Space of modular forms of level 255 and weight 4

• Label: 255.4
• Level: 255
• Weight: 4
• Dimension: 4628
• Nonzero newspaces: 18
• Sturm bound: 18432
• Trace bound: 10

Defining parameters

Level:	\( N \)	=	\( 255 = 3 \cdot 5 \cdot 17 \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 18 \)
Sturm bound:			\(18432\)
Trace bound:			\(10\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(255))\).

	Total	New	Old
Modular forms	7168	4804	2364
Cusp forms	6656	4628	2028
Eisenstein series	512	176	336

Trace form

4628 * q - 8 * q^2 - 4 * q^3 + 16 * q^4 - 12 * q^5 - 48 * q^6 + 8 * q^7 + 72 * q^8 + 20 * q^9 - 64 * q^10 - 336 * q^11 - 424 * q^12 - 232 * q^13 + 112 * q^14 - 36 * q^15 + 1056 * q^16 + 472 * q^17 + 1272 * q^18 + 800 * q^19 + 1096 * q^20 + 936 * q^21 + 112 * q^22 - 256 * q^23 - 3184 * q^24 - 2676 * q^25 - 4592 * q^26 - 1420 * q^27 - 848 * q^28 - 536 * q^29 - 912 * q^30 + 2096 * q^31 + 4728 * q^32 + 2104 * q^33 + 8984 * q^34 + 3024 * q^35 + 2080 * q^36 + 5176 * q^37 + 2864 * q^38 + 4048 * q^39 - 896 * q^40 - 1112 * q^41 - 2224 * q^42 - 6408 * q^43 - 11312 * q^44 - 1708 * q^45 - 8752 * q^46 - 464 * q^47 - 5928 * q^48 - 332 * q^49 + 1192 * q^50 - 2804 * q^51 - 352 * q^52 - 7088 * q^53 - 13040 * q^54 - 5696 * q^55 - 10400 * q^56 - 7464 * q^57 - 5296 * q^58 - 1632 * q^59 + 2528 * q^60 + 2472 * q^61 + 7664 * q^62 + 11312 * q^63 + 10128 * q^64 + 5944 * q^65 + 14048 * q^66 + 8264 * q^67 + 32456 * q^68 + 17152 * q^69 + 37872 * q^70 + 14688 * q^71 + 18488 * q^72 + 22488 * q^73 + 15296 * q^74 + 8580 * q^75 + 3552 * q^76 - 4544 * q^77 - 12416 * q^78 - 12224 * q^79 - 42696 * q^80 - 14476 * q^81 - 51952 * q^82 - 32752 * q^83 - 21120 * q^84 - 34068 * q^85 - 19264 * q^86 + 4472 * q^87 - 32048 * q^88 - 4392 * q^89 + 632 * q^90 - 11344 * q^91 - 11072 * q^92 - 8384 * q^93 - 5328 * q^94 - 1616 * q^95 - 24800 * q^96 + 4216 * q^97 + 13304 * q^98 - 20064 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(255))\)

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
255.4.a	\(\chi_{255}(1, \cdot)\)	255.4.a.a	1	1
		255.4.a.b	1
		255.4.a.c	2
		255.4.a.d	2
		255.4.a.e	2
		255.4.a.f	2
		255.4.a.g	5
		255.4.a.h	5
		255.4.a.i	6
		255.4.a.j	6
255.4.b	\(\chi_{255}(154, \cdot)\)	255.4.b.a	20	1
		255.4.b.b	28
255.4.d	\(\chi_{255}(169, \cdot)\)	255.4.d.a	28	1
		255.4.d.b	28
255.4.g	\(\chi_{255}(16, \cdot)\)	255.4.g.a	16	1
		255.4.g.b	20
255.4.j	\(\chi_{255}(106, \cdot)\)	255.4.j.a	32	2
		255.4.j.b	40
255.4.k	\(\chi_{255}(98, \cdot)\)	n/a	208	2
255.4.m	\(\chi_{255}(137, \cdot)\)	n/a	192	2
255.4.o	\(\chi_{255}(152, \cdot)\)	n/a	208	2
255.4.r	\(\chi_{255}(38, \cdot)\)	n/a	208	2
255.4.s	\(\chi_{255}(4, \cdot)\)	n/a	112	2
255.4.v	\(\chi_{255}(53, \cdot)\)	n/a	416	4
255.4.w	\(\chi_{255}(76, \cdot)\)	n/a	144	4
255.4.z	\(\chi_{255}(19, \cdot)\)	n/a	208	4
255.4.ba	\(\chi_{255}(2, \cdot)\)	n/a	416	4
255.4.bd	\(\chi_{255}(7, \cdot)\)	n/a	432	8
255.4.be	\(\chi_{255}(14, \cdot)\)	n/a	832	8
255.4.bg	\(\chi_{255}(11, \cdot)\)	n/a	576	8
255.4.bi	\(\chi_{255}(22, \cdot)\)	n/a	432	8

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(255))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(255)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(51))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(85))\)\(^{\oplus 2}\)