Space of modular forms of level 384 and weight 8

• Label: 384.8
• Level: 384
• Weight: 8
• Dimension: 12048
• Nonzero newspaces: 10
• Sturm bound: 65536
• Trace bound: 25

Defining parameters

Level:	\( N \)	=	\( 384 = 2^{7} \cdot 3 \)
Weight:	\( k \)	=	\( 8 \)
Nonzero newspaces:			\( 10 \)
Sturm bound:			\(65536\)
Trace bound:			\(25\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_1(384))\).

	Total	New	Old
Modular forms	28992	12144	16848
Cusp forms	28352	12048	16304
Eisenstein series	640	96	544

Trace form

12048 * q - 12 * q^3 - 32 * q^4 - 16 * q^6 - 24 * q^7 - 20 * q^9 - 32 * q^10 - 16 * q^12 - 32 * q^13 - 8 * q^15 - 32 * q^16 - 16 * q^18 - 24 * q^19 + 8732 * q^21 - 32 * q^22 - 286832 * q^23 - 16 * q^24 + 128952 * q^25 + 476076 * q^27 - 32 * q^28 - 206752 * q^29 - 16 * q^30 - 1430000 * q^31 - 396096 * q^33 - 32 * q^34 + 1633008 * q^35 - 16 * q^36 + 1662272 * q^37 - 283956 * q^39 - 32 * q^40 - 3530272 * q^41 - 16 * q^42 + 732344 * q^43 + 312484 * q^45 - 32 * q^46 - 16 * q^48 - 6588392 * q^49 - 9269664 * q^50 + 3002064 * q^51 + 40819744 * q^52 + 7262528 * q^53 - 629872 * q^54 - 8382040 * q^55 - 42949088 * q^56 - 12408788 * q^57 - 41432576 * q^58 - 3671872 * q^59 + 8672816 * q^60 + 18239072 * q^61 + 41390016 * q^62 + 4000720 * q^63 + 91348576 * q^64 + 22830208 * q^65 + 15028400 * q^66 - 3881384 * q^67 - 35000256 * q^68 - 19170556 * q^69 - 143961248 * q^70 - 24697408 * q^71 - 16 * q^72 - 20273064 * q^73 + 16857568 * q^74 + 10948000 * q^75 + 155771616 * q^76 + 47657792 * q^77 + 58970576 * q^78 + 523728 * q^79 - 126217824 * q^80 + 27028744 * q^81 - 32 * q^82 - 16 * q^84 - 1250032 * q^85 - 40789124 * q^87 - 32 * q^88 - 16 * q^90 - 24 * q^91 + 28999520 * q^93 - 32 * q^94 - 16 * q^96 - 64 * q^97 + 9729716 * q^99

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_1(384))\)

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
384.8.a	\(\chi_{384}(1, \cdot)\)	384.8.a.a	1	1
		384.8.a.b	1
		384.8.a.c	1
		384.8.a.d	1
		384.8.a.e	2
		384.8.a.f	2
		384.8.a.g	2
		384.8.a.h	2
		384.8.a.i	3
		384.8.a.j	3
		384.8.a.k	3
		384.8.a.l	3
		384.8.a.m	4
		384.8.a.n	4
		384.8.a.o	4
		384.8.a.p	4
		384.8.a.q	4
		384.8.a.r	4
		384.8.a.s	4
		384.8.a.t	4
384.8.c	\(\chi_{384}(383, \cdot)\)	n/a	112	1
384.8.d	\(\chi_{384}(193, \cdot)\)	384.8.d.a	6	1
		384.8.d.b	6
		384.8.d.c	8
		384.8.d.d	8
		384.8.d.e	12
		384.8.d.f	16
384.8.f	\(\chi_{384}(191, \cdot)\)	n/a	112	1
384.8.j	\(\chi_{384}(97, \cdot)\)	n/a	112	2
384.8.k	\(\chi_{384}(95, \cdot)\)	n/a	216	2
384.8.n	\(\chi_{384}(49, \cdot)\)	n/a	224	4
384.8.o	\(\chi_{384}(47, \cdot)\)	n/a	440	4
384.8.r	\(\chi_{384}(25, \cdot)\)	None	0	8
384.8.s	\(\chi_{384}(23, \cdot)\)	None	0	8
384.8.v	\(\chi_{384}(13, \cdot)\)	n/a	3584	16
384.8.w	\(\chi_{384}(11, \cdot)\)	n/a	7136	16

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

Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_1(384))\) into lower level spaces

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