Space of modular forms of level 79 and weight 2

• Label: 79.2
• Level: 79
• Weight: 2
• Dimension: 222
• Nonzero newspaces: 4
• Newform subspaces: 5
• Sturm bound: 1040
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 79 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 4 \)
Newform subspaces:			\( 5 \)
Sturm bound:			\(1040\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(79))\).

	Total	New	Old
Modular forms	299	299	0
Cusp forms	222	222	0
Eisenstein series	77	77	0

Trace form

222 * q - 36 * q^2 - 35 * q^3 - 32 * q^4 - 33 * q^5 - 27 * q^6 - 31 * q^7 - 24 * q^8 - 26 * q^9 - 21 * q^10 - 27 * q^11 - 11 * q^12 - 25 * q^13 - 15 * q^14 - 15 * q^15 - 8 * q^16 - 21 * q^17 - 19 * q^19 + 3 * q^20 - 7 * q^21 - 3 * q^22 - 15 * q^23 + 21 * q^24 - 8 * q^25 + 3 * q^26 + q^27 + 17 * q^28 - 9 * q^29 + 33 * q^30 - 7 * q^31 + 24 * q^32 + 9 * q^33 + 15 * q^34 + 9 * q^35 + 52 * q^36 - q^37 + 21 * q^38 + 17 * q^39 + 51 * q^40 + 3 * q^41 + 57 * q^42 + 5 * q^43 + 45 * q^44 + 39 * q^45 + 33 * q^46 + 9 * q^47 + 85 * q^48 + 18 * q^49 + 54 * q^50 + 33 * q^51 + 59 * q^52 + 15 * q^53 + 81 * q^54 + 33 * q^55 + 81 * q^56 + 41 * q^57 + 51 * q^58 + 21 * q^59 + 129 * q^60 + 23 * q^61 + 57 * q^62 + 13 * q^63 - 68 * q^64 - 33 * q^65 - 51 * q^66 - 62 * q^67 - 69 * q^68 - 99 * q^69 - 207 * q^70 - 45 * q^71 - 234 * q^72 - 43 * q^73 - 81 * q^74 - 71 * q^75 - 263 * q^76 - 60 * q^77 - 66 * q^78 - 194 * q^79 - 282 * q^80 - 152 * q^81 - 69 * q^82 - 72 * q^83 - 179 * q^84 - 87 * q^85 - 63 * q^86 + 3 * q^87 - 249 * q^88 - 27 * q^89 - 117 * q^90 - 83 * q^91 - 27 * q^92 - 2 * q^93 - 51 * q^94 + 3 * q^95 + 57 * q^96 + 7 * q^97 + 132 * q^98 + 117 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(79))\)

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
79.2.a	\(\chi_{79}(1, \cdot)\)	79.2.a.a	1	1
		79.2.a.b	5
79.2.c	\(\chi_{79}(23, \cdot)\)	79.2.c.a	12	2
79.2.e	\(\chi_{79}(8, \cdot)\)	79.2.e.a	60	12
79.2.g	\(\chi_{79}(2, \cdot)\)	79.2.g.a	144	24