} + 163672794 q^{47} + 150550484 q^{48} - 87555402 q^{49} - 202478270 q^{50} - 127620015 q^{51} + 19477190 q^{52} - 15708482 q^{53} + 183562896 q^{54} + 206828192 q^{55} + 134897440 q^{56} - 121289861 q^{57} + 45847278 q^{58} - 493506095 q^{59} - 1124748066 q^{60} - 107083612 q^{61} - 275977732 q^{62} - 10897312 q^{63} + 98133548 q^{64} + 150728678 q^{65} + 1494205972 q^{66} + 554668823 q^{67} + 183460572 q^{68} - 15910634 q^{69} - 629398354 q^{70} - 403287592 q^{71} - 2075226678 q^{72} - 818617668 q^{73} + 1172175622 q^{74} + 258243577 q^{75} - 429816442 q^{76} + 984178860 q^{77} + 3215569594 q^{78} - 264601716 q^{79} - 1475552448 q^{80} + 412668803 q^{81} + 486196904 q^{82} + 2424487352 q^{83} - 2183632264 q^{84} - 1569998480 q^{85} + 1652767810 q^{86} - 3777159678 q^{87} + 795075022 q^{88} + 1905112522 q^{89} - 4243113650 q^{90} - 1374183624 q^{91} - 1190206746 q^{92} - 122079274 q^{93} + 5227367748 q^{94} + 1730692960 q^{95} + 2745070128 q^{96} - 1042376049 q^{97} - 4121849670 q^{98} - 2514704514 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_1(72))\)

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
72.10.a \(\chi_{72}(1, \cdot)\) 72.10.a.a 1 1
72.10.a.b 1
72.10.a.c 1
72.10.a.d 1
72.10.a.e 1
72.10.a.f 2
72.10.a.g 2
72.10.a.h 2
72.10.c \(\chi_{72}(71, \cdot)\) None 0 1
72.10.d \(\chi_{72}(37, \cdot)\) 72.10.d.a 2 1
72.10.d.b 8
72.10.d.c 16
72.10.d.d 18
72.10.f \(\chi_{72}(35, \cdot)\) 72.10.f.a 36 1
72.10.i \(\chi_{72}(25, \cdot)\) 72.10.i.a 26 2
72.10.i.b 28
72.10.l \(\chi_{72}(11, \cdot)\) 72.10.l.a 4 2
72.10.l.b 208
72.10.n \(\chi_{72}(13, \cdot)\) 72.10.n.a 212 2
72.10.o \(\chi_{72}(23, \cdot)\) None 0 2

Decomposition of \(S_{10}^{\mathrm{old}}(\Gamma_1(72))\) into lower level spaces

\( S_{10}^{\mathrm{old}}(\Gamma_1(72)) \cong \) \(S_{10}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 9}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 8}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 6}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 3}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 4}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 4}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 3}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 2}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 2}\)