Space of modular forms of level 162 and weight 10

• Label: 162.10
• Level: 162
• Weight: 10
• Dimension: 1728
• Nonzero newspaces: 4
• Sturm bound: 14580
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 162 = 2 \cdot 3^{4} \)
Weight:	\( k \)	=	\( 10 \)
Nonzero newspaces:			\( 4 \)
Sturm bound:			\(14580\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_1(162))\).

	Total	New	Old
Modular forms	6669	1728	4941
Cusp forms	6453	1728	4725
Eisenstein series	216	0	216

Trace form

1728 * q + 4776 * q^5 - 2052 * q^7 + 12288 * q^8 - 61344 * q^10 - 167997 * q^11 + 307422 * q^13 - 191136 * q^14 + 1002252 * q^17 - 235152 * q^18 + 2286630 * q^19 - 6113280 * q^20 - 5797224 * q^21 + 3698352 * q^22 + 29711352 * q^23 - 12074346 * q^25 - 41127840 * q^26 - 18649332 * q^27 + 2101248 * q^28 + 57568974 * q^29 + 45825696 * q^30 + 15767298 * q^31 - 74790432 * q^33 - 48866544 * q^34 + 5484828 * q^35 + 46374912 * q^36 + 98513766 * q^37 - 124726992 * q^38 - 15704064 * q^40 - 23211939 * q^41 + 82182681 * q^43 + 22488576 * q^44 - 237517974 * q^45 + 12858048 * q^46 + 170063496 * q^47 + 45122886 * q^49 - 250352064 * q^50 - 129830967 * q^51 + 78700032 * q^52 - 132345930 * q^53 - 247427136 * q^55 - 48930816 * q^56 + 441044298 * q^57 - 237465216 * q^58 + 1471277271 * q^59 + 231859908 * q^61 + 354632064 * q^62 - 1083021894 * q^63 + 452984832 * q^64 - 1571905086 * q^65 - 2683624320 * q^66 + 990520083 * q^67 - 218121216 * q^68 + 3278084814 * q^69 - 1202712192 * q^70 + 1264119600 * q^71 - 636715008 * q^72 + 784846476 * q^73 - 2471867616 * q^74 - 5203125000 * q^75 + 181405440 * q^76 - 455570340 * q^77 + 2802016512 * q^78 - 1978966458 * q^79 + 983040000 * q^80 + 5447543040 * q^81 - 548901792 * q^82 - 2247679494 * q^83 - 730561536 * q^84 + 4525004088 * q^85 - 3958528176 * q^86 - 16894832832 * q^87 + 946778112 * q^88 - 1238581464 * q^89 + 3111840000 * q^90 + 2309130612 * q^91 + 3013727232 * q^92 + 12564428094 * q^93 - 3216363552 * q^94 - 11159443212 * q^95 - 1793064960 * q^96 + 9026638245 * q^97 - 6318073488 * q^98 + 14322578778 * q^99

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_1(162))\)

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
162.10.a	\(\chi_{162}(1, \cdot)\)	162.10.a.a	2	1
		162.10.a.b	2
		162.10.a.c	3
		162.10.a.d	3
		162.10.a.e	4
		162.10.a.f	4
		162.10.a.g	4
		162.10.a.h	4
		162.10.a.i	5
		162.10.a.j	5
162.10.c	\(\chi_{162}(55, \cdot)\)	162.10.c.a	2	2
		162.10.c.b	2
		162.10.c.c	2
		162.10.c.d	2
		162.10.c.e	2
		162.10.c.f	2
		162.10.c.g	2
		162.10.c.h	2
		162.10.c.i	2
		162.10.c.j	2
		162.10.c.k	4
		162.10.c.l	4
		162.10.c.m	4
		162.10.c.n	4
		162.10.c.o	4
		162.10.c.p	4
		162.10.c.q	6
		162.10.c.r	6
		162.10.c.s	8
		162.10.c.t	8
162.10.e	\(\chi_{162}(19, \cdot)\)	n/a	162	6
162.10.g	\(\chi_{162}(7, \cdot)\)	n/a	1458	18

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

Decomposition of \(S_{10}^{\mathrm{old}}(\Gamma_1(162))\) into lower level spaces

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