Space of modular forms of level 51 and weight 2

• Label: 51.2
• Level: 51
• Weight: 2
• Dimension: 55
• Nonzero newspaces: 5
• Newform subspaces: 7
• Sturm bound: 384
• Trace bound: 4

Defining parameters

Level:	\( N \)	=	\( 51 = 3 \cdot 17 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 5 \)
Newform subspaces:			\( 7 \)
Sturm bound:			\(384\)
Trace bound:			\(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(51))\).

	Total	New	Old
Modular forms	128	87	41
Cusp forms	65	55	10
Eisenstein series	63	32	31

Trace form

55 * q - 3 * q^2 - 9 * q^3 - 23 * q^4 - 6 * q^5 - 11 * q^6 - 24 * q^7 - 15 * q^8 - 9 * q^9 - 26 * q^10 + 4 * q^11 + 9 * q^12 - 14 * q^13 + 8 * q^14 + 10 * q^15 + 25 * q^16 - q^17 + 13 * q^18 - 20 * q^19 + 14 * q^20 + 8 * q^21 - 20 * q^22 - 8 * q^23 + 17 * q^24 + 9 * q^25 + 30 * q^26 - 9 * q^27 + 24 * q^28 + 10 * q^29 + 38 * q^30 + 16 * q^31 + 17 * q^32 + 20 * q^33 + 61 * q^34 + 16 * q^35 + 17 * q^36 + 10 * q^37 + 20 * q^38 - 6 * q^39 + 22 * q^40 - 2 * q^41 - 32 * q^42 - 12 * q^43 - 20 * q^44 - 38 * q^45 - 56 * q^46 - 48 * q^47 - 95 * q^48 - 73 * q^49 - 93 * q^50 - 57 * q^51 - 130 * q^52 - 30 * q^53 - 27 * q^54 - 24 * q^55 - 40 * q^56 - 12 * q^57 + 6 * q^58 + 4 * q^59 - 10 * q^60 + 18 * q^61 + 16 * q^62 + 56 * q^63 + 17 * q^64 + 36 * q^65 + 36 * q^66 - 4 * q^67 + 81 * q^68 + 72 * q^69 + 112 * q^70 + 24 * q^71 + 73 * q^72 + 110 * q^73 + 54 * q^74 + 89 * q^75 + 84 * q^76 + 64 * q^77 + 118 * q^78 + 32 * q^79 + 86 * q^80 + 47 * q^81 + 74 * q^82 + 28 * q^83 + 40 * q^84 + 2 * q^85 - 68 * q^86 - 38 * q^87 - 4 * q^88 - 42 * q^89 - 98 * q^90 - 32 * q^91 - 8 * q^92 - 72 * q^93 - 32 * q^94 - 56 * q^95 - 111 * q^96 - 50 * q^97 - 99 * q^98 - 60 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(51))\)

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
51.2.a	\(\chi_{51}(1, \cdot)\)	51.2.a.a	1	1
		51.2.a.b	2
51.2.d	\(\chi_{51}(16, \cdot)\)	51.2.d.a	2	1
		51.2.d.b	2
51.2.e	\(\chi_{51}(4, \cdot)\)	51.2.e.a	8	2
51.2.h	\(\chi_{51}(19, \cdot)\)	51.2.h.a	8	4
51.2.i	\(\chi_{51}(5, \cdot)\)	51.2.i.a	32	8

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(51))\) into lower level spaces

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