Space of modular forms of level 176, weight 9, and Character 176.h

• Label: 176.9.h
• Level: $176$
• Weight: $9$
• Character orbit: 176.h
• Rep. character: $\chi_{176}(65,\cdot)$
• Character field: $\Q$
• Dimension: $47$
• Newform subspaces: $6$
• Sturm bound: $216$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 176 = 2^{4} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 9 \)
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:			\(216\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(176, [\chi])\).

	Total	New	Old
Modular forms	198	49	149
Cusp forms	186	47	139
Eisenstein series	12	2	10

Trace form

\( 47 q + 2 q^{3} - 2 q^{5} + 102221 q^{9} + O(q^{10}) \)

Decomposition of \(S_{9}^{\mathrm{new}}(176, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
176.9.h.a	$176$	$9$	176.h	11.b	$2$	$1$	$1$	$71.699$	\(\Q\)	\(\Q(\sqrt{-11}) \)	✓	$2$	$0$	\(0\)	\(113\)	\(1151\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+113q^{3}+1151q^{5}+6208q^{9}-11^{4}q^{11}+\cdots\)
176.9.h.b	$176$	$9$	176.h	11.b	$2$	$2$	$2$	$71.699$	\(\Q(\sqrt{33}) \)	\(\Q(\sqrt{-11}) \)	✓	$2$	$0$	\(0\)	\(-113\)	\(-1151\)	\(0\)	$7$	$\mathrm{U}(1)[D_{2}]$	\(q+(-59-5\beta )q^{3}+(-565+21\beta )q^{5}+\cdots\)
176.9.h.c	$176$	$9$	176.h	11.b	$2$	$6$	$6$	$71.699$	\(\mathbb{Q}[x]/(x^{6} + \cdots)\)	None		$2$	$0$	\(0\)	\(36\)	\(-448\)	\(0\)	$2^{10}\cdot 5$	$\mathrm{SU}(2)[C_{2}]$	\(q+(6+\beta _{5})q^{3}+(-73-5\beta _{4}-3\beta _{5})q^{5}+\cdots\)
176.9.h.d	$176$	$9$	176.h	11.b	$2$	$6$	$6$	$71.699$	\(\mathbb{Q}[x]/(x^{6} + \cdots)\)	None		$2$	$0$	\(0\)	\(36\)	\(1856\)	\(0\)	$2^{8}\cdot 3^{2}\cdot 11^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(6+\beta _{2})q^{3}+(309+\beta _{5})q^{5}+\beta _{1}q^{7}+\cdots\)
176.9.h.e	$176$	$9$	176.h	11.b	$2$	$8$	$8$	$71.699$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None		$2$	$0$	\(0\)	\(-182\)	\(-1410\)	\(0\)	$2^{20}\cdot 3^{3}\cdot 11^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-23-\beta _{1})q^{3}+(-176+\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)
176.9.h.f	$176$	$9$	176.h	11.b	$2$	$24$	$24$	$71.699$		None		$2$	$0$	\(0\)	\(112\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{9}^{\mathrm{old}}(176, [\chi])\) into lower level spaces

\( S_{9}^{\mathrm{old}}(176, [\chi]) \cong \) \(S_{9}^{\mathrm{new}}(11, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(22, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(44, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(88, [\chi])\)\(^{\oplus 2}\)