Space of modular forms of level 62 and weight 2

• Label: 62.2
• Level: 62
• Weight: 2
• Dimension: 39
• Nonzero newspaces: 4
• Newform subspaces: 8
• Sturm bound: 480
• Trace bound: 3

Defining parameters

Level:	\( N \)	=	\( 62 = 2 \cdot 31 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 4 \)
Newform subspaces:			\( 8 \)
Sturm bound:			\(480\)
Trace bound:			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(62))\).

	Total	New	Old
Modular forms	150	39	111
Cusp forms	91	39	52
Eisenstein series	59	0	59

Trace form

39 * 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 - 6 * q^20 - 22 * q^21 + 18 * q^22 + 6 * q^23 - 4 * q^24 + 39 * q^25 + 16 * q^26 + 50 * q^27 + 32 * q^28 + 30 * q^29 + 36 * q^30 + 29 * q^31 - q^32 + 12 * q^33 + 42 * q^34 + 12 * q^35 + 27 * q^36 + 52 * q^37 + 10 * q^38 + 14 * q^39 - 6 * q^40 - 12 * q^41 - 2 * q^42 - 34 * q^43 - 12 * q^44 - 78 * q^45 - 24 * q^46 - 48 * q^47 - 4 * q^48 - 27 * q^49 - 31 * q^50 + 18 * q^51 - 14 * q^52 - 24 * q^53 - 40 * q^54 - 12 * q^55 - 8 * q^56 + 10 * q^57 - 30 * q^58 - 30 * q^59 - 24 * q^60 + 28 * q^61 - 31 * q^62 + 16 * q^63 - q^64 + 6 * q^65 - 48 * q^66 - 38 * q^67 - 18 * q^68 - 6 * q^69 - 48 * q^70 - 12 * q^71 - 13 * q^72 - 44 * q^73 - 38 * q^74 - 4 * q^75 - 10 * q^76 + 24 * q^77 + 34 * q^78 - 10 * q^79 + 24 * q^80 - q^81 + 18 * q^82 + 126 * q^83 + 28 * q^84 + 12 * q^85 + 76 * q^86 + 48 * q^88 + 60 * q^89 + 102 * q^90 + 18 * q^91 - 24 * q^92 + 116 * q^93 + 12 * q^94 + 120 * q^95 - 4 * q^96 + 32 * q^97 + 123 * q^98 - 6 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(62))\)

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
62.2.a	\(\chi_{62}(1, \cdot)\)	62.2.a.a	1	1
		62.2.a.b	2
62.2.c	\(\chi_{62}(5, \cdot)\)	62.2.c.a	2	2
		62.2.c.b	2
62.2.d	\(\chi_{62}(33, \cdot)\)	62.2.d.a	8	4
		62.2.d.b	8
62.2.g	\(\chi_{62}(7, \cdot)\)	62.2.g.a	8	8
		62.2.g.b	8

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(62))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(62)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(31))\)\(^{\oplus 2}\)