Space of modular forms of level 58 and weight 2

• Label: 58.2
• Level: 58
• Weight: 2
• Dimension: 34
• Nonzero newspaces: 4
• Newform subspaces: 6
• Sturm bound: 420
• Trace bound: 3

Defining parameters

Level:	\( N \)	=	\( 58 = 2 \cdot 29 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 4 \)
Newform subspaces:			\( 6 \)
Sturm bound:			\(420\)
Trace bound:			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(58))\).

	Total	New	Old
Modular forms	133	34	99
Cusp forms	78	34	44
Eisenstein series	55	0	55

Trace form

34 * q - q^2 - 4 * q^3 - q^4 - 6 * q^5 - 4 * q^6 - 8 * q^7 - q^8 - 13 * q^9 - 6 * q^10 - 12 * q^11 - 4 * q^12 - 14 * q^13 - 8 * q^14 - 24 * q^15 - q^16 - 18 * q^17 - 13 * q^18 - 20 * q^19 + q^20 + 24 * q^21 + 16 * q^22 + 4 * q^23 + 24 * q^24 + 25 * q^25 + 21 * q^26 + 44 * q^27 - 8 * q^28 + 27 * q^29 + 60 * q^30 + 24 * q^31 - q^32 + 36 * q^33 + 17 * q^34 + 8 * q^35 + 15 * q^36 - 10 * q^37 + 8 * q^38 + q^40 - 42 * q^41 - 32 * q^42 - 44 * q^43 - 12 * q^44 - 43 * q^45 - 24 * q^46 - 20 * q^47 - 4 * q^48 - q^49 - 31 * q^50 - 16 * q^51 - 14 * q^52 + 9 * q^53 - 40 * q^54 + 40 * q^55 - 8 * q^56 - 24 * q^57 - 29 * q^58 - 32 * q^59 - 24 * q^60 - 6 * q^61 - 32 * q^62 + 8 * q^63 - q^64 - 21 * q^65 - 48 * q^66 - 12 * q^67 - 18 * q^68 - 40 * q^69 - 20 * q^70 + 40 * q^71 - 13 * q^72 + 17 * q^73 + 46 * q^74 + 16 * q^75 + 36 * q^76 + 44 * q^77 + 56 * q^78 - 24 * q^79 - 6 * q^80 + 103 * q^81 + 14 * q^82 + 28 * q^83 + 52 * q^84 + 60 * q^85 + 96 * q^86 + 24 * q^87 - 12 * q^88 + 50 * q^89 + 62 * q^90 + 56 * q^91 + 60 * q^92 - 16 * q^93 + 8 * q^94 + 104 * q^95 - 4 * q^96 - 35 * q^97 + 55 * q^98 + 40 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(58))\)

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
58.2.a	\(\chi_{58}(1, \cdot)\)	58.2.a.a	1	1
		58.2.a.b	1
58.2.b	\(\chi_{58}(57, \cdot)\)	58.2.b.a	2	1
58.2.d	\(\chi_{58}(7, \cdot)\)	58.2.d.a	6	6
		58.2.d.b	12
58.2.e	\(\chi_{58}(5, \cdot)\)	58.2.e.a	12	6

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(58))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(58)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(29))\)\(^{\oplus 2}\)