# Properties

 Label 144.7 Level 144 Weight 7 Dimension 1519 Nonzero newspaces 8 Sturm bound 8064 Trace bound 2

## Defining parameters

 Level: $$N$$ = $$144 = 2^{4} \cdot 3^{2}$$ Weight: $$k$$ = $$7$$ Nonzero newspaces: $$8$$ Sturm bound: $$8064$$ Trace bound: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{7}(\Gamma_1(144))$$.

Total New Old
Modular forms 3568 1559 2009
Cusp forms 3344 1519 1825
Eisenstein series 224 40 184

## Trace form

 $$1519 q - 6 q^{2} - 6 q^{3} + 84 q^{4} - 75 q^{5} - 8 q^{6} + 713 q^{7} + 960 q^{8} - 922 q^{9} + O(q^{10})$$ $$1519 q - 6 q^{2} - 6 q^{3} + 84 q^{4} - 75 q^{5} - 8 q^{6} + 713 q^{7} + 960 q^{8} - 922 q^{9} - 1140 q^{10} + 1357 q^{11} - 8 q^{12} + 1271 q^{13} + 8072 q^{14} + 27 q^{15} - 4284 q^{16} - 27126 q^{17} - 20308 q^{18} + 17938 q^{19} + 77680 q^{20} + 32815 q^{21} + 90768 q^{22} - 13117 q^{23} - 52264 q^{24} - 58169 q^{25} - 166268 q^{26} - 77550 q^{27} + 2680 q^{28} - 35195 q^{29} + 152420 q^{30} + 15045 q^{31} + 224924 q^{32} + 82053 q^{33} - 343520 q^{34} + 12576 q^{35} - 162252 q^{36} - 73576 q^{37} + 527892 q^{38} - 541743 q^{39} + 451428 q^{40} + 49299 q^{41} - 343408 q^{42} + 599131 q^{43} - 755800 q^{44} + 421269 q^{45} - 145908 q^{46} - 62865 q^{47} + 349484 q^{48} + 278749 q^{49} + 1083482 q^{50} - 849392 q^{51} + 346944 q^{52} - 633560 q^{53} + 174012 q^{54} - 177566 q^{55} - 1670176 q^{56} - 940972 q^{57} - 1024188 q^{58} + 2260709 q^{59} + 2730676 q^{60} + 786935 q^{61} + 3260856 q^{62} + 17181 q^{63} + 762408 q^{64} - 812179 q^{65} - 4255808 q^{66} - 407237 q^{67} - 4266416 q^{68} - 1928359 q^{69} - 494612 q^{70} - 267020 q^{71} + 1709672 q^{72} - 784846 q^{73} + 5936352 q^{74} + 1614178 q^{75} + 1761264 q^{76} + 2287501 q^{77} + 1538548 q^{78} - 3016851 q^{79} - 896832 q^{80} - 2630474 q^{81} + 5823320 q^{82} + 3554677 q^{83} - 5085176 q^{84} - 460532 q^{85} - 6821040 q^{86} - 431493 q^{87} - 2754252 q^{88} + 8742174 q^{89} - 1481480 q^{90} - 4579122 q^{91} - 2818996 q^{92} - 1310025 q^{93} + 1349772 q^{94} - 4430166 q^{95} + 1854012 q^{96} - 2680927 q^{97} + 2113670 q^{98} + 6122187 q^{99} + O(q^{100})$$

## Decomposition of $$S_{7}^{\mathrm{new}}(\Gamma_1(144))$$

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
144.7.b $$\chi_{144}(55, \cdot)$$ None 0 1
144.7.e $$\chi_{144}(17, \cdot)$$ 144.7.e.a 2 1
144.7.e.b 2
144.7.e.c 2
144.7.e.d 2
144.7.e.e 4
144.7.g $$\chi_{144}(127, \cdot)$$ 144.7.g.a 1 1
144.7.g.b 2
144.7.g.c 2
144.7.g.d 2
144.7.g.e 2
144.7.g.f 2
144.7.g.g 4
144.7.h $$\chi_{144}(89, \cdot)$$ None 0 1
144.7.j $$\chi_{144}(53, \cdot)$$ 144.7.j.a 96 2
144.7.m $$\chi_{144}(19, \cdot)$$ n/a 118 2
144.7.n $$\chi_{144}(41, \cdot)$$ None 0 2
144.7.o $$\chi_{144}(31, \cdot)$$ 144.7.o.a 24 2
144.7.o.b 24
144.7.o.c 24
144.7.q $$\chi_{144}(65, \cdot)$$ 144.7.q.a 10 2
144.7.q.b 12
144.7.q.c 12
144.7.q.d 36
144.7.t $$\chi_{144}(7, \cdot)$$ None 0 2
144.7.v $$\chi_{144}(43, \cdot)$$ n/a 568 4
144.7.w $$\chi_{144}(5, \cdot)$$ n/a 568 4

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

## Decomposition of $$S_{7}^{\mathrm{old}}(\Gamma_1(144))$$ into lower level spaces

$$S_{7}^{\mathrm{old}}(\Gamma_1(144)) \cong$$ $$S_{7}^{\mathrm{new}}(\Gamma_1(3))$$$$^{\oplus 10}$$$$\oplus$$$$S_{7}^{\mathrm{new}}(\Gamma_1(4))$$$$^{\oplus 9}$$$$\oplus$$$$S_{7}^{\mathrm{new}}(\Gamma_1(6))$$$$^{\oplus 8}$$$$\oplus$$$$S_{7}^{\mathrm{new}}(\Gamma_1(8))$$$$^{\oplus 6}$$$$\oplus$$$$S_{7}^{\mathrm{new}}(\Gamma_1(9))$$$$^{\oplus 5}$$$$\oplus$$$$S_{7}^{\mathrm{new}}(\Gamma_1(12))$$$$^{\oplus 6}$$$$\oplus$$$$S_{7}^{\mathrm{new}}(\Gamma_1(16))$$$$^{\oplus 3}$$$$\oplus$$$$S_{7}^{\mathrm{new}}(\Gamma_1(18))$$$$^{\oplus 4}$$$$\oplus$$$$S_{7}^{\mathrm{new}}(\Gamma_1(24))$$$$^{\oplus 4}$$$$\oplus$$$$S_{7}^{\mathrm{new}}(\Gamma_1(36))$$$$^{\oplus 3}$$$$\oplus$$$$S_{7}^{\mathrm{new}}(\Gamma_1(48))$$$$^{\oplus 2}$$$$\oplus$$$$S_{7}^{\mathrm{new}}(\Gamma_1(72))$$$$^{\oplus 2}$$