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Properties

Label 162.6
Level 162
Weight 6
Dimension 960
Nonzero newspaces 4
Sturm bound 8748
Trace bound 1

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Defining parameters

Level: \( N \) = \( 162 = 2 \cdot 3^{4} \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 4 \)
Sturm bound: \(8748\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(162))\).

Total New Old
Modular forms 3753 960 2793
Cusp forms 3537 960 2577
Eisenstein series 216 0 216

Trace form

\( 960 q - 174 q^{5} + 174 q^{7} + 192 q^{8} + O(q^{10}) \) \( 960 q - 174 q^{5} + 174 q^{7} + 192 q^{8} - 24 q^{10} - 453 q^{11} - 2280 q^{13} - 120 q^{14} + 3468 q^{17} - 8676 q^{18} + 1638 q^{19} + 13920 q^{20} + 27486 q^{21} + 6636 q^{22} - 6918 q^{23} - 23616 q^{25} - 60840 q^{26} - 35046 q^{27} - 11136 q^{28} - 18480 q^{29} + 15336 q^{30} + 29412 q^{31} + 73494 q^{33} + 32532 q^{34} + 66468 q^{35} - 8928 q^{36} - 76278 q^{37} - 111012 q^{38} - 384 q^{40} - 129783 q^{41} + 49509 q^{43} + 11616 q^{44} + 136026 q^{45} + 18960 q^{46} + 187866 q^{47} + 8328 q^{49} - 18864 q^{50} - 126315 q^{51} - 36480 q^{52} - 463350 q^{53} - 262836 q^{55} - 1920 q^{56} - 41526 q^{57} + 61104 q^{58} + 312231 q^{59} + 199818 q^{61} + 92256 q^{62} + 266274 q^{63} + 61440 q^{64} + 896664 q^{65} + 285408 q^{66} - 33489 q^{67} - 73824 q^{68} - 1124370 q^{69} + 176208 q^{70} - 678120 q^{71} - 327168 q^{72} - 59082 q^{73} - 220728 q^{74} + 112500 q^{75} - 53040 q^{76} + 665706 q^{77} + 743616 q^{78} - 511068 q^{79} + 153600 q^{80} + 909936 q^{81} + 55704 q^{82} + 457416 q^{83} + 118080 q^{84} - 264132 q^{85} - 246636 q^{86} - 811872 q^{87} + 106176 q^{88} - 1103262 q^{89} - 1281600 q^{90} - 46722 q^{91} - 509280 q^{92} - 1294362 q^{93} + 446760 q^{94} + 901308 q^{95} + 18432 q^{96} + 167397 q^{97} + 1418748 q^{98} + 2645154 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(162))\)

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
162.6.a \(\chi_{162}(1, \cdot)\) 162.6.a.a 1 1
162.6.a.b 1
162.6.a.c 2
162.6.a.d 2
162.6.a.e 2
162.6.a.f 2
162.6.a.g 2
162.6.a.h 2
162.6.a.i 3
162.6.a.j 3
162.6.c \(\chi_{162}(55, \cdot)\) 162.6.c.a 2 2
162.6.c.b 2
162.6.c.c 2
162.6.c.d 2
162.6.c.e 2
162.6.c.f 2
162.6.c.g 2
162.6.c.h 2
162.6.c.i 2
162.6.c.j 2
162.6.c.k 2
162.6.c.l 2
162.6.c.m 4
162.6.c.n 4
162.6.c.o 4
162.6.c.p 4
162.6.e \(\chi_{162}(19, \cdot)\) 162.6.e.a 42 6
162.6.e.b 48
162.6.g \(\chi_{162}(7, \cdot)\) n/a 810 18

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

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(162))\) into lower level spaces

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