Space of modular forms of level 176, weight 7, and Character 176.h

• Label: 176.7.h
• Level: $176$
• Weight: $7$
• Character orbit: 176.h
• Rep. character: $\chi_{176}(65,\cdot)$
• Character field: $\Q$
• Dimension: $35$
• Newform subspaces: $6$
• Sturm bound: $168$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 176 = 2^{4} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 7 \)
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:			\(168\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(176, [\chi])\).

	Total	New	Old
Modular forms	150	37	113
Cusp forms	138	35	103
Eisenstein series	12	2	10

Trace form

\( 35 q + 2 q^{3} - 2 q^{5} + 7097 q^{9} + O(q^{10}) \)

Decomposition of \(S_{7}^{\mathrm{new}}(176, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
176.7.h.a	$176$	$7$	176.h	11.b	$2$	$1$	$1$	$40.490$	\(\Q\)	\(\Q(\sqrt{-11}) \)	✓				11.7.b.a	$2$	$0$	\(0\)	\(-10\)	\(74\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q-10q^{3}+74q^{5}-629q^{9}+11^{3}q^{11}+\cdots\)
176.7.h.b	$176$	$7$	176.h	11.b	$2$	$2$	$2$	$40.490$	\(\Q(\sqrt{33}) \)	\(\Q(\sqrt{-11}) \)	✓				44.7.d.a	$2$	$0$	\(0\)	\(10\)	\(-74\)	\(0\)	$2^{3}$	$\mathrm{U}(1)[D_{2}]$	\(q+(5+2\beta )q^{3}+(-37-9\beta )q^{5}+(1408+\cdots)q^{9}+\cdots\)
176.7.h.c	$176$	$7$	176.h	11.b	$2$	$4$	$4$	$40.490$	\(\mathbb{Q}[x]/(x^{4} + \cdots)\)	None					11.7.b.b	$2$	$0$	\(0\)	\(-24\)	\(-260\)	\(0\)	$2^{7}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-6+\beta _{3})q^{3}-65q^{5}+\beta _{2}q^{7}+(852+\cdots)q^{9}+\cdots\)
176.7.h.d	$176$	$7$	176.h	11.b	$2$	$4$	$4$	$40.490$	\(\mathbb{Q}[x]/(x^{4} + \cdots)\)	None					44.7.d.b	$2$	$0$	\(0\)	\(-6\)	\(-110\)	\(0\)	$2^{3}\cdot 3\cdot 5$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1-\beta _{3})q^{3}+(-5^{2}-5\beta _{3})q^{5}+\cdots\)
176.7.h.e	$176$	$7$	176.h	11.b	$2$	$6$	$6$	$40.490$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None					22.7.b.a	$2$	$0$	\(0\)	\(52\)	\(368\)	\(0\)	$2^{8}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(9+\beta _{1})q^{3}+(61+2\beta _{1}-3\beta _{2})q^{5}+\cdots\)
176.7.h.f	$176$	$7$	176.h	11.b	$2$	$18$	$18$	$40.490$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None			✓		88.7.h.a	$2$	$0$	\(0\)	\(-20\)	\(0\)	\(0\)	$2^{77}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1-\beta _{1})q^{3}+\beta _{3}q^{5}+\beta _{6}q^{7}+(166+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{7}^{\mathrm{old}}(176, [\chi])\) into lower level spaces

\( S_{7}^{\mathrm{old}}(176, [\chi]) \simeq \) \(S_{7}^{\mathrm{new}}(11, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(22, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(44, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(88, [\chi])\)\(^{\oplus 2}\)