Space of modular forms of level 76 and weight 4

• Label: 76.4
• Level: 76
• Weight: 4
• Dimension: 297
• Nonzero newspaces: 6
• Newform subspaces: 7
• Sturm bound: 1440
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 76 = 2^{2} \cdot 19 \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 6 \)
Newform subspaces:			\( 7 \)
Sturm bound:			\(1440\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(76))\).

	Total	New	Old
Modular forms	585	333	252
Cusp forms	495	297	198
Eisenstein series	90	36	54

Trace form

297 * q - 9 * q^2 - 9 * q^4 - 18 * q^5 - 9 * q^6 - 9 * q^8 - 18 * q^9 - 9 * q^10 - 9 * q^12 - 162 * q^13 - 9 * q^14 + 108 * q^15 - 9 * q^16 + 126 * q^17 + 378 * q^19 - 18 * q^20 + 234 * q^21 - 9 * q^22 - 18 * q^23 - 9 * q^24 - 450 * q^25 - 9 * q^26 + 9 * q^27 + 1422 * q^28 + 612 * q^29 + 1188 * q^30 + 90 * q^31 - 324 * q^32 - 936 * q^33 - 1134 * q^34 - 1116 * q^35 - 3159 * q^36 - 666 * q^37 - 2340 * q^38 - 1890 * q^39 - 1962 * q^40 - 468 * q^41 - 1539 * q^42 - 630 * q^43 + 216 * q^44 - 1044 * q^45 + 1566 * q^46 + 36 * q^47 + 4590 * q^48 + 1692 * q^49 + 3204 * q^50 + 2475 * q^51 - 9 * q^52 + 1566 * q^53 - 252 * q^54 + 1944 * q^55 + 2502 * q^57 - 18 * q^58 + 2250 * q^59 - 2736 * q^60 + 6948 * q^61 - 4824 * q^62 + 2448 * q^63 - 4113 * q^64 + 1152 * q^65 - 1089 * q^66 - 1242 * q^67 + 1188 * q^68 - 7470 * q^69 + 4851 * q^70 - 5148 * q^71 + 8496 * q^72 - 6255 * q^73 + 5319 * q^74 - 3150 * q^75 + 6741 * q^76 - 11142 * q^77 + 6273 * q^78 - 5274 * q^79 + 3951 * q^80 - 6831 * q^81 + 4446 * q^82 - 1368 * q^83 + 315 * q^84 + 2286 * q^85 - 2214 * q^86 + 4788 * q^87 - 5841 * q^88 + 7488 * q^89 - 8604 * q^90 + 6912 * q^91 - 8874 * q^92 + 16308 * q^93 + 10782 * q^95 + 13878 * q^96 + 8082 * q^97 + 12564 * q^98 + 11439 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(76))\)

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
76.4.a	\(\chi_{76}(1, \cdot)\)	76.4.a.a	2	1
		76.4.a.b	3
76.4.d	\(\chi_{76}(75, \cdot)\)	76.4.d.a	28	1
76.4.e	\(\chi_{76}(45, \cdot)\)	76.4.e.a	10	2
76.4.f	\(\chi_{76}(27, \cdot)\)	76.4.f.a	56	2
76.4.i	\(\chi_{76}(5, \cdot)\)	76.4.i.a	30	6
76.4.k	\(\chi_{76}(3, \cdot)\)	76.4.k.a	168	6

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(76))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(76)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 2}\)