Space of modular forms of level 192 and weight 14

• Label: 192.14
• Level: 192
• Weight: 14
• Dimension: 5594
• Nonzero newspaces: 8
• Sturm bound: 28672
• Trace bound: 11

Defining parameters

Level:	\( N \)	=	\( 192 = 2^{6} \cdot 3 \)
Weight:	\( k \)	=	\( 14 \)
Nonzero newspaces:			\( 8 \)
Sturm bound:			\(28672\)
Trace bound:			\(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{14}(\Gamma_1(192))\).

	Total	New	Old
Modular forms	13456	5638	7818
Cusp forms	13168	5594	7574
Eisenstein series	288	44	244

Trace form

5594 * q - 6 * q^3 - 16 * q^4 - 8 * q^6 - 8 * q^7 - 10 * q^9 - 16 * q^10 - 9447992 * q^11 - 8 * q^12 - 70080192 * q^13 + 91124992 * q^15 - 16 * q^16 - 397716784 * q^17 - 8 * q^18 + 844017796 * q^19 - 904336172 * q^21 + 3499787200 * q^22 + 6611303952 * q^24 + 7221820278 * q^25 - 26350220080 * q^26 - 2071888434 * q^27 + 33296477664 * q^28 + 14646655328 * q^29 - 21853773688 * q^30 - 21300088376 * q^31 - 35183383120 * q^32 + 27154992820 * q^33 + 124202800704 * q^34 + 10653142056 * q^35 - 146995444888 * q^36 - 86111945904 * q^37 - 1339214320 * q^38 + 101809618532 * q^39 + 301896316704 * q^40 - 147865028512 * q^41 - 340564827168 * q^42 + 96934925356 * q^43 - 295049375696 * q^44 + 68820219308 * q^45 - 16 * q^46 - 8 * q^48 - 193778020842 * q^49 - 1625941534512 * q^50 - 881385173192 * q^51 + 816352887248 * q^52 - 328532574680 * q^54 - 2279099174568 * q^55 + 3904213124336 * q^56 + 394697418748 * q^57 - 2067829384480 * q^58 + 6712368615520 * q^59 - 3746854550312 * q^60 - 16 * q^61 + 3703290468384 * q^62 - 2500940088360 * q^63 + 9086105678000 * q^64 + 1203600407344 * q^65 - 6029904996456 * q^66 + 17672131781572 * q^67 - 6478438795296 * q^68 - 1675648898372 * q^69 + 19457352570416 * q^70 - 18428583520384 * q^71 - 8 * q^72 + 1358739892204 * q^73 - 21963860860144 * q^74 + 11995207385066 * q^75 - 2104949420432 * q^76 + 865777644528 * q^77 + 8286563263120 * q^78 + 28000369386184 * q^79 - 33415858049232 * q^80 + 9107190215474 * q^81 - 16 * q^82 - 12939183108760 * q^83 - 24146511337432 * q^84 - 7522350292768 * q^85 + 23308444951732 * q^87 - 16 * q^88 + 10468132737952 * q^89 - 75174842250008 * q^90 - 19140993196368 * q^91 - 17084472099344 * q^93 - 16 * q^94 + 61690125665328 * q^95 + 83966542114688 * q^96 - 49511813068188 * q^97 - 26770090512844 * q^99

Decomposition of \(S_{14}^{\mathrm{new}}(\Gamma_1(192))\)

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
192.14.a	\(\chi_{192}(1, \cdot)\)	192.14.a.a	1	1
		192.14.a.b	1
		192.14.a.c	1
		192.14.a.d	1
		192.14.a.e	1
		192.14.a.f	1
		192.14.a.g	1
		192.14.a.h	1
		192.14.a.i	1
		192.14.a.j	1
		192.14.a.k	2
		192.14.a.l	2
		192.14.a.m	2
		192.14.a.n	2
		192.14.a.o	2
		192.14.a.p	2
		192.14.a.q	2
		192.14.a.r	2
		192.14.a.s	3
		192.14.a.t	3
		192.14.a.u	3
		192.14.a.v	3
		192.14.a.w	3
		192.14.a.x	3
		192.14.a.y	4
		192.14.a.z	4
192.14.c	\(\chi_{192}(191, \cdot)\)	n/a	102	1
192.14.d	\(\chi_{192}(97, \cdot)\)	192.14.d.a	8	1
		192.14.d.b	8
		192.14.d.c	16
		192.14.d.d	20
192.14.f	\(\chi_{192}(95, \cdot)\)	n/a	104	1
192.14.j	\(\chi_{192}(49, \cdot)\)	n/a	104	2
192.14.k	\(\chi_{192}(47, \cdot)\)	n/a	204	2
192.14.n	\(\chi_{192}(25, \cdot)\)	None	0	4
192.14.o	\(\chi_{192}(23, \cdot)\)	None	0	4
192.14.r	\(\chi_{192}(13, \cdot)\)	n/a	1664	8
192.14.s	\(\chi_{192}(11, \cdot)\)	n/a	3312	8

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

Decomposition of \(S_{14}^{\mathrm{old}}(\Gamma_1(192))\) into lower level spaces

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