# Properties

 Label 162.4 Level 162 Weight 4 Dimension 576 Nonzero newspaces 4 Newform subspaces 22 Sturm bound 5832 Trace bound 1

## Defining parameters

 Level: $$N$$ = $$162 = 2 \cdot 3^{4}$$ Weight: $$k$$ = $$4$$ Nonzero newspaces: $$4$$ Newform subspaces: $$22$$ Sturm bound: $$5832$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(\Gamma_1(162))$$.

Total New Old
Modular forms 2295 576 1719
Cusp forms 2079 576 1503
Eisenstein series 216 0 216

## Trace form

 $$576 q + 24 q^{5} - 36 q^{7} - 24 q^{8} + O(q^{10})$$ $$576 q + 24 q^{5} - 36 q^{7} - 24 q^{8} - 36 q^{10} + 51 q^{11} + 90 q^{13} + 132 q^{14} - 204 q^{17} - 414 q^{18} - 810 q^{19} - 480 q^{20} - 216 q^{21} + 126 q^{22} + 1416 q^{23} + 1242 q^{25} + 2340 q^{26} + 1404 q^{27} + 576 q^{28} + 1842 q^{29} + 756 q^{30} + 162 q^{31} - 864 q^{33} - 234 q^{34} - 3732 q^{35} - 1152 q^{36} - 2070 q^{37} - 1626 q^{38} - 144 q^{40} - 3873 q^{41} - 2079 q^{43} - 264 q^{44} - 1026 q^{45} - 504 q^{46} + 432 q^{47} + 1530 q^{49} + 792 q^{50} + 2961 q^{51} + 360 q^{52} + 6450 q^{53} + 4320 q^{55} + 528 q^{56} + 2214 q^{57} + 72 q^{58} + 1911 q^{59} - 972 q^{61} - 1488 q^{62} - 1998 q^{63} + 576 q^{64} - 2130 q^{65} + 9360 q^{66} - 7749 q^{67} + 336 q^{68} + 4122 q^{69} - 1368 q^{70} + 1200 q^{71} - 576 q^{72} + 1692 q^{73} - 2388 q^{74} - 9000 q^{75} + 1980 q^{76} - 9276 q^{77} - 10656 q^{78} + 8190 q^{79} - 1920 q^{80} - 11520 q^{81} + 1044 q^{82} - 5958 q^{83} - 2448 q^{84} + 6480 q^{85} - 3582 q^{86} - 10944 q^{87} + 504 q^{88} - 7224 q^{89} + 1440 q^{90} - 6876 q^{91} + 1488 q^{92} + 9090 q^{93} - 6156 q^{94} + 2172 q^{95} + 2880 q^{96} - 9441 q^{97} + 10914 q^{98} + 20754 q^{99} + O(q^{100})$$

## Decomposition of $$S_{4}^{\mathrm{new}}(\Gamma_1(162))$$

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
162.4.a $$\chi_{162}(1, \cdot)$$ 162.4.a.a 1 1
162.4.a.b 1
162.4.a.c 1
162.4.a.d 1
162.4.a.e 2
162.4.a.f 2
162.4.a.g 2
162.4.a.h 2
162.4.c $$\chi_{162}(55, \cdot)$$ 162.4.c.a 2 2
162.4.c.b 2
162.4.c.c 2
162.4.c.d 2
162.4.c.e 2
162.4.c.f 2
162.4.c.g 2
162.4.c.h 2
162.4.c.i 4
162.4.c.j 4
162.4.e $$\chi_{162}(19, \cdot)$$ 162.4.e.a 24 6
162.4.e.b 30
162.4.g $$\chi_{162}(7, \cdot)$$ 162.4.g.a 234 18
162.4.g.b 252

## Decomposition of $$S_{4}^{\mathrm{old}}(\Gamma_1(162))$$ into lower level spaces

$$S_{4}^{\mathrm{old}}(\Gamma_1(162)) \cong$$ $$S_{4}^{\mathrm{new}}(\Gamma_1(6))$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(9))$$$$^{\oplus 6}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(18))$$$$^{\oplus 3}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(27))$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(54))$$$$^{\oplus 2}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(81))$$$$^{\oplus 2}$$