Space of modular forms of level 192 and weight 4

• Label: 192.4
• Level: 192
• Weight: 4
• Dimension: 1274
• Nonzero newspaces: 8
• Newform subspaces: 27
• Sturm bound: 8192
• Trace bound: 11

Defining parameters

Level:	\( N \)	=	\( 192 = 2^{6} \cdot 3 \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 8 \)
Newform subspaces:			\( 27 \)
Sturm bound:			\(8192\)
Trace bound:			\(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(192))\).

	Total	New	Old
Modular forms	3216	1318	1898
Cusp forms	2928	1274	1654
Eisenstein series	288	44	244

Trace form

1274 * q - 6 * q^3 - 16 * q^4 - 8 * q^6 - 8 * q^7 - 10 * q^9 - 16 * q^10 + 40 * q^11 - 8 * q^12 - 160 * q^13 - 128 * q^15 - 16 * q^16 - 208 * q^17 - 8 * q^18 - 60 * q^19 + 4 * q^21 - 960 * q^22 - 1008 * q^24 - 122 * q^25 + 80 * q^26 + 126 * q^27 + 1504 * q^28 + 800 * q^29 + 2312 * q^30 + 712 * q^31 + 2480 * q^32 + 868 * q^33 + 1984 * q^34 + 456 * q^35 + 872 * q^36 + 16 * q^37 - 880 * q^38 - 604 * q^39 - 3296 * q^40 - 1888 * q^41 - 3168 * q^42 - 820 * q^43 - 2000 * q^44 + 476 * q^45 - 16 * q^46 - 8 * q^48 - 714 * q^49 + 5712 * q^50 - 3080 * q^51 + 6608 * q^52 + 424 * q^54 - 1448 * q^55 - 784 * q^56 - 308 * q^57 - 4768 * q^58 + 6880 * q^59 - 4904 * q^60 - 16 * q^61 - 5856 * q^62 + 2520 * q^63 - 12112 * q^64 + 4048 * q^65 - 5544 * q^66 + 12036 * q^67 - 4128 * q^68 + 844 * q^69 - 4048 * q^70 + 896 * q^71 - 8 * q^72 - 2068 * q^73 + 5264 * q^74 - 6982 * q^75 + 11888 * q^76 - 3504 * q^77 + 12112 * q^78 - 17336 * q^79 + 10032 * q^80 + 1202 * q^81 - 16 * q^82 - 2680 * q^83 + 4136 * q^84 - 2368 * q^85 - 1292 * q^87 - 16 * q^88 + 352 * q^89 - 9368 * q^90 + 3056 * q^91 - 176 * q^93 - 16 * q^94 + 7728 * q^95 - 12928 * q^96 + 6788 * q^97 - 844 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(192))\)

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
192.4.a	\(\chi_{192}(1, \cdot)\)	192.4.a.a	1	1
		192.4.a.b	1
		192.4.a.c	1
		192.4.a.d	1
		192.4.a.e	1
		192.4.a.f	1
		192.4.a.g	1
		192.4.a.h	1
		192.4.a.i	1
		192.4.a.j	1
		192.4.a.k	1
		192.4.a.l	1
192.4.c	\(\chi_{192}(191, \cdot)\)	192.4.c.a	2	1
		192.4.c.b	4
		192.4.c.c	4
		192.4.c.d	12
192.4.d	\(\chi_{192}(97, \cdot)\)	192.4.d.a	4	1
		192.4.d.b	4
		192.4.d.c	4
192.4.f	\(\chi_{192}(95, \cdot)\)	192.4.f.a	4	1
		192.4.f.b	4
		192.4.f.c	8
		192.4.f.d	8
192.4.j	\(\chi_{192}(49, \cdot)\)	192.4.j.a	24	2
192.4.k	\(\chi_{192}(47, \cdot)\)	192.4.k.a	44	2
192.4.n	\(\chi_{192}(25, \cdot)\)	None	0	4
192.4.o	\(\chi_{192}(23, \cdot)\)	None	0	4
192.4.r	\(\chi_{192}(13, \cdot)\)	192.4.r.a	384	8
192.4.s	\(\chi_{192}(11, \cdot)\)	192.4.s.a	752	8

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(192))\) into lower level spaces

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