Space of modular forms of level 350 and weight 8

• Label: 350.8
• Level: 350
• Weight: 8
• Dimension: 7418
• Nonzero newspaces: 12
• Sturm bound: 57600
• Trace bound: 4

Defining parameters

Level:	\( N \)	=	\( 350 = 2 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	=	\( 8 \)
Nonzero newspaces:			\( 12 \)
Sturm bound:			\(57600\)
Trace bound:			\(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_1(350))\).

	Total	New	Old
Modular forms	25536	7418	18118
Cusp forms	24864	7418	17446
Eisenstein series	672	0	672

Trace form

7418 * q - 16 * q^2 + 130 * q^3 - 256 * q^4 - 50 * q^5 + 2608 * q^6 + 2592 * q^7 - 1024 * q^8 - 41452 * q^9 + 4080 * q^10 + 50148 * q^11 + 8320 * q^12 - 3006 * q^13 - 62608 * q^14 - 67960 * q^15 + 114688 * q^16 + 537320 * q^17 + 351584 * q^18 - 176042 * q^19 - 107520 * q^20 - 531502 * q^21 - 167648 * q^22 + 1072816 * q^23 + 433152 * q^24 + 1432446 * q^25 + 838032 * q^26 - 722300 * q^27 - 816896 * q^28 - 3826748 * q^29 - 2462592 * q^30 - 717772 * q^31 + 262144 * q^32 + 10150812 * q^33 + 2736144 * q^34 + 976028 * q^35 + 2790144 * q^36 - 2232926 * q^37 - 451184 * q^38 - 2638752 * q^39 + 424960 * q^40 - 1934356 * q^41 + 66896 * q^42 - 7199908 * q^43 + 23808 * q^44 - 2872882 * q^45 + 279616 * q^46 - 658532 * q^47 + 532480 * q^48 + 7911090 * q^49 + 6767600 * q^50 + 7483220 * q^51 - 2504064 * q^52 - 9638226 * q^53 - 16067424 * q^54 - 25528944 * q^55 + 244736 * q^56 + 5982940 * q^57 + 12795648 * q^58 - 5778978 * q^59 + 3706880 * q^60 - 2662406 * q^61 + 22741600 * q^62 - 32958088 * q^63 + 2097152 * q^64 - 53440882 * q^65 - 29281472 * q^66 - 19899304 * q^67 - 16796160 * q^68 + 42333744 * q^69 + 1138880 * q^70 + 5074328 * q^71 + 3838976 * q^72 + 42468476 * q^73 + 57550016 * q^74 + 73744904 * q^75 - 9534080 * q^76 - 58841248 * q^77 - 22054720 * q^78 - 45648640 * q^79 - 204800 * q^80 + 56915216 * q^81 - 60233920 * q^82 - 39486530 * q^83 - 1578624 * q^84 + 28203862 * q^85 - 57522656 * q^86 + 20751820 * q^87 + 20834304 * q^88 + 253203846 * q^89 + 171598704 * q^90 + 55894918 * q^91 - 53459968 * q^92 - 347940572 * q^93 - 73271456 * q^94 - 80561352 * q^95 - 23920640 * q^96 - 130122508 * q^97 - 136714000 * q^98 + 3952412 * q^99

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_1(350))\)

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
350.8.a	\(\chi_{350}(1, \cdot)\)	350.8.a.a	1	1
		350.8.a.b	1
		350.8.a.c	1
		350.8.a.d	1
		350.8.a.e	1
		350.8.a.f	1
		350.8.a.g	1
		350.8.a.h	1
		350.8.a.i	2
		350.8.a.j	2
		350.8.a.k	2
		350.8.a.l	2
		350.8.a.m	2
		350.8.a.n	2
		350.8.a.o	2
		350.8.a.p	2
		350.8.a.q	2
		350.8.a.r	3
		350.8.a.s	3
		350.8.a.t	3
		350.8.a.u	3
		350.8.a.v	4
		350.8.a.w	4
		350.8.a.x	4
		350.8.a.y	4
		350.8.a.z	6
		350.8.a.ba	6
350.8.c	\(\chi_{350}(99, \cdot)\)	350.8.c.a	2	1
		350.8.c.b	2
		350.8.c.c	2
		350.8.c.d	2
		350.8.c.e	4
		350.8.c.f	4
		350.8.c.g	4
		350.8.c.h	4
		350.8.c.i	4
		350.8.c.j	4
		350.8.c.k	4
		350.8.c.l	6
		350.8.c.m	6
		350.8.c.n	8
		350.8.c.o	8
350.8.e	\(\chi_{350}(51, \cdot)\)	n/a	176	2
350.8.g	\(\chi_{350}(293, \cdot)\)	n/a	168	2
350.8.h	\(\chi_{350}(71, \cdot)\)	n/a	424	4
350.8.j	\(\chi_{350}(149, \cdot)\)	n/a	168	2
350.8.m	\(\chi_{350}(29, \cdot)\)	n/a	416	4
350.8.o	\(\chi_{350}(143, \cdot)\)	n/a	336	4
350.8.q	\(\chi_{350}(11, \cdot)\)	n/a	1120	8
350.8.r	\(\chi_{350}(13, \cdot)\)	n/a	1120	8
350.8.u	\(\chi_{350}(9, \cdot)\)	n/a	1120	8
350.8.x	\(\chi_{350}(3, \cdot)\)	n/a	2240	16

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

Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_1(350))\) into lower level spaces

\( S_{8}^{\mathrm{old}}(\Gamma_1(350)) \cong \) \(S_{8}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 8}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 6}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 3}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(70))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(175))\)\(^{\oplus 2}\)