Space of modular forms of level 57 and weight 2

• Label: 57.2
• Level: 57
• Weight: 2
• Dimension: 71
• Nonzero newspaces: 6
• Newform subspaces: 11
• Sturm bound: 480
• Trace bound: 3

Defining parameters

Level:	\( N \)	=	\( 57 = 3 \cdot 19 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 6 \)
Newform subspaces:			\( 11 \)
Sturm bound:			\(480\)
Trace bound:			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(57))\).

	Total	New	Old
Modular forms	156	107	49
Cusp forms	85	71	14
Eisenstein series	71	36	35

Trace form

71 * q - 3 * q^2 - 10 * q^3 - 25 * q^4 - 6 * q^5 - 12 * q^6 - 26 * q^7 - 15 * q^8 - 10 * q^9 - 36 * q^10 - 12 * q^11 - 4 * q^12 - 8 * q^13 + 12 * q^14 + 3 * q^15 + 23 * q^16 - 3 * q^18 + 5 * q^19 + 30 * q^20 + 4 * q^21 - 6 * q^23 + 12 * q^24 - 13 * q^25 - 6 * q^26 + 2 * q^27 + 4 * q^28 + 6 * q^29 + 36 * q^30 - 14 * q^31 + 27 * q^32 + 33 * q^33 + 18 * q^34 + 24 * q^35 + 56 * q^36 - 2 * q^37 + 69 * q^38 + 22 * q^39 + 54 * q^40 - 6 * q^41 + 57 * q^42 + 10 * q^43 + 6 * q^44 + 12 * q^45 - 12 * q^47 - 40 * q^48 - 39 * q^49 - 39 * q^50 - 63 * q^51 - 116 * q^52 - 54 * q^53 - 66 * q^54 - 90 * q^55 - 120 * q^56 - 73 * q^57 - 126 * q^58 - 60 * q^59 - 114 * q^60 - 20 * q^61 - 6 * q^62 - 41 * q^63 - q^64 + 24 * q^65 - 45 * q^66 + 58 * q^67 + 12 * q^69 + 54 * q^70 + 39 * q^72 + 70 * q^73 + 30 * q^74 + 53 * q^75 + 29 * q^76 + 102 * q^77 + 93 * q^78 + 106 * q^79 + 66 * q^80 + 26 * q^81 + 198 * q^82 + 42 * q^83 + 151 * q^84 + 90 * q^85 + 66 * q^86 + 105 * q^87 + 126 * q^88 + 72 * q^89 + 36 * q^90 + 38 * q^91 + 66 * q^92 + 61 * q^93 + 36 * q^94 - 60 * q^95 - 9 * q^96 - 62 * q^97 - 27 * q^98 - 12 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(57))\)

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
57.2.a	\(\chi_{57}(1, \cdot)\)	57.2.a.a	1	1
		57.2.a.b	1
		57.2.a.c	1
57.2.d	\(\chi_{57}(56, \cdot)\)	57.2.d.a	4	1
57.2.e	\(\chi_{57}(7, \cdot)\)	57.2.e.a	2	2
		57.2.e.b	6
57.2.f	\(\chi_{57}(8, \cdot)\)	57.2.f.a	8	2
57.2.i	\(\chi_{57}(4, \cdot)\)	57.2.i.a	6	6
		57.2.i.b	12
57.2.j	\(\chi_{57}(2, \cdot)\)	57.2.j.a	6	6
		57.2.j.b	24

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(57))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(57)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 2}\)