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Properties

Label 72.9
Level 72
Weight 9
Dimension 503
Nonzero newspaces 6
Newform subspaces 11
Sturm bound 2592
Trace bound 2

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Defining parameters

Level: \( N \) = \( 72 = 2^{3} \cdot 3^{2} \)
Weight: \( k \) = \( 9 \)
Nonzero newspaces: \( 6 \)
Newform subspaces: \( 11 \)
Sturm bound: \(2592\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(\Gamma_1(72))\).

Total New Old
Modular forms 1200 521 679
Cusp forms 1104 503 601
Eisenstein series 96 18 78

Trace form

\( 503 q - 60 q^{3} - 334 q^{4} + 508 q^{6} - 3170 q^{7} + 17178 q^{8} - 336 q^{9} + O(q^{10}) \) \( 503 q - 60 q^{3} - 334 q^{4} + 508 q^{6} - 3170 q^{7} + 17178 q^{8} - 336 q^{9} - 53032 q^{10} + 8184 q^{11} + 55426 q^{12} + 6656 q^{13} - 88110 q^{14} - 166242 q^{15} + 39046 q^{16} - 38646 q^{17} - 28320 q^{18} + 28742 q^{19} - 59382 q^{20} - 287568 q^{21} + 524962 q^{22} - 689766 q^{23} - 821112 q^{24} + 1810387 q^{25} + 512688 q^{26} + 1297980 q^{27} + 252840 q^{28} - 2846448 q^{29} - 1410554 q^{30} - 477570 q^{31} + 2122230 q^{32} + 1782644 q^{33} + 4378686 q^{34} - 1135884 q^{35} - 6206398 q^{36} + 2521776 q^{37} - 12072390 q^{38} - 8701302 q^{39} - 3816038 q^{40} + 10467138 q^{41} + 22305218 q^{42} - 4782780 q^{43} + 12385794 q^{44} - 3148336 q^{45} + 14806088 q^{46} - 14112150 q^{47} - 18033796 q^{48} + 10234419 q^{49} + 3292566 q^{50} - 17649456 q^{51} + 8636054 q^{52} + 9956664 q^{54} + 33266204 q^{55} + 6297936 q^{56} - 24234032 q^{57} - 18704394 q^{58} - 24928392 q^{59} - 21101154 q^{60} + 18847760 q^{61} + 204709500 q^{62} - 33922210 q^{63} + 2320652 q^{64} + 56732916 q^{65} - 114155036 q^{66} - 53002972 q^{67} - 231089076 q^{68} - 62720672 q^{69} - 98647474 q^{70} + 198822018 q^{72} + 178425006 q^{73} + 364147374 q^{74} - 164754860 q^{75} - 38117578 q^{76} - 18795168 q^{77} - 197859110 q^{78} - 221382642 q^{79} - 353199120 q^{80} + 124146128 q^{81} + 15966848 q^{82} + 31609200 q^{83} - 81540088 q^{84} + 335678992 q^{85} + 456533730 q^{86} - 237304626 q^{87} + 53827342 q^{88} + 164488650 q^{89} + 303704614 q^{90} - 109155084 q^{91} + 503391126 q^{92} + 13885568 q^{93} - 168060132 q^{94} - 315555408 q^{95} - 810916296 q^{96} + 54136098 q^{97} - 672932778 q^{98} - 248438418 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{9}^{\mathrm{new}}(\Gamma_1(72))\)

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
72.9.b \(\chi_{72}(19, \cdot)\) 72.9.b.a 1 1
72.9.b.b 6
72.9.b.c 16
72.9.b.d 16
72.9.e \(\chi_{72}(17, \cdot)\) 72.9.e.a 4 1
72.9.e.b 4
72.9.g \(\chi_{72}(55, \cdot)\) None 0 1
72.9.h \(\chi_{72}(53, \cdot)\) 72.9.h.a 32 1
72.9.j \(\chi_{72}(5, \cdot)\) 72.9.j.a 188 2
72.9.k \(\chi_{72}(7, \cdot)\) None 0 2
72.9.m \(\chi_{72}(41, \cdot)\) 72.9.m.a 48 2
72.9.p \(\chi_{72}(43, \cdot)\) 72.9.p.a 4 2
72.9.p.b 184

Decomposition of \(S_{9}^{\mathrm{old}}(\Gamma_1(72))\) into lower level spaces

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