# Properties

 Label 162.7 Level 162 Weight 7 Dimension 1152 Nonzero newspaces 4 Sturm bound 10206 Trace bound 1

## Defining parameters

 Level: $$N$$ = $$162 = 2 \cdot 3^{4}$$ Weight: $$k$$ = $$7$$ Nonzero newspaces: $$4$$ Sturm bound: $$10206$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{7}(\Gamma_1(162))$$.

Total New Old
Modular forms 4482 1152 3330
Cusp forms 4266 1152 3114
Eisenstein series 216 0 216

## Trace form

 $$1152 q + 432 q^{5} - 720 q^{7} + O(q^{10})$$ $$1152 q + 432 q^{5} - 720 q^{7} + 1872 q^{10} + 378 q^{11} - 3384 q^{13} - 4752 q^{14} + 33120 q^{18} - 30780 q^{19} - 69120 q^{20} - 41040 q^{21} + 25200 q^{22} + 195912 q^{23} + 54000 q^{25} - 112320 q^{27} - 92160 q^{28} - 408348 q^{29} - 223776 q^{30} - 113400 q^{31} + 302400 q^{33} + 199440 q^{34} + 1073088 q^{35} + 92160 q^{36} - 116892 q^{37} - 589248 q^{38} - 59904 q^{40} + 523854 q^{41} - 541674 q^{43} - 582768 q^{45} + 135072 q^{46} + 1096092 q^{47} + 871704 q^{49} + 311040 q^{50} + 882378 q^{51} + 108288 q^{52} - 1682640 q^{55} - 152064 q^{56} - 1372680 q^{57} - 222768 q^{58} - 2081970 q^{59} + 117612 q^{61} + 1778220 q^{63} - 589824 q^{64} + 1875744 q^{65} + 262080 q^{66} - 927234 q^{67} + 1237248 q^{68} + 4444704 q^{69} - 1259856 q^{70} + 855360 q^{71} - 700416 q^{72} - 1885212 q^{73} - 5250528 q^{74} - 9000000 q^{75} + 745920 q^{76} - 6680664 q^{77} - 4901760 q^{78} + 3177972 q^{79} + 2787840 q^{81} - 167040 q^{82} + 4233060 q^{83} + 2310912 q^{84} - 5279580 q^{85} + 8059824 q^{86} + 16240896 q^{87} - 806400 q^{88} + 5545260 q^{89} - 2448000 q^{90} - 1835280 q^{91} - 5405184 q^{92} - 17804268 q^{93} + 3166128 q^{94} - 19467324 q^{95} - 1474560 q^{96} - 1542330 q^{97} + 4393440 q^{98} + 26461584 q^{99} + O(q^{100})$$

## Decomposition of $$S_{7}^{\mathrm{new}}(\Gamma_1(162))$$

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
162.7.b $$\chi_{162}(161, \cdot)$$ 162.7.b.a 4 1
162.7.b.b 8
162.7.b.c 12
162.7.d $$\chi_{162}(53, \cdot)$$ 162.7.d.a 4 2
162.7.d.b 4
162.7.d.c 4
162.7.d.d 4
162.7.d.e 8
162.7.d.f 8
162.7.d.g 16
162.7.f $$\chi_{162}(17, \cdot)$$ n/a 108 6
162.7.h $$\chi_{162}(5, \cdot)$$ n/a 972 18

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

## Decomposition of $$S_{7}^{\mathrm{old}}(\Gamma_1(162))$$ into lower level spaces

$$S_{7}^{\mathrm{old}}(\Gamma_1(162)) \cong$$ $$S_{7}^{\mathrm{new}}(\Gamma_1(3))$$$$^{\oplus 8}$$$$\oplus$$$$S_{7}^{\mathrm{new}}(\Gamma_1(6))$$$$^{\oplus 4}$$$$\oplus$$$$S_{7}^{\mathrm{new}}(\Gamma_1(9))$$$$^{\oplus 6}$$$$\oplus$$$$S_{7}^{\mathrm{new}}(\Gamma_1(18))$$$$^{\oplus 3}$$$$\oplus$$$$S_{7}^{\mathrm{new}}(\Gamma_1(27))$$$$^{\oplus 4}$$$$\oplus$$$$S_{7}^{\mathrm{new}}(\Gamma_1(54))$$$$^{\oplus 2}$$$$\oplus$$$$S_{7}^{\mathrm{new}}(\Gamma_1(81))$$$$^{\oplus 2}$$