Space of modular forms of level 192 and weight 3

• Label: 192.3
• Level: 192
• Weight: 3
• Dimension: 842
• Nonzero newspaces: 8
• Newform subspaces: 19
• Sturm bound: 6144
• Trace bound: 11

Defining parameters

Level:	\( N \)	=	\( 192 = 2^{6} \cdot 3 \)
Weight:	\( k \)	=	\( 3 \)
Nonzero newspaces:			\( 8 \)
Newform subspaces:			\( 19 \)
Sturm bound:			\(6144\)
Trace bound:			\(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(192))\).

	Total	New	Old
Modular forms	2192	886	1306
Cusp forms	1904	842	1062
Eisenstein series	288	44	244

Trace form

842 * q - 6 * q^3 - 16 * q^4 - 8 * q^6 - 16 * q^7 - 10 * q^9 - 16 * q^10 - 32 * q^11 - 8 * q^12 - 48 * q^13 - 4 * q^15 - 16 * q^16 + 32 * q^17 - 8 * q^18 + 52 * q^19 + 76 * q^21 + 128 * q^22 + 128 * q^23 + 272 * q^24 + 222 * q^25 + 400 * q^26 + 42 * q^27 + 224 * q^28 + 64 * q^29 + 72 * q^30 + 8 * q^31 - 80 * q^32 - 52 * q^33 - 256 * q^34 - 96 * q^35 - 408 * q^36 - 208 * q^37 - 560 * q^38 - 8 * q^39 - 736 * q^40 - 320 * q^41 - 448 * q^42 - 108 * q^43 - 208 * q^44 - 60 * q^45 - 16 * q^46 - 8 * q^48 + 70 * q^49 - 624 * q^50 + 376 * q^51 - 1072 * q^52 - 152 * q^54 + 1264 * q^55 - 784 * q^56 - 92 * q^57 - 736 * q^58 + 640 * q^59 - 296 * q^60 - 16 * q^61 - 96 * q^62 - 208 * q^63 + 176 * q^64 - 288 * q^65 + 248 * q^66 - 1100 * q^67 + 480 * q^68 - 284 * q^69 + 1328 * q^70 - 1536 * q^71 - 8 * q^72 - 532 * q^73 + 1232 * q^74 - 1146 * q^75 + 1648 * q^76 - 96 * q^77 + 304 * q^78 - 1288 * q^79 + 816 * q^80 - 398 * q^81 - 16 * q^82 + 160 * q^83 - 1240 * q^84 + 272 * q^85 - 8 * q^87 - 16 * q^88 + 320 * q^89 - 728 * q^90 + 176 * q^91 + 160 * q^93 - 16 * q^94 + 128 * q^96 - 172 * q^97 + 188 * q^99

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(192))\)

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
192.3.b	\(\chi_{192}(31, \cdot)\)	192.3.b.a	4	1
		192.3.b.b	4
192.3.e	\(\chi_{192}(65, \cdot)\)	192.3.e.a	1	1
		192.3.e.b	1
		192.3.e.c	2
		192.3.e.d	2
		192.3.e.e	4
		192.3.e.f	4
192.3.g	\(\chi_{192}(127, \cdot)\)	192.3.g.a	2	1
		192.3.g.b	2
		192.3.g.c	4
192.3.h	\(\chi_{192}(161, \cdot)\)	192.3.h.a	4	1
		192.3.h.b	4
		192.3.h.c	8
192.3.i	\(\chi_{192}(17, \cdot)\)	192.3.i.a	8	2
		192.3.i.b	20
192.3.l	\(\chi_{192}(79, \cdot)\)	192.3.l.a	16	2
192.3.m	\(\chi_{192}(7, \cdot)\)	None	0	4
192.3.p	\(\chi_{192}(41, \cdot)\)	None	0	4
192.3.q	\(\chi_{192}(5, \cdot)\)	192.3.q.a	496	8
192.3.t	\(\chi_{192}(19, \cdot)\)	192.3.t.a	256	8

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(192))\) into lower level spaces

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