Space of modular forms of level 435 and weight 4

• Label: 435.4
• Level: 435
• Weight: 4
• Dimension: 13664
• Nonzero newspaces: 20
• Sturm bound: 53760
• Trace bound: 6

Defining parameters

Level:	\( N \)	=	\( 435 = 3 \cdot 5 \cdot 29 \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 20 \)
Sturm bound:			\(53760\)
Trace bound:			\(6\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(435))\).

	Total	New	Old
Modular forms	20608	13984	6624
Cusp forms	19712	13664	6048
Eisenstein series	896	320	576

Trace form

13664 * q - 8 * q^2 - 16 * q^3 - 8 * q^4 - 12 * q^5 - 84 * q^6 - 16 * q^7 + 72 * q^8 + 8 * q^9 + 108 * q^10 + 112 * q^11 - 244 * q^12 - 384 * q^13 - 528 * q^14 - 390 * q^15 - 776 * q^16 - 80 * q^17 + 380 * q^18 + 456 * q^19 - 976 * q^20 - 476 * q^21 - 584 * q^22 + 464 * q^23 + 1892 * q^24 + 640 * q^25 + 2616 * q^26 + 752 * q^27 + 4768 * q^28 + 2348 * q^29 - 132 * q^30 + 1032 * q^31 + 3352 * q^32 + 668 * q^33 + 800 * q^34 + 256 * q^35 - 3396 * q^36 - 6160 * q^38 - 3372 * q^39 - 4148 * q^40 + 728 * q^41 - 604 * q^42 - 960 * q^43 - 8456 * q^44 - 1680 * q^45 - 21952 * q^46 - 6400 * q^47 - 5860 * q^48 - 3716 * q^49 + 1388 * q^50 + 2484 * q^51 + 11752 * q^52 + 9100 * q^53 + 404 * q^54 + 11388 * q^55 + 21560 * q^56 + 4336 * q^57 + 38192 * q^58 + 5168 * q^59 + 7262 * q^60 + 7680 * q^61 + 13880 * q^62 - 1300 * q^63 + 5056 * q^64 - 1250 * q^65 - 6036 * q^66 - 7696 * q^67 - 21080 * q^68 - 8716 * q^69 - 19140 * q^70 - 12624 * q^71 + 16484 * q^72 - 19716 * q^73 - 5288 * q^74 + 10150 * q^75 + 7672 * q^76 + 3456 * q^77 - 1244 * q^78 + 2984 * q^79 - 2008 * q^80 - 14176 * q^81 - 7880 * q^82 - 2736 * q^83 - 32656 * q^84 - 8268 * q^85 - 8768 * q^86 - 11312 * q^87 - 4480 * q^88 + 1752 * q^89 - 11170 * q^90 - 3352 * q^91 - 2112 * q^92 - 8844 * q^93 - 6888 * q^94 - 6608 * q^95 - 26632 * q^96 - 49516 * q^97 - 54288 * q^98 - 27412 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(435))\)

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
435.4.a	\(\chi_{435}(1, \cdot)\)	435.4.a.a	1	1
		435.4.a.b	1
		435.4.a.c	1
		435.4.a.d	2
		435.4.a.e	2
		435.4.a.f	5
		435.4.a.g	6
		435.4.a.h	6
		435.4.a.i	7
		435.4.a.j	7
		435.4.a.k	8
		435.4.a.l	10
435.4.c	\(\chi_{435}(349, \cdot)\)	435.4.c.a	42	1
		435.4.c.b	42
435.4.d	\(\chi_{435}(376, \cdot)\)	435.4.d.a	30	1
		435.4.d.b	30
435.4.f	\(\chi_{435}(289, \cdot)\)	435.4.f.a	2	1
		435.4.f.b	2
		435.4.f.c	4
		435.4.f.d	4
		435.4.f.e	38
		435.4.f.f	38
435.4.j	\(\chi_{435}(133, \cdot)\)	n/a	180	2
435.4.l	\(\chi_{435}(104, \cdot)\)	n/a	352	2
435.4.m	\(\chi_{435}(233, \cdot)\)	n/a	336	2
435.4.p	\(\chi_{435}(173, \cdot)\)	n/a	352	2
435.4.q	\(\chi_{435}(41, \cdot)\)	n/a	240	2
435.4.s	\(\chi_{435}(307, \cdot)\)	n/a	180	2
435.4.u	\(\chi_{435}(16, \cdot)\)	n/a	360	6
435.4.x	\(\chi_{435}(4, \cdot)\)	n/a	528	6
435.4.z	\(\chi_{435}(91, \cdot)\)	n/a	360	6
435.4.ba	\(\chi_{435}(49, \cdot)\)	n/a	552	6
435.4.bd	\(\chi_{435}(73, \cdot)\)	n/a	1080	12
435.4.bf	\(\chi_{435}(11, \cdot)\)	n/a	1440	12
435.4.bg	\(\chi_{435}(38, \cdot)\)	n/a	2112	12
435.4.bj	\(\chi_{435}(23, \cdot)\)	n/a	2112	12
435.4.bk	\(\chi_{435}(14, \cdot)\)	n/a	2112	12
435.4.bm	\(\chi_{435}(37, \cdot)\)	n/a	1080	12

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(435))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(435)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(29))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(87))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(145))\)\(^{\oplus 2}\)