Properties

Label 162.8
Level 162
Weight 8
Dimension 1344
Nonzero newspaces 4
Sturm bound 11664
Trace bound 1

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 162 = 2 \cdot 3^{4} \)
Weight: \( k \) = \( 8 \)
Nonzero newspaces: \( 4 \)
Sturm bound: \(11664\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_1(162))\).

Total New Old
Modular forms 5211 1344 3867
Cusp forms 4995 1344 3651
Eisenstein series 216 0 216

Trace form

\( 1344 q - 426 q^{5} - 498 q^{7} - 1536 q^{8} + O(q^{10}) \) \( 1344 q - 426 q^{5} - 498 q^{7} - 1536 q^{8} + 3984 q^{10} + 18267 q^{11} - 2184 q^{13} - 26832 q^{14} - 58956 q^{17} - 108792 q^{18} + 270198 q^{19} + 136320 q^{20} - 372006 q^{21} - 246792 q^{22} - 706614 q^{23} + 351072 q^{25} + 1581840 q^{26} + 833922 q^{27} + 127488 q^{28} - 804792 q^{29} - 1355184 q^{30} - 1229292 q^{31} - 308502 q^{33} + 346872 q^{34} + 4112148 q^{35} + 1243008 q^{36} + 30198 q^{37} - 2549256 q^{38} + 254976 q^{40} - 3188109 q^{41} + 947277 q^{43} - 511104 q^{44} - 1459026 q^{45} - 602016 q^{46} - 10966158 q^{47} + 1120632 q^{49} + 1347552 q^{50} + 4677309 q^{51} - 139776 q^{52} + 13943310 q^{53} + 8693100 q^{55} - 1717248 q^{56} - 3123738 q^{57} + 1937472 q^{58} - 17655369 q^{59} - 12974922 q^{61} - 5719872 q^{62} + 1006938 q^{63} + 5505024 q^{64} + 51701880 q^{65} - 22506048 q^{66} + 31392855 q^{67} + 624000 q^{68} - 42561702 q^{69} + 2534592 q^{70} + 35316120 q^{71} + 29159424 q^{72} + 2608386 q^{73} + 26608560 q^{74} + 36562500 q^{75} - 4758720 q^{76} - 45461058 q^{77} - 48198528 q^{78} + 52584780 q^{79} - 12288000 q^{80} - 70916976 q^{81} - 1895088 q^{82} - 25611408 q^{83} - 675072 q^{84} - 38781540 q^{85} + 39577608 q^{86} + 184319136 q^{87} - 15794688 q^{88} + 64189758 q^{89} + 90864000 q^{90} + 31485558 q^{91} + 8118912 q^{92} - 52912422 q^{93} + 38182896 q^{94} - 138443388 q^{95} - 25362432 q^{96} + 38952255 q^{97} - 7234104 q^{98} + 145779930 q^{99} + O(q^{100}) \)

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_1(162))\)

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 available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
162.8.a \(\chi_{162}(1, \cdot)\) 162.8.a.a 1 1
162.8.a.b 1
162.8.a.c 2
162.8.a.d 2
162.8.a.e 3
162.8.a.f 3
162.8.a.g 4
162.8.a.h 4
162.8.a.i 4
162.8.a.j 4
162.8.c \(\chi_{162}(55, \cdot)\) 162.8.c.a 2 2
162.8.c.b 2
162.8.c.c 2
162.8.c.d 2
162.8.c.e 2
162.8.c.f 2
162.8.c.g 2
162.8.c.h 2
162.8.c.i 2
162.8.c.j 2
162.8.c.k 2
162.8.c.l 2
162.8.c.m 4
162.8.c.n 4
162.8.c.o 4
162.8.c.p 4
162.8.c.q 8
162.8.c.r 8
162.8.e \(\chi_{162}(19, \cdot)\) n/a 126 6
162.8.g \(\chi_{162}(7, \cdot)\) n/a 1134 18

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

Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_1(162))\) into lower level spaces

\( S_{8}^{\mathrm{old}}(\Gamma_1(162)) \cong \) \(S_{8}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 10}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 5}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 8}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 6}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 3}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(54))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(81))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(162))\)\(^{\oplus 1}\)