Properties

 Label 144.6 Level 144 Weight 6 Dimension 1262 Nonzero newspaces 8 Sturm bound 6912 Trace bound 2

Defining parameters

 Level: $$N$$ = $$144 = 2^{4} \cdot 3^{2}$$ Weight: $$k$$ = $$6$$ Nonzero newspaces: $$8$$ Sturm bound: $$6912$$ Trace bound: $$2$$

Dimensions

The following table gives the dimensions of various subspaces of $$M_{6}(\Gamma_1(144))$$.

Total New Old
Modular forms 2992 1303 1689
Cusp forms 2768 1262 1506
Eisenstein series 224 41 183

Trace form

 $$1262q - 6q^{2} - 6q^{3} - 28q^{4} - 25q^{5} - 8q^{6} - 15q^{7} + 240q^{8} - 46q^{9} + O(q^{10})$$ $$1262q - 6q^{2} - 6q^{3} - 28q^{4} - 25q^{5} - 8q^{6} - 15q^{7} + 240q^{8} - 46q^{9} - 452q^{10} + 177q^{11} - 8q^{12} + 285q^{13} - 360q^{14} - 1683q^{15} - 5756q^{16} + 1390q^{17} + 8012q^{18} - 658q^{19} + 6272q^{20} - 3047q^{21} - 15696q^{22} - 2441q^{23} - 16168q^{24} - 5646q^{25} + 3844q^{26} + 6168q^{27} + 25816q^{28} + 39991q^{29} + 31172q^{30} - 5617q^{31} - 16356q^{32} - 20631q^{33} - 57024q^{34} - 40590q^{35} + 30324q^{36} + 4734q^{37} - 15580q^{38} + 58161q^{39} - 44988q^{40} + 31557q^{41} - 30448q^{42} - 20487q^{43} + 32824q^{44} + 8703q^{45} + 33852q^{46} - 183243q^{47} + 112364q^{48} - 59690q^{49} + 42714q^{50} - 57110q^{51} + 55024q^{52} + 55900q^{53} - 115332q^{54} + 264258q^{55} - 54528q^{56} + 186596q^{57} - 128668q^{58} + 155003q^{59} - 234380q^{60} - 30115q^{61} - 175848q^{62} - 143043q^{63} - 74200q^{64} - 113703q^{65} + 3712q^{66} - 122145q^{67} + 291088q^{68} + 201569q^{69} + 186988q^{70} - 85552q^{71} + 556520q^{72} - 243840q^{73} + 346448q^{74} + 69166q^{75} - 121120q^{76} - 146491q^{77} - 46412q^{78} + 360393q^{79} - 749600q^{80} - 395030q^{81} + 8520q^{82} - 235413q^{83} - 1105976q^{84} + 644642q^{85} - 252560q^{86} - 70737q^{87} + 127540q^{88} + 200982q^{89} + 614584q^{90} - 164026q^{91} + 691180q^{92} - 236691q^{93} + 360620q^{94} + 589988q^{95} + 607164q^{96} - 236805q^{97} + 378454q^{98} + 371241q^{99} + O(q^{100})$$

Decomposition of $$S_{6}^{\mathrm{new}}(\Gamma_1(144))$$

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 the newforms together with their dimension.

Label $$\chi$$ Newforms Dimension $$\chi$$ degree
144.6.a $$\chi_{144}(1, \cdot)$$ 144.6.a.a 1 1
144.6.a.b 1
144.6.a.c 1
144.6.a.d 1
144.6.a.e 1
144.6.a.f 1
144.6.a.g 1
144.6.a.h 1
144.6.a.i 1
144.6.a.j 1
144.6.a.k 1
144.6.a.l 1
144.6.c $$\chi_{144}(143, \cdot)$$ 144.6.c.a 2 1
144.6.c.b 8
144.6.d $$\chi_{144}(73, \cdot)$$ None 0 1
144.6.f $$\chi_{144}(71, \cdot)$$ None 0 1
144.6.i $$\chi_{144}(49, \cdot)$$ 144.6.i.a 4 2
144.6.i.b 6
144.6.i.c 8
144.6.i.d 10
144.6.i.e 14
144.6.i.f 16
144.6.k $$\chi_{144}(37, \cdot)$$ 144.6.k.a 18 2
144.6.k.b 40
144.6.k.c 40
144.6.l $$\chi_{144}(35, \cdot)$$ 144.6.l.a 80 2
144.6.p $$\chi_{144}(23, \cdot)$$ None 0 2
144.6.r $$\chi_{144}(25, \cdot)$$ None 0 2
144.6.s $$\chi_{144}(47, \cdot)$$ 144.6.s.a 20 2
144.6.s.b 20
144.6.s.c 20
144.6.u $$\chi_{144}(11, \cdot)$$ n/a 472 4
144.6.x $$\chi_{144}(13, \cdot)$$ n/a 472 4

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

Decomposition of $$S_{6}^{\mathrm{old}}(\Gamma_1(144))$$ into lower level spaces

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