Space of modular forms of level 76 and weight 3

• Label: 76.3
• Level: 76
• Weight: 3
• Dimension: 192
• Nonzero newspaces: 6
• Newform subspaces: 10
• Sturm bound: 1080
• Trace bound: 2

Defining parameters

Level:	\( N \)	=	\( 76 = 2^{2} \cdot 19 \)
Weight:	\( k \)	=	\( 3 \)
Nonzero newspaces:			\( 6 \)
Newform subspaces:			\( 10 \)
Sturm bound:			\(1080\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(76))\).

	Total	New	Old
Modular forms	405	224	181
Cusp forms	315	192	123
Eisenstein series	90	32	58

Trace form

192 * 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 + 42 * q^13 - 9 * q^14 + 54 * q^15 - 9 * q^16 - 9 * q^17 - 18 * q^18 - 21 * q^19 - 18 * q^20 - 81 * q^21 - 9 * q^22 - 45 * q^23 - 9 * q^24 - 144 * q^25 - 9 * q^26 - 198 * q^27 - 252 * q^28 - 162 * q^29 - 450 * q^30 - 108 * q^31 - 234 * q^32 - 234 * q^33 - 144 * q^34 - 72 * q^35 - 99 * q^36 - 36 * q^37 + 54 * q^38 + 108 * q^39 + 180 * q^40 + 54 * q^41 + 441 * q^42 + 255 * q^43 + 306 * q^44 + 711 * q^45 + 396 * q^46 + 423 * q^47 + 684 * q^48 + 345 * q^49 + 342 * q^50 + 351 * q^51 - 9 * q^52 + 90 * q^53 + 72 * q^54 + 36 * q^55 - 18 * q^56 - 63 * q^57 - 18 * q^58 - 135 * q^59 + 342 * q^60 - 786 * q^61 + 576 * q^62 - 540 * q^63 + 783 * q^64 - 963 * q^65 + 639 * q^66 - 519 * q^67 + 432 * q^68 - 1233 * q^69 + 531 * q^70 - 477 * q^71 + 396 * q^72 - 231 * q^73 + 27 * q^74 - 99 * q^76 + 369 * q^77 - 243 * q^78 + 438 * q^79 - 369 * q^80 + 936 * q^81 - 954 * q^82 + 441 * q^83 - 981 * q^84 + 1746 * q^85 - 702 * q^86 + 936 * q^87 - 945 * q^88 + 873 * q^89 - 1314 * q^90 + 492 * q^91 - 774 * q^92 + 810 * q^93 - 702 * q^94 - 675 * q^95 - 1242 * q^96 - 675 * q^97 - 1494 * q^98 - 1242 * q^99

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(76))\)

We only show spaces with odd 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
76.3.b	\(\chi_{76}(39, \cdot)\)	76.3.b.a	4	1
		76.3.b.b	14
76.3.c	\(\chi_{76}(37, \cdot)\)	76.3.c.a	2	1
		76.3.c.b	2
76.3.g	\(\chi_{76}(7, \cdot)\)	76.3.g.a	4	2
		76.3.g.b	4
		76.3.g.c	28
76.3.h	\(\chi_{76}(65, \cdot)\)	76.3.h.a	8	2
76.3.j	\(\chi_{76}(13, \cdot)\)	76.3.j.a	18	6
76.3.l	\(\chi_{76}(23, \cdot)\)	76.3.l.a	108	6

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(76))\) into lower level spaces

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