Space of modular forms of level 51 and weight 5

• Label: 51.5
• Level: 51
• Weight: 5
• Dimension: 272
• Nonzero newspaces: 5
• Newform subspaces: 7
• Sturm bound: 960
• Trace bound: 3

Defining parameters

Level:	\( N \)	=	\( 51 = 3 \cdot 17 \)
Weight:	\( k \)	=	\( 5 \)
Nonzero newspaces:			\( 5 \)
Newform subspaces:			\( 7 \)
Sturm bound:			\(960\)
Trace bound:			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(\Gamma_1(51))\).

	Total	New	Old
Modular forms	416	300	116
Cusp forms	352	272	80
Eisenstein series	64	28	36

Trace form

272 * q - 8 * q^3 - 16 * q^4 - 8 * q^6 - 16 * q^7 - 8 * q^9 - 784 * q^10 - 240 * q^11 + 760 * q^12 + 800 * q^13 + 1536 * q^14 + 688 * q^15 - 32 * q^16 - 528 * q^17 - 2064 * q^18 - 1408 * q^19 - 5376 * q^20 - 2048 * q^21 - 1552 * q^22 + 336 * q^23 - 1688 * q^24 - 32 * q^25 + 5184 * q^26 - 8 * q^27 + 14864 * q^28 + 6720 * q^29 + 9784 * q^30 + 7408 * q^31 + 5040 * q^32 - 16 * q^33 - 8592 * q^34 - 8448 * q^35 - 2904 * q^36 - 14864 * q^37 - 20400 * q^38 - 504 * q^39 - 27792 * q^40 - 5760 * q^41 - 8984 * q^42 + 6704 * q^43 + 23232 * q^44 - 5224 * q^45 + 32016 * q^46 - 15376 * q^48 - 16 * q^49 + 3224 * q^51 - 32 * q^52 - 30240 * q^53 - 11120 * q^54 - 26128 * q^55 - 7920 * q^56 + 26032 * q^57 + 35264 * q^58 + 27648 * q^59 + 64480 * q^60 + 49520 * q^61 + 55440 * q^62 + 28816 * q^63 + 30160 * q^64 + 30240 * q^65 - 2128 * q^66 - 32 * q^67 - 69840 * q^68 - 46624 * q^69 - 119104 * q^70 - 43488 * q^71 - 63936 * q^72 - 57216 * q^73 - 31968 * q^74 - 46184 * q^75 + 18528 * q^76 - 4800 * q^77 + 6032 * q^78 + 31792 * q^79 + 105264 * q^80 + 26648 * q^81 + 116704 * q^82 + 100080 * q^83 + 164544 * q^84 + 50288 * q^85 - 21504 * q^86 - 8984 * q^87 - 122896 * q^88 - 36720 * q^89 - 79800 * q^90 - 89392 * q^91 - 153600 * q^92 - 92712 * q^93 - 112656 * q^94 - 48576 * q^95 - 174160 * q^96 - 20816 * q^97 - 71016 * q^99

Decomposition of \(S_{5}^{\mathrm{new}}(\Gamma_1(51))\)

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
51.5.b	\(\chi_{51}(35, \cdot)\)	51.5.b.a	22	1
51.5.c	\(\chi_{51}(50, \cdot)\)	51.5.c.a	1	1
		51.5.c.b	1
		51.5.c.c	20
51.5.f	\(\chi_{51}(38, \cdot)\)	51.5.f.a	44	2
51.5.g	\(\chi_{51}(2, \cdot)\)	51.5.g.a	88	4
51.5.j	\(\chi_{51}(7, \cdot)\)	51.5.j.a	96	8

Decomposition of \(S_{5}^{\mathrm{old}}(\Gamma_1(51))\) into lower level spaces

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