Space of modular forms of level 192, weight 11, and Character 192.e

• Label: 192.11.e
• Level: $192$
• Weight: $11$
• Character orbit: 192.e
• Rep. character: $\chi_{192}(65,\cdot)$
• Character field: $\Q$
• Dimension: $78$
• Newform subspaces: $12$
• Sturm bound: $352$
• Trace bound: $9$

Defining parameters

Level:	\( N \)	\(=\)	\( 192 = 2^{6} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	192.e (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 3 \)
Character field:			\(\Q\)
Newform subspaces:			\( 12 \)
Sturm bound:			\(352\)
Trace bound:			\(9\)
Distinguishing \(T_p\):			\(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{11}(192, [\chi])\).

	Total	New	Old
Modular forms	332	82	250
Cusp forms	308	78	230
Eisenstein series	24	4	20

Trace form

\( 78 q - 2 q^{9} + O(q^{10}) \)

Decomposition of \(S_{11}^{\mathrm{new}}(192, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
192.11.e.a	$192$	$11$	192.e	3.b	$2$	$1$	$1$	$121.989$	\(\Q\)	\(\Q(\sqrt{-3}) \)	✓	$2$	$0$	\(0\)	\(-243\)	\(0\)	\(-22082\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q-3^{5}q^{3}-22082q^{7}+3^{10}q^{9}-702218q^{13}+\cdots\)
192.11.e.b	$192$	$11$	192.e	3.b	$2$	$1$	$1$	$121.989$	\(\Q\)	\(\Q(\sqrt{-3}) \)	✓	$2$	$0$	\(0\)	\(243\)	\(0\)	\(22082\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+3^{5}q^{3}+22082q^{7}+3^{10}q^{9}-702218q^{13}+\cdots\)
192.11.e.c	$192$	$11$	192.e	3.b	$2$	$2$	$2$	$121.989$	\(\Q(\sqrt{-35}) \)	None		$2$	$0$	\(0\)	\(-234\)	\(0\)	\(-20636\)	$2^{3}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-117-\beta )q^{3}-6\beta q^{5}-10318q^{7}+\cdots\)
192.11.e.d	$192$	$11$	192.e	3.b	$2$	$2$	$2$	$121.989$	\(\Q(\sqrt{-5}) \)	None		$2$	$0$	\(0\)	\(-54\)	\(0\)	\(-34468\)	$2^{2}\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-3^{3}+9\beta )q^{3}+106\beta q^{5}-17234q^{7}+\cdots\)
192.11.e.e	$192$	$11$	192.e	3.b	$2$	$2$	$2$	$121.989$	\(\Q(\sqrt{-5}) \)	None		$2$	$0$	\(0\)	\(54\)	\(0\)	\(34468\)	$2^{2}\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	\(q+(3^{3}-9\beta )q^{3}+106\beta q^{5}+17234q^{7}+\cdots\)
192.11.e.f	$192$	$11$	192.e	3.b	$2$	$2$	$2$	$121.989$	\(\Q(\sqrt{-35}) \)	None		$2$	$0$	\(0\)	\(234\)	\(0\)	\(20636\)	$2^{3}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(117+\beta )q^{3}-6\beta q^{5}+10318q^{7}+\cdots\)
192.11.e.g	$192$	$11$	192.e	3.b	$2$	$4$	$4$	$121.989$	\(\Q(\sqrt{-2}, \sqrt{85})\)	None		$2$	$0$	\(0\)	\(-84\)	\(0\)	\(-45112\)	$2^{14}\cdot 3^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-21-\beta _{1})q^{3}+(-4\beta _{1}+2\beta _{2}+\beta _{3})q^{5}+\cdots\)
192.11.e.h	$192$	$11$	192.e	3.b	$2$	$4$	$4$	$121.989$	\(\Q(\sqrt{-2}, \sqrt{85})\)	None		$2$	$0$	\(0\)	\(84\)	\(0\)	\(45112\)	$2^{14}\cdot 3^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(21+\beta _{1})q^{3}+(-4\beta _{1}+2\beta _{2}+\beta _{3})q^{5}+\cdots\)
192.11.e.i	$192$	$11$	192.e	3.b	$2$	$10$	$10$	$121.989$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None		$2$	$0$	\(0\)	\(-22\)	\(0\)	\(5436\)	$2^{72}\cdot 3^{16}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-2+\beta _{1})q^{3}+(-\beta _{1}-\beta _{2})q^{5}+(545+\cdots)q^{7}+\cdots\)
192.11.e.j	$192$	$11$	192.e	3.b	$2$	$10$	$10$	$121.989$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None		$2$	$0$	\(0\)	\(22\)	\(0\)	\(-5436\)	$2^{72}\cdot 3^{16}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(2-\beta _{1})q^{3}+(-\beta _{1}-\beta _{2})q^{5}+(-545+\cdots)q^{7}+\cdots\)
192.11.e.k	$192$	$11$	192.e	3.b	$2$	$20$	$20$	$121.989$	\(\mathbb{Q}[x]/(x^{20} + \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{176}\cdot 3^{47}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{3}q^{3}-\beta _{6}q^{5}+(-10\beta _{3}-\beta _{4})q^{7}+\cdots\)
192.11.e.l	$192$	$11$	192.e	3.b	$2$	$20$	$20$	$121.989$	\(\mathbb{Q}[x]/(x^{20} + \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{176}\cdot 3^{36}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{3}-\beta _{2}q^{5}+(15\beta _{1}+\beta _{3})q^{7}+\cdots\)

Decomposition of \(S_{11}^{\mathrm{old}}(192, [\chi])\) into lower level spaces

\( S_{11}^{\mathrm{old}}(192, [\chi]) \cong \) \(S_{11}^{\mathrm{new}}(3, [\chi])\)\(^{\oplus 7}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(6, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 2}\)