Space of modular forms of level 192 and weight 13

• Label: 192.13
• Level: 192
• Weight: 13
• Dimension: 5162
• Nonzero newspaces: 8
• Sturm bound: 26624
• Trace bound: 11

Defining parameters

Level:	\( N \)	=	\( 192 = 2^{6} \cdot 3 \)
Weight:	\( k \)	=	\( 13 \)
Nonzero newspaces:			\( 8 \)
Sturm bound:			\(26624\)
Trace bound:			\(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{13}(\Gamma_1(192))\).

	Total	New	Old
Modular forms	12432	5206	7226
Cusp forms	12144	5162	6982
Eisenstein series	288	44	244

Trace form

5162 * q - 6 * q^3 - 16 * q^4 - 8 * q^6 - 16 * q^7 - 10 * q^9 - 16 * q^10 + 5336640 * q^11 - 8 * q^12 - 5100496 * q^13 - 4 * q^15 - 16 * q^16 - 19356480 * q^17 - 8 * q^18 + 103737204 * q^19 - 147989924 * q^21 - 391368256 * q^22 + 596540160 * q^23 + 278046992 * q^24 - 1447860978 * q^25 + 743547600 * q^26 + 968990874 * q^27 + 2298581984 * q^28 - 2818281600 * q^29 - 9514391928 * q^30 + 8 * q^31 + 13313991600 * q^32 + 6308734556 * q^33 + 427985984 * q^34 - 6653503296 * q^35 - 28819027608 * q^36 - 1457193616 * q^37 + 38951312400 * q^38 - 8 * q^39 - 5524992736 * q^40 - 36885214080 * q^41 - 25227243808 * q^42 + 18414740148 * q^43 - 58675266000 * q^44 - 30265098156 * q^45 - 16 * q^46 - 8 * q^48 + 27682574374 * q^49 + 266640598224 * q^50 + 88473772792 * q^51 - 339158967856 * q^52 + 68186006056 * q^54 - 372459041296 * q^55 - 223779692304 * q^56 + 143075474068 * q^57 - 583435092256 * q^58 + 17625404160 * q^59 + 424044043480 * q^60 - 16 * q^61 + 479312048160 * q^62 - 55365148816 * q^63 - 1126998073168 * q^64 + 316857119040 * q^65 - 786524524648 * q^66 + 238070290548 * q^67 + 636059144160 * q^68 + 388390976788 * q^69 + 2654319560240 * q^70 - 1129511126016 * q^71 - 8 * q^72 + 100179256300 * q^73 - 2478938161392 * q^74 + 741656324310 * q^75 + 2644729785968 * q^76 + 1124627371200 * q^77 + 1241258184592 * q^78 + 3846893191672 * q^79 - 2758624068816 * q^80 - 2508055931150 * q^81 - 16 * q^82 - 686759112000 * q^83 + 5321045983784 * q^84 + 1540152266672 * q^85 - 8 * q^87 - 16 * q^88 - 810609022080 * q^89 - 488738250008 * q^90 - 2389778176912 * q^91 + 5237479280320 * q^93 - 16 * q^94 - 6255845408128 * q^96 - 3414636688332 * q^97 - 511511795332 * q^99

Decomposition of \(S_{13}^{\mathrm{new}}(\Gamma_1(192))\)

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
192.13.b	\(\chi_{192}(31, \cdot)\)	192.13.b.a	16	1
		192.13.b.b	16
		192.13.b.c	16
192.13.e	\(\chi_{192}(65, \cdot)\)	192.13.e.a	1	1
		192.13.e.b	1
		192.13.e.c	2
		192.13.e.d	2
		192.13.e.e	4
		192.13.e.f	4
		192.13.e.g	4
		192.13.e.h	4
		192.13.e.i	12
		192.13.e.j	12
		192.13.e.k	24
		192.13.e.l	24
192.13.g	\(\chi_{192}(127, \cdot)\)	192.13.g.a	4	1
		192.13.g.b	4
		192.13.g.c	4
		192.13.g.d	12
		192.13.g.e	12
		192.13.g.f	12
192.13.h	\(\chi_{192}(161, \cdot)\)	192.13.h.a	4	1
		192.13.h.b	4
		192.13.h.c	24
		192.13.h.d	64
192.13.i	\(\chi_{192}(17, \cdot)\)	n/a	188	2
192.13.l	\(\chi_{192}(79, \cdot)\)	192.13.l.a	96	2
192.13.m	\(\chi_{192}(7, \cdot)\)	None	0	4
192.13.p	\(\chi_{192}(41, \cdot)\)	None	0	4
192.13.q	\(\chi_{192}(5, \cdot)\)	n/a	3056	8
192.13.t	\(\chi_{192}(19, \cdot)\)	n/a	1536	8

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

Decomposition of \(S_{13}^{\mathrm{old}}(\Gamma_1(192))\) into lower level spaces

\( S_{13}^{\mathrm{old}}(\Gamma_1(192)) \cong \) \(S_{13}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 14}\)\(\oplus\)\(S_{13}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 12}\)\(\oplus\)\(S_{13}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 7}\)\(\oplus\)\(S_{13}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 10}\)\(\oplus\)\(S_{13}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 6}\)\(\oplus\)\(S_{13}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 8}\)\(\oplus\)\(S_{13}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 5}\)\(\oplus\)\(S_{13}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 6}\)\(\oplus\)\(S_{13}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 4}\)\(\oplus\)\(S_{13}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 4}\)\(\oplus\)\(S_{13}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 3}\)\(\oplus\)\(S_{13}^{\mathrm{new}}(\Gamma_1(64))\)\(^{\oplus 2}\)\(\oplus\)\(S_{13}^{\mathrm{new}}(\Gamma_1(96))\)\(^{\oplus 2}\)