Space of modular forms of level 176, weight 5, and Character 176.h

• Label: 176.5.h
• Level: $176$
• Weight: $5$
• Character orbit: 176.h
• Rep. character: $\chi_{176}(65,\cdot)$
• Character field: $\Q$
• Dimension: $23$
• Newform subspaces: $6$
• Sturm bound: $120$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 176 = 2^{4} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 5 \)
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:			\(120\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(3\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(176, [\chi])\).

	Total	New	Old
Modular forms	102	25	77
Cusp forms	90	23	67
Eisenstein series	12	2	10

Trace form

\( 23 q + 2 q^{3} - 2 q^{5} + 677 q^{9} + O(q^{10}) \)

Decomposition of \(S_{5}^{\mathrm{new}}(176, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
176.5.h.a	$176$	$5$	176.h	11.b	$2$	$1$	$1$	$18.193$	\(\Q\)	\(\Q(\sqrt{-11}) \)	✓				11.5.b.a	$2$	$0$	\(0\)	\(-7\)	\(-49\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q-7q^{3}-7^{2}q^{5}-2^{5}q^{9}-11^{2}q^{11}+\cdots\)
176.5.h.b	$176$	$5$	176.h	11.b	$2$	$2$	$2$	$18.193$	\(\Q(\sqrt{-206}) \)	None					44.5.d.b	$2$	$0$	\(0\)	\(6\)	\(-34\)	\(0\)	$2\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	\(q+3q^{3}-17q^{5}+\beta q^{7}-72q^{9}+(85+\cdots)q^{11}+\cdots\)
176.5.h.c	$176$	$5$	176.h	11.b	$2$	$2$	$2$	$18.193$	\(\Q(\sqrt{-30}) \)	None					11.5.b.b	$2$	$0$	\(0\)	\(6\)	\(62\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+3q^{3}+31q^{5}+5\beta q^{7}-72q^{9}+(-11+\cdots)q^{11}+\cdots\)
176.5.h.d	$176$	$5$	176.h	11.b	$2$	$2$	$2$	$18.193$	\(\Q(\sqrt{33}) \)	\(\Q(\sqrt{-11}) \)	✓				44.5.d.a	$2$	$0$	\(0\)	\(7\)	\(49\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+(1+5\beta )q^{3}+(23+3\beta )q^{5}+(120+35\beta )q^{9}+\cdots\)
176.5.h.e	$176$	$5$	176.h	11.b	$2$	$4$	$4$	$18.193$	\(\Q(\sqrt{-2}, \sqrt{553})\)	None					22.5.b.a	$2$	$0$	\(0\)	\(-2\)	\(-30\)	\(0\)	$2^{4}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1-\beta _{1})q^{3}+(-7+\beta _{1})q^{5}-\beta _{2}q^{7}+\cdots\)
176.5.h.f	$176$	$5$	176.h	11.b	$2$	$12$	$12$	$18.193$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None			✓		88.5.h.a	$2$	$0$	\(0\)	\(-8\)	\(0\)	\(0\)	$2^{32}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1-\beta _{1})q^{3}+\beta _{2}q^{5}+\beta _{5}q^{7}+(42+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{5}^{\mathrm{old}}(176, [\chi])\) into lower level spaces

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