Space of modular forms of level 363 and weight 10

• Label: 363.10
• Level: 363
• Weight: 10
• Dimension: 31992
• Nonzero newspaces: 8
• Sturm bound: 96800
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 363 = 3 \cdot 11^{2} \)
Weight:	\( k \)	=	\( 10 \)
Nonzero newspaces:			\( 8 \)
Sturm bound:			\(96800\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_1(363))\).

	Total	New	Old
Modular forms	43880	32272	11608
Cusp forms	43240	31992	11248
Eisenstein series	640	280	360

Trace form

31992 * q - 18 * q^2 - 45 * q^3 + 506 * q^4 - 2844 * q^5 + 19529 * q^6 - 33562 * q^7 + 151688 * q^8 + 4597 * q^9 - 380346 * q^10 - 30700 * q^11 + 678943 * q^12 + 351842 * q^13 - 80076 * q^14 - 1149761 * q^15 - 7622810 * q^16 + 3435180 * q^17 + 1851317 * q^18 + 4676314 * q^19 - 9328636 * q^20 - 6677047 * q^21 - 8093080 * q^22 + 864104 * q^23 + 7801087 * q^24 + 29012276 * q^25 + 11281544 * q^26 - 3523065 * q^27 - 85181774 * q^28 - 15203812 * q^29 + 31405281 * q^30 + 75400582 * q^31 - 141695752 * q^32 + 57082535 * q^33 + 4549922 * q^34 - 158204000 * q^35 - 249234409 * q^36 + 14022338 * q^37 + 167340236 * q^38 + 256149151 * q^39 + 230399978 * q^40 - 66086868 * q^41 - 222508991 * q^42 - 77109822 * q^43 - 243313070 * q^44 + 18424691 * q^45 - 89753358 * q^46 + 376490536 * q^47 + 908832917 * q^48 + 1141780800 * q^49 + 509058974 * q^50 + 3163901 * q^51 - 1408325430 * q^52 - 1041098156 * q^53 - 141363361 * q^54 + 64946020 * q^55 + 948870000 * q^56 + 629605421 * q^57 + 393595102 * q^58 + 652944216 * q^59 - 879675339 * q^60 - 77711950 * q^61 + 796917216 * q^62 + 894625463 * q^63 - 3889105946 * q^64 - 2455822632 * q^65 - 71003395 * q^66 + 670869790 * q^67 + 3679833064 * q^68 + 545722029 * q^69 + 298821370 * q^70 + 999818184 * q^71 - 694899987 * q^72 + 3971135554 * q^73 - 1427684136 * q^74 - 3041063431 * q^75 - 13048274814 * q^76 - 2658485700 * q^77 - 285567485 * q^78 + 3951602350 * q^79 + 12685807044 * q^80 - 56168003 * q^81 + 5984927866 * q^82 + 5788882336 * q^83 + 4198083041 * q^84 - 2961703058 * q^85 - 11137213912 * q^86 - 5956633783 * q^87 - 11754955780 * q^88 - 7215657316 * q^89 - 12205670571 * q^90 - 1112024378 * q^91 + 31359082028 * q^92 + 16788614807 * q^93 + 20540793906 * q^94 + 916293024 * q^95 - 4821696927 * q^96 - 8767566530 * q^97 - 25620198602 * q^98 + 1154049960 * q^99

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_1(363))\)

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
363.10.a	\(\chi_{363}(1, \cdot)\)	363.10.a.a	1	1
		363.10.a.b	1
		363.10.a.c	3
		363.10.a.d	3
		363.10.a.e	4
		363.10.a.f	4
		363.10.a.g	6
		363.10.a.h	6
		363.10.a.i	8
		363.10.a.j	8
		363.10.a.k	8
		363.10.a.l	8
		363.10.a.m	14
		363.10.a.n	18
		363.10.a.o	18
		363.10.a.p	18
		363.10.a.q	18
		363.10.a.r	18
363.10.d	\(\chi_{363}(362, \cdot)\)	n/a	316	1
363.10.e	\(\chi_{363}(124, \cdot)\)	n/a	648	4
363.10.f	\(\chi_{363}(161, \cdot)\)	n/a	1264	4
363.10.i	\(\chi_{363}(34, \cdot)\)	n/a	1980	10
363.10.j	\(\chi_{363}(32, \cdot)\)	n/a	3940	10
363.10.m	\(\chi_{363}(4, \cdot)\)	n/a	7920	40
363.10.p	\(\chi_{363}(2, \cdot)\)	n/a	15760	40

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

Decomposition of \(S_{10}^{\mathrm{old}}(\Gamma_1(363))\) into lower level spaces

\( S_{10}^{\mathrm{old}}(\Gamma_1(363)) \cong \) \(S_{10}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 3}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 4}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 2}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(121))\)\(^{\oplus 2}\)