Space of modular forms of level 192 and weight 9

• Label: 192.9
• Level: 192
• Weight: 9
• Dimension: 3434
• Nonzero newspaces: 8
• Sturm bound: 18432
• Trace bound: 11

Defining parameters

Level:	\( N \)	=	\( 192 = 2^{6} \cdot 3 \)
Weight:	\( k \)	=	\( 9 \)
Nonzero newspaces:			\( 8 \)
Sturm bound:			\(18432\)
Trace bound:			\(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(\Gamma_1(192))\).

	Total	New	Old
Modular forms	8336	3478	4858
Cusp forms	8048	3434	4614
Eisenstein series	288	44	244

Trace form

3434 * q - 6 * q^3 - 16 * q^4 - 8 * q^6 - 16 * q^7 - 10 * q^9 - 16 * q^10 - 39552 * q^11 - 8 * q^12 + 102768 * q^13 - 4 * q^15 - 16 * q^16 - 309120 * q^17 - 8 * q^18 + 335092 * q^19 + 269884 * q^21 + 2136512 * q^22 - 1691136 * q^23 - 322288 * q^24 + 3614382 * q^25 + 6728400 * q^26 + 25530 * q^27 - 7230496 * q^28 - 4264704 * q^29 - 7934328 * q^30 + 8 * q^31 + 9681840 * q^32 + 6623804 * q^33 + 16553024 * q^34 + 2415744 * q^35 - 7200408 * q^36 - 9441040 * q^37 - 32644080 * q^38 - 8 * q^39 + 2303264 * q^40 + 17498880 * q^41 + 35148512 * q^42 + 1859700 * q^43 - 45304272 * q^44 - 15374796 * q^45 - 16 * q^46 - 8 * q^48 + 11529574 * q^49 + 10290384 * q^50 - 54228488 * q^51 + 91896272 * q^52 - 19840472 * q^54 + 231633904 * q^55 - 113749776 * q^56 - 11029580 * q^57 + 101752544 * q^58 - 224693760 * q^59 + 163708120 * q^60 - 16 * q^61 + 87863328 * q^62 - 23059216 * q^63 - 193535824 * q^64 + 120408960 * q^65 - 227317864 * q^66 + 492471028 * q^67 - 163729440 * q^68 - 73697612 * q^69 + 185779760 * q^70 - 478992384 * q^71 - 8 * q^72 - 95283220 * q^73 + 340057872 * q^74 + 35256630 * q^75 - 318607760 * q^76 + 153244800 * q^77 - 667571312 * q^78 + 361016312 * q^79 + 404319024 * q^80 + 62519794 * q^81 - 16 * q^82 - 209328000 * q^83 - 689231320 * q^84 - 135303568 * q^85 - 8 * q^87 - 16 * q^88 + 243559680 * q^89 + 873269992 * q^90 + 197542640 * q^91 + 184082560 * q^93 - 16 * q^94 - 468840832 * q^96 - 54952588 * q^97 - 315415300 * q^99

Decomposition of \(S_{9}^{\mathrm{new}}(\Gamma_1(192))\)

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
192.9.b	\(\chi_{192}(31, \cdot)\)	192.9.b.a	8	1
		192.9.b.b	12
		192.9.b.c	12
192.9.e	\(\chi_{192}(65, \cdot)\)	192.9.e.a	1	1
		192.9.e.b	1
		192.9.e.c	2
		192.9.e.d	2
		192.9.e.e	2
		192.9.e.f	2
		192.9.e.g	2
		192.9.e.h	2
		192.9.e.i	8
		192.9.e.j	8
		192.9.e.k	16
		192.9.e.l	16
192.9.g	\(\chi_{192}(127, \cdot)\)	192.9.g.a	2	1
		192.9.g.b	2
		192.9.g.c	4
		192.9.g.d	8
		192.9.g.e	8
		192.9.g.f	8
192.9.h	\(\chi_{192}(161, \cdot)\)	192.9.h.a	4	1
		192.9.h.b	4
		192.9.h.c	16
		192.9.h.d	40
192.9.i	\(\chi_{192}(17, \cdot)\)	n/a	124	2
192.9.l	\(\chi_{192}(79, \cdot)\)	192.9.l.a	64	2
192.9.m	\(\chi_{192}(7, \cdot)\)	None	0	4
192.9.p	\(\chi_{192}(41, \cdot)\)	None	0	4
192.9.q	\(\chi_{192}(5, \cdot)\)	n/a	2032	8
192.9.t	\(\chi_{192}(19, \cdot)\)	n/a	1024	8

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

Decomposition of \(S_{9}^{\mathrm{old}}(\Gamma_1(192))\) into lower level spaces

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