Space of modular forms of level 350 and weight 6

• Label: 350.6
• Level: 350
• Weight: 6
• Dimension: 5300
• Nonzero newspaces: 12
• Sturm bound: 43200
• Trace bound: 4

Defining parameters

Level:	\( N \)	=	\( 350 = 2 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	=	\( 6 \)
Nonzero newspaces:			\( 12 \)
Sturm bound:			\(43200\)
Trace bound:			\(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(350))\).

	Total	New	Old
Modular forms	18336	5300	13036
Cusp forms	17664	5300	12364
Eisenstein series	672	0	672

Trace form

5300 * q - 16 * q^2 + 34 * q^3 + 32 * q^4 + 170 * q^5 - 104 * q^6 - 392 * q^7 - 256 * q^8 + 1394 * q^9 - 360 * q^10 - 3404 * q^11 + 544 * q^12 + 4106 * q^13 + 3016 * q^14 + 1640 * q^15 + 4608 * q^16 - 7196 * q^17 + 2120 * q^18 + 16318 * q^19 - 1280 * q^20 + 10910 * q^21 - 2800 * q^22 - 26416 * q^23 - 15744 * q^24 - 77334 * q^25 - 4312 * q^26 + 64804 * q^27 + 34752 * q^28 + 132656 * q^29 + 80448 * q^30 + 44316 * q^31 + 6144 * q^32 - 102324 * q^33 - 69672 * q^34 - 141572 * q^35 - 31200 * q^36 - 166286 * q^37 - 58760 * q^38 + 52344 * q^39 - 640 * q^40 + 254624 * q^41 + 282776 * q^42 + 339012 * q^43 + 44096 * q^44 - 27502 * q^45 - 57040 * q^46 - 250060 * q^47 + 8704 * q^48 - 44540 * q^49 - 22600 * q^50 - 93700 * q^51 - 14944 * q^52 - 315354 * q^53 - 218208 * q^54 - 86064 * q^55 - 51840 * q^56 + 405556 * q^57 + 120912 * q^58 + 463646 * q^59 - 225280 * q^60 + 349594 * q^61 + 343312 * q^62 + 652016 * q^63 + 57344 * q^64 + 577738 * q^65 + 124960 * q^66 - 128496 * q^67 + 177984 * q^68 - 280704 * q^69 - 47360 * q^70 - 733960 * q^71 - 225280 * q^72 - 1302024 * q^73 - 1104528 * q^74 - 1671736 * q^75 - 152480 * q^76 + 3776 * q^77 + 113120 * q^78 + 591216 * q^79 + 43520 * q^80 + 1225430 * q^81 + 609040 * q^82 + 923310 * q^83 + 140832 * q^84 + 1309922 * q^85 - 597264 * q^86 - 104204 * q^87 - 84480 * q^88 + 1356646 * q^89 + 126744 * q^90 + 1836430 * q^91 + 214784 * q^92 + 2492356 * q^93 + 1212128 * q^94 + 680728 * q^95 + 133120 * q^96 - 624120 * q^97 - 1264 * q^98 - 3029740 * q^99

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(350))\)

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
350.6.a	\(\chi_{350}(1, \cdot)\)	350.6.a.a	1	1
		350.6.a.b	1
		350.6.a.c	1
		350.6.a.d	1
		350.6.a.e	1
		350.6.a.f	1
		350.6.a.g	1
		350.6.a.h	1
		350.6.a.i	1
		350.6.a.j	1
		350.6.a.k	1
		350.6.a.l	1
		350.6.a.m	1
		350.6.a.n	1
		350.6.a.o	2
		350.6.a.p	2
		350.6.a.q	2
		350.6.a.r	2
		350.6.a.s	2
		350.6.a.t	2
		350.6.a.u	3
		350.6.a.v	3
		350.6.a.w	3
		350.6.a.x	3
		350.6.a.y	5
		350.6.a.z	5
350.6.c	\(\chi_{350}(99, \cdot)\)	350.6.c.a	2	1
		350.6.c.b	2
		350.6.c.c	2
		350.6.c.d	2
		350.6.c.e	2
		350.6.c.f	2
		350.6.c.g	2
		350.6.c.h	2
		350.6.c.i	4
		350.6.c.j	4
		350.6.c.k	4
		350.6.c.l	4
		350.6.c.m	6
		350.6.c.n	6
350.6.e	\(\chi_{350}(51, \cdot)\)	n/a	128	2
350.6.g	\(\chi_{350}(293, \cdot)\)	n/a	120	2
350.6.h	\(\chi_{350}(71, \cdot)\)	n/a	296	4
350.6.j	\(\chi_{350}(149, \cdot)\)	n/a	120	2
350.6.m	\(\chi_{350}(29, \cdot)\)	n/a	304	4
350.6.o	\(\chi_{350}(143, \cdot)\)	n/a	240	4
350.6.q	\(\chi_{350}(11, \cdot)\)	n/a	800	8
350.6.r	\(\chi_{350}(13, \cdot)\)	n/a	800	8
350.6.u	\(\chi_{350}(9, \cdot)\)	n/a	800	8
350.6.x	\(\chi_{350}(3, \cdot)\)	n/a	1600	16

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

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(350))\) into lower level spaces

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