Space of modular forms of level 768 and weight 3

• Label: 768.3
• Level: 768
• Weight: 3
• Dimension: 13720
• Nonzero newspaces: 12
• Sturm bound: 98304
• Trace bound: 49

Defining parameters

Level:	\( N \)	=	\( 768 = 2^{8} \cdot 3 \)
Weight:	\( k \)	=	\( 3 \)
Nonzero newspaces:			\( 12 \)
Sturm bound:			\(98304\)
Trace bound:			\(49\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(768))\).

	Total	New	Old
Modular forms	33472	13928	19544
Cusp forms	32064	13720	18344
Eisenstein series	1408	208	1200

Trace form

13720 * q - 24 * q^3 - 64 * q^4 - 32 * q^6 - 48 * q^7 - 40 * q^9 - 64 * q^10 - 32 * q^12 - 64 * q^13 - 24 * q^15 - 64 * q^16 - 32 * q^18 - 48 * q^19 - 32 * q^21 - 64 * q^22 - 32 * q^24 - 80 * q^25 - 24 * q^27 - 64 * q^28 - 32 * q^30 - 64 * q^31 - 56 * q^33 - 64 * q^34 - 32 * q^36 - 64 * q^37 - 24 * q^39 - 64 * q^40 - 32 * q^42 - 48 * q^43 - 32 * q^45 - 64 * q^46 - 32 * q^48 - 488 * q^49 - 408 * q^51 - 64 * q^52 - 640 * q^53 - 32 * q^54 - 1072 * q^55 - 424 * q^57 - 64 * q^58 - 512 * q^59 - 32 * q^60 - 320 * q^61 - 16 * q^63 - 64 * q^64 + 256 * q^65 - 32 * q^66 + 592 * q^67 + 352 * q^69 - 64 * q^70 + 1024 * q^71 - 32 * q^72 + 1200 * q^73 + 744 * q^75 - 64 * q^76 + 896 * q^77 - 32 * q^78 + 976 * q^79 - 48 * q^81 - 64 * q^82 - 32 * q^84 + 336 * q^85 - 24 * q^87 - 64 * q^88 - 32 * q^90 - 48 * q^91 + 112 * q^93 - 64 * q^94 - 32 * q^96 - 112 * q^97 - 24 * q^99

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(768))\)

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
768.3.b	\(\chi_{768}(127, \cdot)\)	768.3.b.a	4	1
		768.3.b.b	4
		768.3.b.c	4
		768.3.b.d	4
		768.3.b.e	8
		768.3.b.f	8
768.3.e	\(\chi_{768}(257, \cdot)\)	768.3.e.a	2	1
		768.3.e.b	2
		768.3.e.c	2
		768.3.e.d	2
		768.3.e.e	2
		768.3.e.f	2
		768.3.e.g	4
		768.3.e.h	4
		768.3.e.i	4
		768.3.e.j	4
		768.3.e.k	4
		768.3.e.l	4
		768.3.e.m	4
		768.3.e.n	4
		768.3.e.o	8
		768.3.e.p	8
768.3.g	\(\chi_{768}(511, \cdot)\)	768.3.g.a	2	1
		768.3.g.b	2
		768.3.g.c	4
		768.3.g.d	4
		768.3.g.e	4
		768.3.g.f	4
		768.3.g.g	4
		768.3.g.h	8
768.3.h	\(\chi_{768}(641, \cdot)\)	768.3.h.a	2	1
		768.3.h.b	2
		768.3.h.c	4
		768.3.h.d	4
		768.3.h.e	8
		768.3.h.f	8
		768.3.h.g	16
		768.3.h.h	16
768.3.i	\(\chi_{768}(65, \cdot)\)	n/a	128	2
768.3.l	\(\chi_{768}(319, \cdot)\)	768.3.l.a	8	2
		768.3.l.b	8
		768.3.l.c	8
		768.3.l.d	8
		768.3.l.e	16
		768.3.l.f	16
768.3.m	\(\chi_{768}(31, \cdot)\)	n/a	128	4
768.3.p	\(\chi_{768}(161, \cdot)\)	n/a	240	4
768.3.q	\(\chi_{768}(17, \cdot)\)	n/a	496	8
768.3.t	\(\chi_{768}(79, \cdot)\)	n/a	256	8
768.3.u	\(\chi_{768}(7, \cdot)\)	None	0	16
768.3.x	\(\chi_{768}(41, \cdot)\)	None	0	16
768.3.y	\(\chi_{768}(5, \cdot)\)	n/a	8128	32
768.3.bb	\(\chi_{768}(19, \cdot)\)	n/a	4096	32

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(768))\) into lower level spaces

\( S_{3}^{\mathrm{old}}(\Gamma_1(768)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 18}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 16}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 9}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 14}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 7}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 10}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 5}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(64))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(96))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(128))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(192))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(256))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(384))\)\(^{\oplus 2}\)