Space of modular forms of level 82 and weight 2

• Label: 82.2
• Level: 82
• Weight: 2
• Dimension: 69
• Nonzero newspaces: 6
• Newform subspaces: 14
• Sturm bound: 840
• Trace bound: 2

Defining parameters

Level:	\( N \)	=	\( 82 = 2 \cdot 41 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 6 \)
Newform subspaces:			\( 14 \)
Sturm bound:			\(840\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(82))\).

	Total	New	Old
Modular forms	250	69	181
Cusp forms	171	69	102
Eisenstein series	79	0	79

Trace form

69 * 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 - 32 * q^21 - 12 * q^22 - 24 * q^23 - 4 * q^24 - 31 * q^25 - 14 * q^26 - 40 * q^27 - 8 * q^28 - 30 * q^29 + 16 * q^30 + 8 * q^31 + 9 * q^32 + 72 * q^33 + 32 * q^34 + 32 * q^35 + 7 * q^36 + 82 * q^37 + 20 * q^38 + 104 * q^39 + 34 * q^40 - q^41 + 128 * q^42 - 4 * q^43 + 28 * q^44 + 82 * q^45 + 16 * q^46 + 72 * q^47 + 16 * q^48 + 23 * q^49 + 19 * q^50 + 48 * q^51 - 4 * q^52 - 14 * q^53 - 72 * q^55 - 8 * q^56 - 80 * q^57 - 30 * q^58 - 60 * q^59 - 24 * q^60 - 62 * q^61 - 32 * q^62 - 104 * q^63 - q^64 - 74 * q^65 - 48 * q^66 - 8 * q^67 - 18 * q^68 - 16 * q^69 - 48 * q^70 + 8 * q^71 - 13 * q^72 + 6 * q^73 - 38 * q^74 + 36 * q^75 - 20 * q^76 - 16 * q^77 - 56 * q^78 - 6 * q^80 + 49 * q^81 - 41 * q^82 - 4 * q^83 - 32 * q^84 + 62 * q^85 - 44 * q^86 - 40 * q^87 - 12 * q^88 - 10 * q^89 - 78 * q^90 + 48 * q^91 - 24 * q^92 - 48 * q^93 - 48 * q^94 - 40 * q^95 - 4 * q^96 - 18 * q^97 - 57 * q^98 - 96 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(82))\)

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
82.2.a	\(\chi_{82}(1, \cdot)\)	82.2.a.a	1	1
		82.2.a.b	2
82.2.b	\(\chi_{82}(81, \cdot)\)	82.2.b.a	2	1
		82.2.b.b	2
82.2.c	\(\chi_{82}(9, \cdot)\)	82.2.c.a	2	2
		82.2.c.b	2
		82.2.c.c	2
82.2.d	\(\chi_{82}(37, \cdot)\)	82.2.d.a	4	4
		82.2.d.b	4
		82.2.d.c	8
82.2.f	\(\chi_{82}(23, \cdot)\)	82.2.f.a	8	4
		82.2.f.b	8
82.2.g	\(\chi_{82}(5, \cdot)\)	82.2.g.a	8	8
		82.2.g.b	16

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(82))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(82)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(41))\)\(^{\oplus 2}\)