Space of modular forms of level 51 and weight 4

• Label: 51.4
• Level: 51
• Weight: 4
• Dimension: 200
• Nonzero newspaces: 5
• Newform subspaces: 9
• Sturm bound: 768
• Trace bound: 2

Defining parameters

Level:	\( N \)	=	\( 51 = 3 \cdot 17 \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 5 \)
Newform subspaces:			\( 9 \)
Sturm bound:			\(768\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(51))\).

	Total	New	Old
Modular forms	320	232	88
Cusp forms	256	200	56
Eisenstein series	64	32	32

Trace form

200 * q - 8 * q^3 - 16 * q^4 - 8 * q^6 - 16 * q^7 - 8 * q^9 + 192 * q^10 + 224 * q^11 + 88 * q^12 - 80 * q^13 - 320 * q^14 - 344 * q^15 - 896 * q^16 - 256 * q^17 - 464 * q^18 - 176 * q^19 - 224 * q^20 + 88 * q^21 + 432 * q^22 + 416 * q^23 + 1864 * q^24 + 2440 * q^25 + 2064 * q^26 - 8 * q^27 - 304 * q^28 - 520 * q^29 - 1352 * q^30 - 1744 * q^31 - 2480 * q^32 - 1056 * q^33 - 4240 * q^34 - 1984 * q^35 - 376 * q^36 - 1360 * q^37 - 1040 * q^38 - 1416 * q^39 + 1136 * q^40 + 920 * q^41 + 808 * q^42 + 2720 * q^43 + 4928 * q^44 + 1424 * q^45 + 3920 * q^46 + 3728 * q^48 - 16 * q^49 + 1592 * q^51 - 32 * q^52 + 3432 * q^53 + 6720 * q^54 + 5680 * q^55 + 5200 * q^56 + 2720 * q^57 + 2560 * q^58 + 320 * q^59 - 3712 * q^60 - 2416 * q^61 - 4144 * q^62 - 7064 * q^63 - 4272 * q^64 - 7320 * q^65 - 8352 * q^66 - 4288 * q^67 - 7280 * q^68 - 3760 * q^69 - 2560 * q^70 - 384 * q^71 - 3680 * q^72 - 616 * q^73 - 528 * q^74 - 872 * q^75 - 992 * q^76 + 416 * q^77 + 1776 * q^78 + 688 * q^79 - 272 * q^80 + 6432 * q^81 + 816 * q^82 + 7136 * q^83 - 8064 * q^84 - 2344 * q^85 - 5248 * q^86 - 8984 * q^87 - 13840 * q^88 - 3072 * q^89 - 3160 * q^90 - 4048 * q^91 - 4480 * q^92 + 1464 * q^93 + 752 * q^94 + 1664 * q^95 + 15584 * q^96 + 4592 * q^97 + 7056 * q^98 + 13040 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(51))\)

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
51.4.a	\(\chi_{51}(1, \cdot)\)	51.4.a.a	1	1
		51.4.a.b	1
		51.4.a.c	1
		51.4.a.d	2
		51.4.a.e	3
51.4.d	\(\chi_{51}(16, \cdot)\)	51.4.d.a	8	1
51.4.e	\(\chi_{51}(4, \cdot)\)	51.4.e.a	16	2
51.4.h	\(\chi_{51}(19, \cdot)\)	51.4.h.a	40	4
51.4.i	\(\chi_{51}(5, \cdot)\)	51.4.i.a	128	8

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(51))\) into lower level spaces

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