↑

Properties

Label 144.12
Level 144
Weight 12
Dimension 2801
Nonzero newspaces 8
Sturm bound 13824
Trace bound 2

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 144 = 2^{4} \cdot 3^{2} \)
Weight: \( k \) = \( 12 \)
Nonzero newspaces: \( 8 \)
Sturm bound: \(13824\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{12}(\Gamma_1(144))\).

Total New Old
Modular forms 6448 2842 3606
Cusp forms 6224 2801 3423
Eisenstein series 224 41 183

Trace form

\( 2801 q - 6 q^{2} - 6 q^{3} + 3076 q^{4} - 1327 q^{5} - 8 q^{6} + 34537 q^{7} + 74832 q^{8} + 207242 q^{9} + O(q^{10}) \) \( 2801 q - 6 q^{2} - 6 q^{3} + 3076 q^{4} - 1327 q^{5} - 8 q^{6} + 34537 q^{7} + 74832 q^{8} + 207242 q^{9} - 988964 q^{10} - 2260731 q^{11} - 8 q^{12} + 3210751 q^{13} - 1846344 q^{14} - 5237307 q^{15} + 19239172 q^{16} - 12438380 q^{17} + 37283852 q^{18} - 10386838 q^{19} - 86065504 q^{20} - 50087039 q^{21} + 10946224 q^{22} + 62126431 q^{23} + 110525144 q^{24} - 80917825 q^{25} - 481816124 q^{26} - 295503648 q^{27} + 282063768 q^{28} + 859509145 q^{29} + 200522372 q^{30} + 160667567 q^{31} - 1298934756 q^{32} + 149462241 q^{33} + 321335936 q^{34} + 107890002 q^{35} - 1799710476 q^{36} - 401743784 q^{37} + 4643041412 q^{38} - 1338970119 q^{39} - 8241187324 q^{40} + 1334783283 q^{41} + 1975165712 q^{42} - 7395068363 q^{43} + 9359874904 q^{44} - 4481788113 q^{45} - 10130215268 q^{46} + 14344855269 q^{47} - 9307187092 q^{48} + 173879369 q^{49} + 29917120794 q^{50} - 22800980030 q^{51} + 5016034384 q^{52} - 3121712282 q^{53} - 15634017924 q^{54} + 44158476874 q^{55} - 17051123136 q^{56} - 24102258148 q^{57} + 35393445988 q^{58} - 57549598153 q^{59} + 66975924724 q^{60} + 19310151279 q^{61} - 79621325736 q^{62} - 12935416947 q^{63} + 32489743912 q^{64} + 42487666341 q^{65} + 150924335872 q^{66} + 9011727819 q^{67} + 46692665488 q^{68} - 40982396143 q^{69} + 36749631468 q^{70} + 7547876120 q^{71} - 173009644312 q^{72} + 21539937550 q^{73} + 58260272240 q^{74} - 2999992850 q^{75} - 138614904896 q^{76} + 100942930037 q^{77} + 89490051892 q^{78} - 133920380231 q^{79} - 189051637472 q^{80} - 302902435982 q^{81} + 475357587496 q^{82} + 45538725663 q^{83} + 176338776904 q^{84} + 84420780990 q^{85} - 224891976848 q^{86} - 10401392409 q^{87} + 256646288692 q^{88} + 97785352236 q^{89} + 682262551864 q^{90} + 216968393990 q^{91} - 11674226900 q^{92} - 234526208355 q^{93} - 434566556948 q^{94} - 453161575132 q^{95} - 469908268356 q^{96} + 294983012889 q^{97} + 2426046454 q^{98} + 319235423769 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{12}^{\mathrm{new}}(\Gamma_1(144))\)

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
144.12.a \(\chi_{144}(1, \cdot)\) 144.12.a.a 1 1
144.12.a.b 1
144.12.a.c 1
144.12.a.d 1
144.12.a.e 1
144.12.a.f 1
144.12.a.g 1
144.12.a.h 1
144.12.a.i 1
144.12.a.j 1
144.12.a.k 1
144.12.a.l 1
144.12.a.m 1
144.12.a.n 1
144.12.a.o 1
144.12.a.p 2
144.12.a.q 2
144.12.a.r 2
144.12.a.s 3
144.12.a.t 3
144.12.c \(\chi_{144}(143, \cdot)\) 144.12.c.a 2 1
144.12.c.b 4
144.12.c.c 16
144.12.d \(\chi_{144}(73, \cdot)\) None 0 1
144.12.f \(\chi_{144}(71, \cdot)\) None 0 1
144.12.i \(\chi_{144}(49, \cdot)\) n/a 130 2
144.12.k \(\chi_{144}(37, \cdot)\) n/a 218 2
144.12.l \(\chi_{144}(35, \cdot)\) n/a 176 2
144.12.p \(\chi_{144}(23, \cdot)\) None 0 2
144.12.r \(\chi_{144}(25, \cdot)\) None 0 2
144.12.s \(\chi_{144}(47, \cdot)\) n/a 132 2
144.12.u \(\chi_{144}(11, \cdot)\) n/a 1048 4
144.12.x \(\chi_{144}(13, \cdot)\) n/a 1048 4

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

Decomposition of \(S_{12}^{\mathrm{old}}(\Gamma_1(144))\) into lower level spaces

\( S_{12}^{\mathrm{old}}(\Gamma_1(144)) \cong \) \(S_{12}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 15}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 12}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 10}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 9}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 8}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 6}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 5}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 6}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 3}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 4}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 4}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 3}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 2}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 2}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(144))\)\(^{\oplus 1}\)