Space of modular forms of level 192 and weight 2

• Label: 192.2
• Level: 192
• Weight: 2
• Dimension: 410
• Nonzero newspaces: 8
• Newform subspaces: 13
• Sturm bound: 4096
• Trace bound: 11

Defining parameters

Level:	\( N \)	=	\( 192 = 2^{6} \cdot 3 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 8 \)
Newform subspaces:			\( 13 \)
Sturm bound:			\(4096\)
Trace bound:			\(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(192))\).

	Total	New	Old
Modular forms	1168	454	714
Cusp forms	881	410	471
Eisenstein series	287	44	243

Trace form

410 * q - 6 * q^3 - 16 * q^4 - 8 * q^6 - 8 * q^7 - 10 * q^9 - 16 * q^10 + 8 * q^11 - 8 * q^12 - 16 * q^16 + 16 * q^17 - 8 * q^18 + 4 * q^19 - 12 * q^21 - 32 * q^22 - 48 * q^24 - 42 * q^25 - 80 * q^26 - 18 * q^27 - 96 * q^28 - 32 * q^29 - 88 * q^30 - 56 * q^31 - 80 * q^32 - 44 * q^33 - 96 * q^34 - 24 * q^35 - 88 * q^36 - 48 * q^37 - 80 * q^38 - 28 * q^39 - 96 * q^40 - 32 * q^41 - 48 * q^42 - 20 * q^43 - 16 * q^44 - 52 * q^45 - 16 * q^46 - 8 * q^48 - 42 * q^49 + 48 * q^50 - 72 * q^51 + 80 * q^52 + 8 * q^54 - 168 * q^55 + 112 * q^56 - 36 * q^57 + 128 * q^58 - 160 * q^59 + 88 * q^60 - 16 * q^61 + 96 * q^62 - 40 * q^63 + 176 * q^64 - 16 * q^65 + 72 * q^66 - 188 * q^67 + 96 * q^68 + 28 * q^69 + 176 * q^70 - 128 * q^71 - 8 * q^72 - 20 * q^73 + 112 * q^74 - 54 * q^75 + 112 * q^76 + 48 * q^77 + 64 * q^78 - 56 * q^79 + 48 * q^80 + 50 * q^81 - 16 * q^82 + 40 * q^83 + 104 * q^84 + 32 * q^85 + 52 * q^87 - 16 * q^88 + 32 * q^89 + 136 * q^90 + 48 * q^91 + 48 * q^93 - 16 * q^94 + 48 * q^95 + 128 * q^96 + 36 * q^97 + 52 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(192))\)

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
192.2.a	\(\chi_{192}(1, \cdot)\)	192.2.a.a	1	1
		192.2.a.b	1
		192.2.a.c	1
		192.2.a.d	1
192.2.c	\(\chi_{192}(191, \cdot)\)	192.2.c.a	2	1
		192.2.c.b	4
192.2.d	\(\chi_{192}(97, \cdot)\)	192.2.d.a	4	1
192.2.f	\(\chi_{192}(95, \cdot)\)	192.2.f.a	4	1
		192.2.f.b	4
192.2.j	\(\chi_{192}(49, \cdot)\)	192.2.j.a	8	2
192.2.k	\(\chi_{192}(47, \cdot)\)	192.2.k.a	12	2
192.2.n	\(\chi_{192}(25, \cdot)\)	None	0	4
192.2.o	\(\chi_{192}(23, \cdot)\)	None	0	4
192.2.r	\(\chi_{192}(13, \cdot)\)	192.2.r.a	128	8
192.2.s	\(\chi_{192}(11, \cdot)\)	192.2.s.a	240	8

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(192))\) into lower level spaces

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