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Properties

Label 144.9
Level 144
Weight 9
Dimension 2032
Nonzero newspaces 8
Sturm bound 10368
Trace bound 2

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Defining parameters

Level: \( N \) = \( 144 = 2^{4} \cdot 3^{2} \)
Weight: \( k \) = \( 9 \)
Nonzero newspaces: \( 8 \)
Sturm bound: \(10368\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(\Gamma_1(144))\).

Total New Old
Modular forms 4720 2072 2648
Cusp forms 4496 2032 2464
Eisenstein series 224 40 184

Trace form

\( 2032 q - 6 q^{2} - 6 q^{3} + 180 q^{4} - 513 q^{5} - 8 q^{6} + 3001 q^{7} - 8736 q^{8} + 3806 q^{9} + O(q^{10}) \) \( 2032 q - 6 q^{2} - 6 q^{3} + 180 q^{4} - 513 q^{5} - 8 q^{6} + 3001 q^{7} - 8736 q^{8} + 3806 q^{9} - 1876 q^{10} - 19779 q^{11} - 8 q^{12} - 68543 q^{13} - 56856 q^{14} + 91899 q^{15} - 179260 q^{16} - 181956 q^{17} + 579692 q^{18} + 296818 q^{19} - 973872 q^{20} - 676841 q^{21} - 832688 q^{22} - 845565 q^{23} + 1589720 q^{24} + 1249706 q^{25} + 3918468 q^{26} - 1316454 q^{27} - 4421960 q^{28} - 934785 q^{29} - 3620956 q^{30} + 602461 q^{31} + 7369884 q^{32} - 532083 q^{33} - 3001120 q^{34} + 3551616 q^{35} + 973236 q^{36} + 2334514 q^{37} + 4204404 q^{38} + 14329497 q^{39} - 27838300 q^{40} - 8799483 q^{41} - 554608 q^{42} - 14953349 q^{43} + 39046920 q^{44} - 976779 q^{45} + 25094188 q^{46} + 20714391 q^{47} - 21819988 q^{48} + 10368150 q^{49} - 78403494 q^{50} + 24014488 q^{51} - 16722592 q^{52} + 12921282 q^{53} + 42722364 q^{54} - 43568078 q^{55} + 59135904 q^{56} + 12025628 q^{57} - 67832316 q^{58} + 83437149 q^{59} - 79259852 q^{60} - 38989375 q^{61} - 72099336 q^{62} - 102399531 q^{63} + 128508456 q^{64} + 23168577 q^{65} + 175715392 q^{66} + 49492731 q^{67} + 211189968 q^{68} + 221517689 q^{69} - 24441620 q^{70} - 79832076 q^{71} - 161457304 q^{72} + 13852036 q^{73} - 363476352 q^{74} - 149718734 q^{75} - 26712432 q^{76} + 27332541 q^{77} - 93787532 q^{78} + 208545085 q^{79} + 801982080 q^{80} + 405240910 q^{81} - 63910664 q^{82} - 209952483 q^{83} - 360758648 q^{84} + 72851624 q^{85} - 925798896 q^{86} - 356528517 q^{87} - 44616652 q^{88} + 135861480 q^{89} + 781008760 q^{90} + 402363502 q^{91} + 644375052 q^{92} - 128911113 q^{93} + 71235660 q^{94} + 476132538 q^{95} - 234420420 q^{96} + 357892059 q^{97} - 526340250 q^{98} - 546769989 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{9}^{\mathrm{new}}(\Gamma_1(144))\)

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
144.9.b \(\chi_{144}(55, \cdot)\) None 0 1
144.9.e \(\chi_{144}(17, \cdot)\) 144.9.e.a 2 1
144.9.e.b 2
144.9.e.c 2
144.9.e.d 2
144.9.e.e 4
144.9.e.f 4
144.9.g \(\chi_{144}(127, \cdot)\) 144.9.g.a 1 1
144.9.g.b 1
144.9.g.c 2
144.9.g.d 2
144.9.g.e 2
144.9.g.f 2
144.9.g.g 2
144.9.g.h 4
144.9.g.i 4
144.9.h \(\chi_{144}(89, \cdot)\) None 0 1
144.9.j \(\chi_{144}(53, \cdot)\) n/a 128 2
144.9.m \(\chi_{144}(19, \cdot)\) n/a 158 2
144.9.n \(\chi_{144}(41, \cdot)\) None 0 2
144.9.o \(\chi_{144}(31, \cdot)\) 144.9.o.a 32 2
144.9.o.b 32
144.9.o.c 32
144.9.q \(\chi_{144}(65, \cdot)\) 144.9.q.a 14 2
144.9.q.b 16
144.9.q.c 16
144.9.q.d 48
144.9.t \(\chi_{144}(7, \cdot)\) None 0 2
144.9.v \(\chi_{144}(43, \cdot)\) n/a 760 4
144.9.w \(\chi_{144}(5, \cdot)\) n/a 760 4

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{9}^{\mathrm{old}}(\Gamma_1(144))\) into lower level spaces

\( S_{9}^{\mathrm{old}}(\Gamma_1(144)) \cong \) \(S_{9}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 10}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 9}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 8}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 6}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 5}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 6}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 3}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 4}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 4}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 3}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 2}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 2}\)