# Properties

 Label 144.8 Level 144 Weight 8 Dimension 1775 Nonzero newspaces 8 Sturm bound 9216 Trace bound 2

## Defining parameters

 Level: $$N$$ = $$144 = 2^{4} \cdot 3^{2}$$ Weight: $$k$$ = $$8$$ Nonzero newspaces: $$8$$ Sturm bound: $$9216$$ Trace bound: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{8}(\Gamma_1(144))$$.

Total New Old
Modular forms 4144 1816 2328
Cusp forms 3920 1775 2145
Eisenstein series 224 41 183

## Trace form

 $$1775 q - 6 q^{2} - 6 q^{3} - 188 q^{4} + 133 q^{5} - 8 q^{6} - 1351 q^{7} - 1008 q^{8} + 2234 q^{9} + O(q^{10})$$ $$1775 q - 6 q^{2} - 6 q^{3} - 188 q^{4} + 133 q^{5} - 8 q^{6} - 1351 q^{7} - 1008 q^{8} + 2234 q^{9} + 12956 q^{10} - 10179 q^{11} - 8 q^{12} + 3779 q^{13} + 21240 q^{14} + 16533 q^{15} + 65540 q^{16} + 35216 q^{17} - 42868 q^{18} + 60434 q^{19} - 302624 q^{20} + 6865 q^{21} + 332592 q^{22} - 6001 q^{23} + 335576 q^{24} + 161425 q^{25} - 620092 q^{26} + 247728 q^{27} - 920808 q^{28} - 571747 q^{29} + 137732 q^{30} + 455887 q^{31} + 1888284 q^{32} + 460497 q^{33} - 396032 q^{34} + 27282 q^{35} + 299508 q^{36} + 572780 q^{37} - 3826748 q^{38} - 628215 q^{39} + 1684356 q^{40} - 1369569 q^{41} + 2995472 q^{42} - 2463971 q^{43} - 558952 q^{44} + 2648847 q^{45} - 3096996 q^{46} + 7737765 q^{47} - 5044372 q^{48} - 2588601 q^{49} - 1778406 q^{50} - 1783118 q^{51} + 7969808 q^{52} + 1522970 q^{53} + 7445628 q^{54} - 7865606 q^{55} + 2628288 q^{56} + 2017100 q^{57} - 12561692 q^{58} + 4726399 q^{59} - 26449676 q^{60} + 2848083 q^{61} + 27430872 q^{62} + 1781133 q^{63} - 10529240 q^{64} + 18969501 q^{65} + 21033472 q^{66} - 272237 q^{67} - 12033136 q^{68} - 16758799 q^{69} - 7071252 q^{70} - 16470584 q^{71} - 38360344 q^{72} - 856390 q^{73} - 20947664 q^{74} + 11830510 q^{75} + 7947904 q^{76} + 34240213 q^{77} + 71195188 q^{78} - 9466599 q^{79} + 23565728 q^{80} + 20022466 q^{81} - 33584920 q^{82} - 31517001 q^{83} - 44863928 q^{84} - 24154570 q^{85} - 25777168 q^{86} + 20723511 q^{87} - 8857804 q^{88} + 8761320 q^{89} + 54130744 q^{90} + 28698886 q^{91} - 32760916 q^{92} + 56721405 q^{93} + 2505580 q^{94} - 91602332 q^{95} - 56434500 q^{96} - 1130491 q^{97} - 47532490 q^{98} - 68033799 q^{99} + O(q^{100})$$

## Decomposition of $$S_{8}^{\mathrm{new}}(\Gamma_1(144))$$

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
144.8.a $$\chi_{144}(1, \cdot)$$ 144.8.a.a 1 1
144.8.a.b 1
144.8.a.c 1
144.8.a.d 1
144.8.a.e 1
144.8.a.f 1
144.8.a.g 1
144.8.a.h 1
144.8.a.i 1
144.8.a.j 1
144.8.a.k 1
144.8.a.l 2
144.8.a.m 2
144.8.a.n 2
144.8.c $$\chi_{144}(143, \cdot)$$ 144.8.c.a 2 1
144.8.c.b 4
144.8.c.c 8
144.8.d $$\chi_{144}(73, \cdot)$$ None 0 1
144.8.f $$\chi_{144}(71, \cdot)$$ None 0 1
144.8.i $$\chi_{144}(49, \cdot)$$ 144.8.i.a 6 2
144.8.i.b 8
144.8.i.c 12
144.8.i.d 14
144.8.i.e 20
144.8.i.f 22
144.8.k $$\chi_{144}(37, \cdot)$$ n/a 138 2
144.8.l $$\chi_{144}(35, \cdot)$$ n/a 112 2
144.8.p $$\chi_{144}(23, \cdot)$$ None 0 2
144.8.r $$\chi_{144}(25, \cdot)$$ None 0 2
144.8.s $$\chi_{144}(47, \cdot)$$ 144.8.s.a 28 2
144.8.s.b 28
144.8.s.c 28
144.8.u $$\chi_{144}(11, \cdot)$$ n/a 664 4
144.8.x $$\chi_{144}(13, \cdot)$$ n/a 664 4

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

## Decomposition of $$S_{8}^{\mathrm{old}}(\Gamma_1(144))$$ into lower level spaces

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