Space of modular forms of level 162 and weight 6

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

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 - 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

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

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