Space of modular forms of level 51 and weight 3

• Label: 51.3
• Level: 51
• Weight: 3
• Dimension: 128
• Nonzero newspaces: 5
• Newform subspaces: 9
• Sturm bound: 576
• Trace bound: 3

Defining parameters

Level:	\( N \)	=	\( 51 = 3 \cdot 17 \)
Weight:	\( k \)	=	\( 3 \)
Nonzero newspaces:			\( 5 \)
Newform subspaces:			\( 9 \)
Sturm bound:			\(576\)
Trace bound:			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(51))\).

	Total	New	Old
Modular forms	224	156	68
Cusp forms	160	128	32
Eisenstein series	64	28	36

Trace form

128 * q - 8 * q^3 - 16 * q^4 - 8 * q^6 - 16 * q^7 - 8 * q^9 - 64 * q^10 - 80 * q^11 - 104 * q^12 - 64 * q^13 - 64 * q^14 - 32 * q^15 - 32 * q^16 + 16 * q^17 + 48 * q^18 + 32 * q^19 + 224 * q^20 + 112 * q^21 + 176 * q^22 + 112 * q^23 + 40 * q^24 - 192 * q^25 - 368 * q^26 - 8 * q^27 - 496 * q^28 - 160 * q^29 - 200 * q^30 - 144 * q^31 - 80 * q^32 - 16 * q^33 + 112 * q^34 + 128 * q^35 + 72 * q^36 + 240 * q^37 + 400 * q^38 + 360 * q^39 + 880 * q^40 + 320 * q^41 + 808 * q^42 + 464 * q^43 + 704 * q^44 + 248 * q^45 + 400 * q^46 + 80 * q^48 - 16 * q^49 - 40 * q^51 - 32 * q^52 - 336 * q^53 - 752 * q^54 - 784 * q^55 - 880 * q^56 - 848 * q^57 - 1024 * q^58 - 512 * q^59 - 1376 * q^60 - 592 * q^61 - 560 * q^62 - 704 * q^63 - 560 * q^64 - 240 * q^65 - 208 * q^66 - 32 * q^67 - 208 * q^68 - 64 * q^69 - 320 * q^70 - 160 * q^71 + 96 * q^72 - 176 * q^73 - 48 * q^74 + 472 * q^75 - 32 * q^76 + 512 * q^77 + 752 * q^78 + 432 * q^79 + 816 * q^80 + 776 * q^81 + 912 * q^82 + 976 * q^83 + 1344 * q^84 + 512 * q^85 + 128 * q^86 + 808 * q^87 + 752 * q^88 + 240 * q^89 + 1560 * q^90 + 656 * q^91 + 1280 * q^92 + 792 * q^93 + 1264 * q^94 + 704 * q^95 + 1232 * q^96 + 816 * q^97 + 1008 * q^98 + 72 * q^99

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(51))\)

We only show spaces with odd 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
51.3.b	\(\chi_{51}(35, \cdot)\)	51.3.b.a	10	1
51.3.c	\(\chi_{51}(50, \cdot)\)	51.3.c.a	1	1
		51.3.c.b	1
		51.3.c.c	8
51.3.f	\(\chi_{51}(38, \cdot)\)	51.3.f.a	20	2
51.3.g	\(\chi_{51}(2, \cdot)\)	51.3.g.a	4	4
		51.3.g.b	4
		51.3.g.c	32
51.3.j	\(\chi_{51}(7, \cdot)\)	51.3.j.a	48	8

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(51))\) into lower level spaces

\( S_{3}^{\mathrm{old}}(\Gamma_1(51)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 2}\)