Properties

Label 144.5
Level 144
Weight 5
Dimension 1006
Nonzero newspaces 8
Newform subspaces 23
Sturm bound 5760
Trace bound 2

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Defining parameters

Level: \( N \) = \( 144 = 2^{4} \cdot 3^{2} \)
Weight: \( k \) = \( 5 \)
Nonzero newspaces: \( 8 \)
Newform subspaces: \( 23 \)
Sturm bound: \(5760\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(\Gamma_1(144))\).

Total New Old
Modular forms 2416 1046 1370
Cusp forms 2192 1006 1186
Eisenstein series 224 40 184

Trace form

\( 1006 q - 6 q^{2} - 6 q^{3} - 12 q^{4} + 27 q^{5} - 8 q^{6} - 39 q^{7} - 96 q^{8} + 110 q^{9} + O(q^{10}) \) \( 1006 q - 6 q^{2} - 6 q^{3} - 12 q^{4} + 27 q^{5} - 8 q^{6} - 39 q^{7} - 96 q^{8} + 110 q^{9} - 116 q^{10} + 93 q^{11} - 8 q^{12} - 3 q^{13} + 168 q^{14} - 261 q^{15} + 1732 q^{16} + 24 q^{17} - 1108 q^{18} - 590 q^{19} - 3312 q^{20} - 1145 q^{21} - 1168 q^{22} + 1155 q^{23} + 1496 q^{24} + 1716 q^{25} + 4836 q^{26} + 1866 q^{27} + 3640 q^{28} + 1179 q^{29} + 2084 q^{30} + 1709 q^{31} - 2916 q^{32} - 4803 q^{33} - 1824 q^{34} + 6336 q^{35} - 7500 q^{36} + 174 q^{37} + 1044 q^{38} + 2505 q^{39} + 8740 q^{40} + 321 q^{41} + 11792 q^{42} - 22469 q^{43} + 6216 q^{44} - 4299 q^{45} + 620 q^{46} - 10809 q^{47} - 4948 q^{48} + 6020 q^{49} - 8454 q^{50} + 20680 q^{51} - 4832 q^{52} + 20862 q^{53} - 18180 q^{54} + 27922 q^{55} - 38880 q^{56} - 14452 q^{57} - 5916 q^{58} - 23379 q^{59} + 16948 q^{60} - 18115 q^{61} + 41784 q^{62} - 10011 q^{63} - 24024 q^{64} + 4377 q^{65} + 64192 q^{66} - 17029 q^{67} + 39888 q^{68} + 6329 q^{69} + 8620 q^{70} + 19956 q^{71} - 16024 q^{72} + 18816 q^{73} - 47136 q^{74} + 5266 q^{75} + 6480 q^{76} + 2781 q^{77} - 104972 q^{78} - 15715 q^{79} - 103680 q^{80} - 32738 q^{81} + 44856 q^{82} - 4083 q^{83} + 30088 q^{84} - 44016 q^{85} + 112176 q^{86} + 41403 q^{87} + 47668 q^{88} + 7092 q^{89} + 108280 q^{90} - 2002 q^{91} + 67212 q^{92} - 23433 q^{93} + 18252 q^{94} - 27942 q^{95} - 12996 q^{96} - 7961 q^{97} - 69210 q^{98} - 55845 q^{99} + O(q^{100}) \)

Decomposition of \(S_{5}^{\mathrm{new}}(\Gamma_1(144))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
144.5.b \(\chi_{144}(55, \cdot)\) None 0 1
144.5.e \(\chi_{144}(17, \cdot)\) 144.5.e.a 2 1
144.5.e.b 2
144.5.e.c 2
144.5.e.d 2
144.5.g \(\chi_{144}(127, \cdot)\) 144.5.g.a 1 1
144.5.g.b 1
144.5.g.c 2
144.5.g.d 2
144.5.g.e 2
144.5.g.f 2
144.5.h \(\chi_{144}(89, \cdot)\) None 0 1
144.5.j \(\chi_{144}(53, \cdot)\) 144.5.j.a 64 2
144.5.m \(\chi_{144}(19, \cdot)\) 144.5.m.a 14 2
144.5.m.b 32
144.5.m.c 32
144.5.n \(\chi_{144}(41, \cdot)\) None 0 2
144.5.o \(\chi_{144}(31, \cdot)\) 144.5.o.a 16 2
144.5.o.b 16
144.5.o.c 16
144.5.q \(\chi_{144}(65, \cdot)\) 144.5.q.a 6 2
144.5.q.b 8
144.5.q.c 8
144.5.q.d 24
144.5.t \(\chi_{144}(7, \cdot)\) None 0 2
144.5.v \(\chi_{144}(43, \cdot)\) 144.5.v.a 376 4
144.5.w \(\chi_{144}(5, \cdot)\) 144.5.w.a 376 4

Decomposition of \(S_{5}^{\mathrm{old}}(\Gamma_1(144))\) into lower level spaces

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