Space of modular forms of level 162 and weight 8

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

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 + 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

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

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