Space of modular forms of level 77 and weight 4

• Label: 77.4
• Level: 77
• Weight: 4
• Dimension: 634
• Nonzero newspaces: 8
• Newform subspaces: 17
• Sturm bound: 1920
• Trace bound: 2

Defining parameters

Level:	\( N \)	=	\( 77 = 7 \cdot 11 \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 8 \)
Newform subspaces:			\( 17 \)
Sturm bound:			\(1920\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(77))\).

	Total	New	Old
Modular forms	780	726	54
Cusp forms	660	634	26
Eisenstein series	120	92	28

Trace form

634 * q - 14 * q^2 - 2 * q^3 - 14 * q^4 - 38 * q^5 + 20 * q^6 - 57 * q^7 - 64 * q^8 - 90 * q^9 - 150 * q^10 - 117 * q^11 - 444 * q^12 - 60 * q^13 + 128 * q^14 + 438 * q^15 + 626 * q^16 + 130 * q^17 + 32 * q^18 - 152 * q^19 - 554 * q^20 + 22 * q^21 - 1298 * q^22 - 254 * q^23 + 84 * q^24 - 314 * q^25 + 330 * q^26 + 130 * q^27 - 238 * q^28 + 38 * q^29 + 862 * q^30 + 1030 * q^31 + 172 * q^32 + 339 * q^33 + 916 * q^34 + 31 * q^35 - 110 * q^36 + 630 * q^37 - 814 * q^38 - 1644 * q^39 - 926 * q^40 - 2804 * q^41 - 816 * q^42 + 1600 * q^43 + 2174 * q^44 - 776 * q^45 - 2350 * q^46 - 798 * q^47 - 2258 * q^48 - 1309 * q^49 + 640 * q^50 + 712 * q^51 + 2774 * q^52 + 4870 * q^53 + 6450 * q^54 + 3378 * q^55 + 2934 * q^56 + 948 * q^57 - 2418 * q^58 - 4480 * q^59 - 10750 * q^60 - 5430 * q^61 - 14402 * q^62 - 10380 * q^63 - 12508 * q^64 - 7982 * q^65 - 10844 * q^66 - 2238 * q^67 - 1086 * q^68 + 5774 * q^69 + 6706 * q^70 + 7794 * q^71 + 19414 * q^72 + 10018 * q^73 + 11694 * q^74 + 18550 * q^75 + 21604 * q^76 + 8814 * q^77 + 21872 * q^78 + 6274 * q^79 + 24554 * q^80 + 13530 * q^81 + 13224 * q^82 + 226 * q^83 + 8578 * q^84 - 6390 * q^85 - 4600 * q^86 - 11778 * q^87 - 19220 * q^88 - 10858 * q^89 - 27138 * q^90 - 12329 * q^91 - 16632 * q^92 - 10134 * q^93 - 10502 * q^94 - 7074 * q^95 - 14394 * q^96 + 1210 * q^97 - 528 * q^98 - 3254 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(77))\)

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
77.4.a	\(\chi_{77}(1, \cdot)\)	77.4.a.a	1	1
		77.4.a.b	2
		77.4.a.c	4
		77.4.a.d	4
		77.4.a.e	5
77.4.b	\(\chi_{77}(76, \cdot)\)	77.4.b.a	2	1
		77.4.b.b	20
77.4.e	\(\chi_{77}(23, \cdot)\)	77.4.e.a	2	2
		77.4.e.b	18
		77.4.e.c	20
77.4.f	\(\chi_{77}(15, \cdot)\)	77.4.f.a	32	4
		77.4.f.b	40
77.4.i	\(\chi_{77}(10, \cdot)\)	77.4.i.a	44	2
77.4.l	\(\chi_{77}(6, \cdot)\)	77.4.l.a	8	4
		77.4.l.b	80
77.4.m	\(\chi_{77}(4, \cdot)\)	77.4.m.a	176	8
77.4.n	\(\chi_{77}(17, \cdot)\)	77.4.n.a	176	8

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(77))\) into lower level spaces

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