Space of modular forms of level 77 and weight 2

• Label: 77.2
• Level: 77
• Weight: 2
• Dimension: 179
• Nonzero newspaces: 8
• Newform subspaces: 16
• Sturm bound: 960
• Trace bound: 3

Defining parameters

Level:	\( N \)	=	\( 77 = 7 \cdot 11 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 8 \)
Newform subspaces:			\( 16 \)
Sturm bound:			\(960\)
Trace bound:			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(77))\).

	Total	New	Old
Modular forms	300	271	29
Cusp forms	181	179	2
Eisenstein series	119	92	27

Trace form

179 * q - 23 * q^2 - 24 * q^3 - 27 * q^4 - 26 * q^5 - 22 * q^6 - 21 * q^7 - 45 * q^8 - 13 * q^9 - 8 * q^10 - 21 * q^11 - 28 * q^12 - 24 * q^13 - 13 * q^14 - 34 * q^15 + 9 * q^16 - 8 * q^17 + q^18 - 10 * q^19 + 8 * q^20 - 4 * q^21 - 23 * q^22 - 34 * q^23 + 30 * q^24 + 9 * q^25 + 28 * q^26 + 23 * q^28 - 30 * q^29 + 38 * q^30 - 12 * q^31 + 17 * q^32 + 16 * q^33 - 14 * q^34 + 14 * q^35 + 39 * q^36 + 2 * q^37 + 30 * q^38 + 34 * q^39 + 60 * q^40 + 28 * q^41 + 58 * q^42 - 4 * q^43 + 43 * q^44 + 22 * q^45 + 38 * q^46 + 2 * q^47 + 86 * q^48 + 29 * q^49 + 17 * q^50 + 38 * q^51 + 52 * q^52 + 36 * q^53 + 110 * q^54 + 34 * q^55 + 45 * q^56 + 20 * q^57 + 60 * q^58 + 20 * q^59 - 38 * q^60 - 22 * q^61 + 34 * q^62 - 33 * q^63 - 37 * q^64 - 44 * q^65 - 142 * q^66 - 38 * q^67 - 76 * q^68 - 86 * q^69 - 88 * q^70 - 102 * q^71 - 195 * q^72 - 54 * q^73 - 24 * q^74 - 154 * q^75 - 220 * q^76 - 41 * q^77 - 208 * q^78 - 20 * q^79 - 136 * q^80 - 151 * q^81 - 56 * q^82 - 24 * q^83 - 198 * q^84 - 68 * q^85 - 102 * q^86 - 60 * q^87 - 45 * q^88 - 60 * q^89 - 44 * q^90 - 14 * q^91 - 8 * q^92 + 22 * q^93 + 86 * q^94 + 60 * q^95 - 2 * q^96 + 82 * q^97 + 97 * q^98 + 87 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(77))\)

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
77.2.a	\(\chi_{77}(1, \cdot)\)	77.2.a.a	1	1
		77.2.a.b	1
		77.2.a.c	1
		77.2.a.d	2
77.2.b	\(\chi_{77}(76, \cdot)\)	77.2.b.a	2	1
		77.2.b.b	4
77.2.e	\(\chi_{77}(23, \cdot)\)	77.2.e.a	6	2
		77.2.e.b	6
77.2.f	\(\chi_{77}(15, \cdot)\)	77.2.f.a	8	4
		77.2.f.b	16
77.2.i	\(\chi_{77}(10, \cdot)\)	77.2.i.a	12	2
77.2.l	\(\chi_{77}(6, \cdot)\)	77.2.l.a	8	4
		77.2.l.b	16
77.2.m	\(\chi_{77}(4, \cdot)\)	77.2.m.a	8	8
		77.2.m.b	40
77.2.n	\(\chi_{77}(17, \cdot)\)	77.2.n.a	48	8

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(77))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(77)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 2}\)