Space of modular forms of level 192 and weight 8

• Label: 192.8
• Level: 192
• Weight: 8
• Dimension: 3002
• Nonzero newspaces: 8
• Sturm bound: 16384
• Trace bound: 11

Defining parameters

Level:	\( N \)	=	\( 192 = 2^{6} \cdot 3 \)
Weight:	\( k \)	=	\( 8 \)
Nonzero newspaces:			\( 8 \)
Sturm bound:			\(16384\)
Trace bound:			\(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_1(192))\).

	Total	New	Old
Modular forms	7312	3046	4266
Cusp forms	7024	3002	4022
Eisenstein series	288	44	244

Trace form

3002 * q - 6 * q^3 - 16 * q^4 - 8 * q^6 - 8 * q^7 - 10 * q^9 - 16 * q^10 + 2408 * q^11 - 8 * q^12 + 14112 * q^13 - 27008 * q^15 - 16 * q^16 + 11632 * q^17 - 8 * q^18 + 121156 * q^19 - 36188 * q^21 - 548928 * q^22 + 598032 * q^24 + 27238 * q^25 - 1455920 * q^26 - 238050 * q^27 - 781856 * q^28 + 206752 * q^29 + 1739912 * q^30 + 714952 * q^31 + 2142640 * q^32 + 391684 * q^33 - 806336 * q^34 - 816504 * q^35 - 4069528 * q^36 - 1662320 * q^37 - 2489840 * q^38 + 283940 * q^39 + 5372704 * q^40 + 3530272 * q^41 + 3858912 * q^42 - 366196 * q^43 - 6740944 * q^44 + 792956 * q^45 - 16 * q^46 - 8 * q^48 - 1647114 * q^49 + 4634832 * q^50 + 6361720 * q^51 - 20409904 * q^52 + 314920 * q^54 - 20955048 * q^55 + 21474544 * q^56 - 1725140 * q^57 + 20716256 * q^58 - 9179680 * q^59 - 4336424 * q^60 - 16 * q^61 - 20695008 * q^62 + 10001880 * q^63 - 45674320 * q^64 + 1520528 * q^65 - 7515240 * q^66 - 18891644 * q^67 + 17500128 * q^68 + 1882924 * q^69 + 71980592 * q^70 - 49394816 * q^71 - 8 * q^72 + 5672940 * q^73 - 8428784 * q^74 + 29037338 * q^75 - 77885840 * q^76 - 15375984 * q^77 + 9862288 * q^78 - 18412216 * q^79 + 63108912 * q^80 - 39201358 * q^81 - 16 * q^82 - 503480 * q^83 + 17056808 * q^84 + 21231872 * q^85 + 40789108 * q^87 - 16 * q^88 + 19124192 * q^89 + 31733992 * q^90 + 1768304 * q^91 - 42564464 * q^93 - 16 * q^94 - 64673232 * q^95 - 112868992 * q^96 - 22760636 * q^97 + 6456500 * q^99

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_1(192))\)

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
192.8.a	\(\chi_{192}(1, \cdot)\)	192.8.a.a	1	1
		192.8.a.b	1
		192.8.a.c	1
		192.8.a.d	1
		192.8.a.e	1
		192.8.a.f	1
		192.8.a.g	1
		192.8.a.h	1
		192.8.a.i	1
		192.8.a.j	1
		192.8.a.k	1
		192.8.a.l	1
		192.8.a.m	1
		192.8.a.n	1
		192.8.a.o	1
		192.8.a.p	1
		192.8.a.q	2
		192.8.a.r	2
		192.8.a.s	2
		192.8.a.t	2
		192.8.a.u	2
		192.8.a.v	2
192.8.c	\(\chi_{192}(191, \cdot)\)	192.8.c.a	2	1
		192.8.c.b	4
		192.8.c.c	4
		192.8.c.d	8
		192.8.c.e	8
		192.8.c.f	28
192.8.d	\(\chi_{192}(97, \cdot)\)	192.8.d.a	4	1
		192.8.d.b	4
		192.8.d.c	8
		192.8.d.d	12
192.8.f	\(\chi_{192}(95, \cdot)\)	192.8.f.a	4	1
		192.8.f.b	4
		192.8.f.c	16
		192.8.f.d	32
192.8.j	\(\chi_{192}(49, \cdot)\)	192.8.j.a	56	2
192.8.k	\(\chi_{192}(47, \cdot)\)	n/a	108	2
192.8.n	\(\chi_{192}(25, \cdot)\)	None	0	4
192.8.o	\(\chi_{192}(23, \cdot)\)	None	0	4
192.8.r	\(\chi_{192}(13, \cdot)\)	n/a	896	8
192.8.s	\(\chi_{192}(11, \cdot)\)	n/a	1776	8

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

Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_1(192))\) into lower level spaces

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