Space of modular forms of level 176, weight 4, and Character 176.e

• Label: 176.4.e
• Level: $176$
• Weight: $4$
• Character orbit: 176.e
• Rep. character: $\chi_{176}(175,\cdot)$
• Character field: $\Q$
• Dimension: $18$
• Newform subspaces: $5$
• Sturm bound: $96$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 176 = 2^{4} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	176.e (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 44 \)
Character field:			\(\Q\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(96\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(3\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(176, [\chi])\).

	Total	New	Old
Modular forms	78	18	60
Cusp forms	66	18	48
Eisenstein series	12	0	12

Trace form

\( 18 q - 102 q^{9} - 54 q^{25} - 192 q^{33} + 492 q^{45} - 30 q^{49} - 1380 q^{53} + 2748 q^{69} + 384 q^{77} + 1218 q^{81} - 768 q^{89} - 3636 q^{93} + 3072 q^{97}+O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(176, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
176.4.e.a	$176$	$4$	176.e	44.c	$2$	$2$	$2$	$10.384$	\(\Q(\sqrt{-11}) \)	\(\Q(\sqrt{-11}) \)		✓			176.4.e.a	$4$	$0$	\(0\)	\(0\)	\(-36\)	\(0\)	$2$	$\mathrm{U}(1)[D_{2}]$	\(q-2\beta q^{3}-18q^{5}-17q^{9}+11\beta q^{11}+\cdots\)
176.4.e.b	$176$	$4$	176.e	44.c	$2$	$2$	$2$	$10.384$	\(\Q(\sqrt{-19}) \)	None		✓			176.4.e.b	$2$	$0$	\(0\)	\(0\)	\(14\)	\(-40\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta q^{3}+7q^{5}-20q^{7}+8q^{9}+(20+\cdots)q^{11}+\cdots\)
176.4.e.c	$176$	$4$	176.e	44.c	$2$	$2$	$2$	$10.384$	\(\Q(\sqrt{-19}) \)	None		✓			176.4.e.b	$2$	$0$	\(0\)	\(0\)	\(14\)	\(40\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta q^{3}+7q^{5}+20q^{7}+8q^{9}+(-20+\cdots)q^{11}+\cdots\)
176.4.e.d	$176$	$4$	176.e	44.c	$2$	$4$	$4$	$10.384$	\(\Q(\sqrt{-3}, \sqrt{-11})\)	\(\Q(\sqrt{-11}) \)		✓			176.4.e.d	$4$	$0$	\(0\)	\(0\)	\(36\)	\(0\)	$2^{6}$	$\mathrm{U}(1)[D_{2}]$	\(q+(-2\beta _{1}-\beta _{2})q^{3}+(9+\beta _{3})q^{5}+(-2^{5}+\cdots)q^{9}+\cdots\)
176.4.e.e	$176$	$4$	176.e	44.c	$2$	$8$	$8$	$10.384$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None		✓	✓		176.4.e.e	$4$	$0$	\(0\)	\(0\)	\(-28\)	\(0\)	$2^{12}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\beta _{2}+\beta _{3})q^{3}+(-4+\beta _{1})q^{5}-\beta _{4}q^{7}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(176, [\chi])\) into lower level spaces

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