Space of modular forms of level 176, weight 11, and Character 176.h

• Label: 176.11.h
• Level: $176$
• Weight: $11$
• Character orbit: 176.h
• Rep. character: $\chi_{176}(65,\cdot)$
• Character field: $\Q$
• Dimension: $59$
• Newform subspaces: $6$
• Sturm bound: $264$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 176 = 2^{4} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	176.h (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 11 \)
Character field:			\(\Q\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(264\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{11}(176, [\chi])\).

	Total	New	Old
Modular forms	246	61	185
Cusp forms	234	59	175
Eisenstein series	12	2	10

Trace form

\( 59 q + 2 q^{3} - 2 q^{5} + 1143137 q^{9} + O(q^{10}) \)

Decomposition of \(S_{11}^{\mathrm{new}}(176, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
176.11.h.a	$176$	$11$	176.h	11.b	$2$	$1$	$1$	$111.823$	\(\Q\)	\(\Q(\sqrt{-11}) \)	✓	$2$	$0$	\(0\)	\(-475\)	\(-3001\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q-475q^{3}-3001q^{5}+166576q^{9}+\cdots\)
176.11.h.b	$176$	$11$	176.h	11.b	$2$	$2$	$2$	$111.823$	\(\Q(\sqrt{33}) \)	\(\Q(\sqrt{-11}) \)	✓	$2$	$0$	\(0\)	\(475\)	\(3001\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+(253-31\beta )q^{3}+(2327-1653\beta )q^{5}+\cdots\)
176.11.h.c	$176$	$11$	176.h	11.b	$2$	$8$	$8$	$111.823$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None		$2$	$0$	\(0\)	\(-462\)	\(-3570\)	\(0\)	$2^{18}\cdot 3^{7}\cdot 5\cdot 11^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-58-\beta _{1})q^{3}+(-446+\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)
176.11.h.d	$176$	$11$	176.h	11.b	$2$	$8$	$8$	$111.823$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None		$2$	$0$	\(0\)	\(402\)	\(2430\)	\(0\)	$2^{18}\cdot 3^{3}\cdot 11^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(50-\beta _{5})q^{3}+(304+\beta _{5}+\beta _{6})q^{5}+\cdots\)
176.11.h.e	$176$	$11$	176.h	11.b	$2$	$10$	$10$	$111.823$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None		$2$	$0$	\(0\)	\(106\)	\(1138\)	\(0\)	$2^{31}\cdot 3^{5}\cdot 11^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(11+\beta _{1})q^{3}+(113-2\beta _{1}-\beta _{6})q^{5}+\cdots\)
176.11.h.f	$176$	$11$	176.h	11.b	$2$	$30$	$30$	$111.823$		None		$2$	$0$	\(0\)	\(-44\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{11}^{\mathrm{old}}(176, [\chi])\) into lower level spaces

\( S_{11}^{\mathrm{old}}(176, [\chi]) \cong \) \(S_{11}^{\mathrm{new}}(11, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(22, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(44, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(88, [\chi])\)\(^{\oplus 2}\)