Space of modular forms of level 350 and weight 4

• Label: 350.4
• Level: 350
• Weight: 4
• Dimension: 3180
• Nonzero newspaces: 12
• Sturm bound: 28800
• Trace bound: 4

Defining parameters

Level:	\( N \)	=	\( 350 = 2 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 12 \)
Sturm bound:			\(28800\)
Trace bound:			\(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(350))\).

	Total	New	Old
Modular forms	11136	3180	7956
Cusp forms	10464	3180	7284
Eisenstein series	672	0	672

Trace form

3180 * q + 8 * q^2 - 20 * q^3 - 16 * q^4 - 10 * q^5 - 68 * q^6 - 56 * q^7 + 32 * q^8 + 374 * q^9 + 100 * q^10 - 134 * q^11 - 80 * q^12 - 166 * q^13 - 92 * q^14 - 160 * q^15 + 192 * q^16 - 1166 * q^17 - 772 * q^18 - 460 * q^19 + 160 * q^20 + 680 * q^21 + 1320 * q^22 + 1994 * q^23 + 528 * q^24 + 1286 * q^25 - 868 * q^26 - 752 * q^27 - 56 * q^28 + 200 * q^29 + 288 * q^30 + 466 * q^31 - 192 * q^32 + 2886 * q^33 + 1108 * q^34 + 1228 * q^35 + 2760 * q^36 + 2868 * q^37 + 1420 * q^38 - 108 * q^39 - 240 * q^40 - 2296 * q^41 - 2716 * q^42 - 3476 * q^43 - 1432 * q^44 - 922 * q^45 - 4744 * q^46 - 3250 * q^47 - 608 * q^48 - 900 * q^49 - 700 * q^50 + 3638 * q^51 - 616 * q^52 + 5520 * q^53 + 816 * q^54 - 1184 * q^55 + 816 * q^56 - 5960 * q^57 - 1224 * q^58 - 12280 * q^59 - 5440 * q^60 - 3608 * q^61 - 8504 * q^62 - 6280 * q^63 + 128 * q^64 - 2642 * q^65 - 1808 * q^66 + 8822 * q^67 + 4296 * q^68 + 20940 * q^69 + 4800 * q^70 + 8264 * q^71 + 512 * q^72 + 23318 * q^73 + 12264 * q^74 + 27824 * q^75 + 3704 * q^76 + 14882 * q^77 + 17264 * q^78 + 10778 * q^79 - 160 * q^80 - 1936 * q^81 - 1608 * q^82 - 16926 * q^83 - 2448 * q^84 - 21418 * q^85 - 11496 * q^86 - 56240 * q^87 - 6336 * q^88 - 50480 * q^89 - 27516 * q^90 - 19198 * q^91 - 12592 * q^92 - 20138 * q^93 - 7216 * q^94 + 6808 * q^95 + 832 * q^96 + 17744 * q^97 + 12536 * q^98 + 33188 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(350))\)

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
350.4.a	\(\chi_{350}(1, \cdot)\)	350.4.a.a	1	1
		350.4.a.b	1
		350.4.a.c	1
		350.4.a.d	1
		350.4.a.e	1
		350.4.a.f	1
		350.4.a.g	1
		350.4.a.h	1
		350.4.a.i	1
		350.4.a.j	1
		350.4.a.k	1
		350.4.a.l	1
		350.4.a.m	1
		350.4.a.n	1
		350.4.a.o	1
		350.4.a.p	1
		350.4.a.q	1
		350.4.a.r	1
		350.4.a.s	1
		350.4.a.t	1
		350.4.a.u	1
		350.4.a.v	1
		350.4.a.w	3
		350.4.a.x	3
350.4.c	\(\chi_{350}(99, \cdot)\)	350.4.c.a	2	1
		350.4.c.b	2
		350.4.c.c	2
		350.4.c.d	2
		350.4.c.e	2
		350.4.c.f	2
		350.4.c.g	2
		350.4.c.h	2
		350.4.c.i	2
		350.4.c.j	2
		350.4.c.k	2
		350.4.c.l	2
		350.4.c.m	2
		350.4.c.n	2
350.4.e	\(\chi_{350}(51, \cdot)\)	350.4.e.a	2	2
		350.4.e.b	2
		350.4.e.c	2
		350.4.e.d	2
		350.4.e.e	2
		350.4.e.f	2
		350.4.e.g	2
		350.4.e.h	4
		350.4.e.i	6
		350.4.e.j	6
		350.4.e.k	6
		350.4.e.l	8
		350.4.e.m	8
		350.4.e.n	12
		350.4.e.o	12
350.4.g	\(\chi_{350}(293, \cdot)\)	350.4.g.a	16	2
		350.4.g.b	24
		350.4.g.c	32
350.4.h	\(\chi_{350}(71, \cdot)\)	n/a	184	4
350.4.j	\(\chi_{350}(149, \cdot)\)	350.4.j.a	4	2
		350.4.j.b	4
		350.4.j.c	4
		350.4.j.d	4
		350.4.j.e	4
		350.4.j.f	4
		350.4.j.g	8
		350.4.j.h	12
		350.4.j.i	12
		350.4.j.j	16
350.4.m	\(\chi_{350}(29, \cdot)\)	n/a	176	4
350.4.o	\(\chi_{350}(143, \cdot)\)	n/a	144	4
350.4.q	\(\chi_{350}(11, \cdot)\)	n/a	480	8
350.4.r	\(\chi_{350}(13, \cdot)\)	n/a	480	8
350.4.u	\(\chi_{350}(9, \cdot)\)	n/a	480	8
350.4.x	\(\chi_{350}(3, \cdot)\)	n/a	960	16

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(350))\) into lower level spaces

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