Newform orbit 176.3.r.b

• Label: 176.3.r.b
• Level: $176$
• Weight: $3$
• Character orbit: 176.r
• Analytic conductor: $4.796$
• Analytic rank: $0$
• Dimension: $32$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 176 = 2^{4} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	176.r (of order \(10\), degree \(4\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(4.79565265274\)
Analytic rank:	\(0\)
Dimension:	\(32\)
Relative dimension:	\(8\) over \(\Q(\zeta_{10})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

$q$-expansion

The dimension is sufficiently large that we do not compute an algebraic \(q\)-expansion, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 32 q - 2 q^{5} + 6 q^{9}+O(q^{10}) \)

Embeddings

For each embedding \(\iota_m\) of the coefficient field, the values \(\iota_m(a_n)\) are shown below.

For more information on an embedded modular form you can click on its label.

Label	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
15.1		0		−4.99762	−	1.62382i		0		−4.45057	+	3.23353i		0		2.29193	−	0.744694i		0		15.0582	+	10.9404i		0
15.2		0		−3.76597	−	1.22364i		0		1.21365	−	0.881768i		0		−5.97156	+	1.94028i		0		5.40411	+	3.92632i		0
15.3		0		−1.53649	−	0.499236i		0		6.18491	−	4.49360i		0		−5.21866	+	1.69564i		0		−5.16959	−	3.75593i		0
15.4		0		−1.12085	−	0.364187i		0		−4.87504	+	3.54192i		0		6.09906	−	1.98171i		0		−6.15747	−	4.47367i		0
15.5		0		1.12085	+	0.364187i		0		−4.87504	+	3.54192i		0		−6.09906	+	1.98171i		0		−6.15747	−	4.47367i		0
15.6		0		1.53649	+	0.499236i		0		6.18491	−	4.49360i		0		5.21866	−	1.69564i		0		−5.16959	−	3.75593i		0
15.7		0		3.76597	+	1.22364i		0		1.21365	−	0.881768i		0		5.97156	−	1.94028i		0		5.40411	+	3.92632i		0
15.8		0		4.99762	+	1.62382i		0		−4.45057	+	3.23353i		0		−2.29193	+	0.744694i		0		15.0582	+	10.9404i		0
31.1		0		−3.22216	−	4.43492i		0		−1.15261	−	3.54738i		0		7.65493	−	10.5361i		0		−6.50505	+	20.0205i		0
31.2		0		−3.00482	−	4.13578i		0		2.22535	+	6.84891i		0		−2.84068	+	3.90986i		0		−5.29460	+	16.2951i		0
31.3		0		−1.18851	−	1.63584i		0		1.31885	+	4.05901i		0		−6.22760	+	8.57156i		0		1.51773	−	4.67110i		0
31.4		0		−0.387766	−	0.533714i		0		−0.964532	−	2.96853i		0		−0.673821	+	0.927435i		0		2.64666	−	8.14560i		0
31.5		0		0.387766	+	0.533714i		0		−0.964532	−	2.96853i		0		0.673821	−	0.927435i		0		2.64666	−	8.14560i		0
31.6		0		1.18851	+	1.63584i		0		1.31885	+	4.05901i		0		6.22760	−	8.57156i		0		1.51773	−	4.67110i		0
31.7		0		3.00482	+	4.13578i		0		2.22535	+	6.84891i		0		2.84068	−	3.90986i		0		−5.29460	+	16.2951i		0
31.8		0		3.22216	+	4.43492i		0		−1.15261	−	3.54738i		0		−7.65493	+	10.5361i		0		−6.50505	+	20.0205i		0
47.1		0		−4.99762	+	1.62382i		0		−4.45057	−	3.23353i		0		2.29193	+	0.744694i		0		15.0582	−	10.9404i		0
47.2		0		−3.76597	+	1.22364i		0		1.21365	+	0.881768i		0		−5.97156	−	1.94028i		0		5.40411	−	3.92632i		0
47.3		0		−1.53649	+	0.499236i		0		6.18491	+	4.49360i		0		−5.21866	−	1.69564i		0		−5.16959	+	3.75593i		0
47.4		0		−1.12085	+	0.364187i		0		−4.87504	−	3.54192i		0		6.09906	+	1.98171i		0		−6.15747	+	4.47367i		0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
4.b	odd	2	1	inner
11.c	even	5	1	inner
44.h	odd	10	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	176.3.r.b	✓	32
4.b	odd	2	1	inner	176.3.r.b	✓	32
11.c	even	5	1	inner	176.3.r.b	✓	32
44.h	odd	10	1	inner	176.3.r.b	✓	32

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
176.3.r.b	✓	32	1.a	even	1	1	trivial
176.3.r.b	✓	32	4.b	odd	2	1	inner
176.3.r.b	✓	32	11.c	even	5	1	inner
176.3.r.b	✓	32	44.h	odd	10	1	inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T3^32 - 39*T3^30 + 1743*T3^28 - 67368*T3^26 + 2135159*T3^24 - 43611648*T3^22 + 1016544571*T3^20 - 17504691534*T3^18 + 183945610728*T3^16 - 743792756580*T3^14 + 3368436765955*T3^12 - 12914694351585*T3^10 + 31949841725247*T3^8 - 37673424149313*T3^6 + 20058073909876*T3^4 - 1593373678533*T3^2 + 4810832476321