Space of modular forms of level 192 and weight 7

• Label: 192.7
• Level: 192
• Weight: 7
• Dimension: 2570
• Nonzero newspaces: 8
• Sturm bound: 14336
• Trace bound: 11

Defining parameters

Level:	\( N \)	=	\( 192 = 2^{6} \cdot 3 \)
Weight:	\( k \)	=	\( 7 \)
Nonzero newspaces:			\( 8 \)
Sturm bound:			\(14336\)
Trace bound:			\(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(\Gamma_1(192))\).

	Total	New	Old
Modular forms	6288	2614	3674
Cusp forms	6000	2570	3430
Eisenstein series	288	44	244

Trace form

2570 * q - 6 * q^3 - 16 * q^4 - 8 * q^6 - 16 * q^7 - 10 * q^9 - 16 * q^10 + 2720 * q^11 - 8 * q^12 - 10096 * q^13 - 4 * q^15 - 16 * q^16 + 19552 * q^17 - 8 * q^18 + 7860 * q^19 - 16532 * q^21 + 127424 * q^22 - 26240 * q^23 - 161008 * q^24 - 51138 * q^25 + 21200 * q^26 + 34314 * q^27 + 341984 * q^28 + 132800 * q^29 + 206472 * q^30 + 8 * q^31 - 235600 * q^32 - 174868 * q^33 - 558016 * q^34 - 162336 * q^35 - 365208 * q^36 - 14416 * q^37 + 400400 * q^38 - 8 * q^39 + 1151264 * q^40 + 434240 * q^41 + 173792 * q^42 - 145452 * q^43 - 962000 * q^44 + 195300 * q^45 - 16 * q^46 - 8 * q^48 + 235270 * q^49 - 1410864 * q^50 - 786824 * q^51 + 2550224 * q^52 + 314920 * q^54 - 1163536 * q^55 - 653072 * q^56 + 759172 * q^57 - 3540256 * q^58 + 4430720 * q^59 - 2511656 * q^60 - 16 * q^61 - 1083360 * q^62 - 470608 * q^63 + 2310320 * q^64 - 775008 * q^65 + 3102104 * q^66 - 6283980 * q^67 + 3694560 * q^68 + 793156 * q^69 + 4544048 * q^70 - 1602048 * q^71 - 8 * q^72 - 271892 * q^73 - 5848304 * q^74 + 3951654 * q^75 - 9130384 * q^76 - 1590816 * q^77 - 5687408 * q^78 - 4304648 * q^79 + 8356656 * q^80 + 3599218 * q^81 - 16 * q^82 + 2497760 * q^83 + 5971496 * q^84 + 3090512 * q^85 - 8 * q^87 - 16 * q^88 - 587840 * q^89 - 11466008 * q^90 - 3096016 * q^91 - 6713120 * q^93 - 16 * q^94 + 3708032 * q^96 + 6370836 * q^97 + 4709180 * q^99

Decomposition of \(S_{7}^{\mathrm{new}}(\Gamma_1(192))\)

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
192.7.b	\(\chi_{192}(31, \cdot)\)	192.7.b.a	8	1
		192.7.b.b	8
		192.7.b.c	8
192.7.e	\(\chi_{192}(65, \cdot)\)	192.7.e.a	1	1
		192.7.e.b	1
		192.7.e.c	2
		192.7.e.d	2
		192.7.e.e	2
		192.7.e.f	2
		192.7.e.g	6
		192.7.e.h	6
		192.7.e.i	12
		192.7.e.j	12
192.7.g	\(\chi_{192}(127, \cdot)\)	192.7.g.a	2	1
		192.7.g.b	2
		192.7.g.c	2
		192.7.g.d	4
		192.7.g.e	6
		192.7.g.f	8
192.7.h	\(\chi_{192}(161, \cdot)\)	192.7.h.a	4	1
		192.7.h.b	4
		192.7.h.c	8
		192.7.h.d	32
192.7.i	\(\chi_{192}(17, \cdot)\)	192.7.i.a	92	2
192.7.l	\(\chi_{192}(79, \cdot)\)	192.7.l.a	48	2
192.7.m	\(\chi_{192}(7, \cdot)\)	None	0	4
192.7.p	\(\chi_{192}(41, \cdot)\)	None	0	4
192.7.q	\(\chi_{192}(5, \cdot)\)	n/a	1520	8
192.7.t	\(\chi_{192}(19, \cdot)\)	n/a	768	8

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

Decomposition of \(S_{7}^{\mathrm{old}}(\Gamma_1(192))\) into lower level spaces

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