Newform orbit 176.2.j.a

• Label: 176.2.j.a
• Level: $176$
• Weight: $2$
• Character orbit: 176.j
• Analytic conductor: $1.405$
• Analytic rank: $0$
• Dimension: $40$
• CM: no
• Inner twists: $2$

Newspace parameters

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

Newform invariants

Self dual:	no
Analytic conductor:	\(1.40536707557\)
Analytic rank:	\(0\)
Dimension:	\(40\)
Relative dimension:	\(20\) over \(\Q(i)\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 40 q - 12 q^{6} - 12 q^{8}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
45.1	−1.41184	+	0.0819819i	0.529792	+	0.529792i	1.98656	−	0.231490i	1.79526	−	1.79526i	−0.791413	−	0.704546i			1.13150i	−2.78571	+	0.489687i		−	2.43864i	−2.38743	+	2.68179i
45.2	−1.39935	+	0.204478i	−2.27066	−	2.27066i	1.91638	−	0.572275i	1.24014	−	1.24014i	3.64176	+	2.71316i		−	3.02382i	−2.56467	+	1.19267i			7.31182i	−1.48181	+	1.98898i
45.3	−1.25745	−	0.647159i	−0.273979	−	0.273979i	1.16237	+	1.62754i	−2.48024	+	2.48024i	0.167207	+	0.521823i		−	4.65464i	−0.408346	−	2.79880i		−	2.84987i	4.72389	−	1.51367i
45.4	−1.21415	−	0.725142i	−1.27582	−	1.27582i	0.948339	+	1.76087i	−0.795196	+	0.795196i	0.623892	+	2.47419i			4.67475i	0.125448	−	2.82564i			0.255441i	1.54212	−	0.388861i
45.5	−1.15225	−	0.819948i	2.04787	+	2.04787i	0.655370	+	1.88957i	0.814963	−	0.814963i	−0.680516	−	4.03881i		−	2.42498i	0.794202	−	2.71464i			5.38755i	−1.60727	+	0.270815i
45.6	−1.15173	+	0.820676i	2.16054	+	2.16054i	0.652980	−	1.89040i	−1.53482	+	1.53482i	−4.26148	−	0.715263i		−	0.310169i	0.799348	+	2.71312i			6.33589i	0.508112	−	3.02729i
45.7	−0.526471	−	1.31257i	−0.151436	−	0.151436i	−1.44566	+	1.38205i	1.85628	−	1.85628i	−0.119043	+	0.278497i		−	0.615059i	2.57513	+	1.16991i		−	2.95413i	−3.41376	−	1.45921i
45.8	−0.403781	−	1.35535i	1.28225	+	1.28225i	−1.67392	+	1.09452i	−2.06176	+	2.06176i	1.22014	−	2.25564i			3.54041i	2.15936	+	1.82679i			0.288318i	3.62690	+	1.96190i
45.9	−0.398671	+	1.35686i	1.34498	+	1.34498i	−1.68212	−	1.08188i	2.40794	−	2.40794i	−2.36114	+	1.28874i			4.88654i	2.13857	−	1.85109i			0.617917i	2.30726	+	4.22721i
45.10	−0.0986166	+	1.41077i	−1.15526	−	1.15526i	−1.98055	−	0.278251i	0.731846	−	0.731846i	1.74374	−	1.51588i		−	2.61186i	0.587863	−	2.76666i		−	0.330747i	0.960295	+	1.10464i
45.11	0.0241205	+	1.41401i	0.791470	+	0.791470i	−1.99884	+	0.0682132i	−2.78615	+	2.78615i	−1.10005	+	1.13823i		−	0.0391973i	−0.144667	−	2.82473i		−	1.74715i	−4.00683	−	3.87243i
45.12	0.494240	−	1.32504i	0.190424	+	0.190424i	−1.51145	−	1.30977i	0.291418	−	0.291418i	0.346435	−	0.158204i		−	2.64639i	−2.48252	+	1.35539i		−	2.92748i	−0.242109	−	0.530170i
45.13	0.686639	+	1.23634i	1.72812	+	1.72812i	−1.05705	+	1.69783i	0.893733	−	0.893733i	−0.949940	+	3.32312i		−	2.98840i	−2.82491	−	0.141074i			2.97277i	1.71863	+	0.491282i
45.14	0.783980	−	1.17702i	−1.97112	−	1.97112i	−0.770751	−	1.84552i	2.29075	−	2.29075i	−3.86537	+	0.774730i			3.79929i	−2.77647	−	0.539662i			4.77065i	−0.900354	−	4.49215i
45.15	0.947542	+	1.04984i	−2.24228	−	2.24228i	−0.204327	+	1.98954i	−2.71114	+	2.71114i	0.229379	−	4.47868i			1.46050i	−2.28230	+	1.67066i			7.05562i	−5.41518	−	0.277342i
45.16	0.988599	−	1.01127i	1.60387	+	1.60387i	−0.0453448	−	1.99949i	−0.215519	+	0.215519i	3.20753	−	0.0363659i			1.18021i	−2.06685	−	1.93083i			2.14479i	0.00488664	+	0.431010i
45.17	1.10124	+	0.887278i	−1.15765	−	1.15765i	0.425474	+	1.95422i	2.69017	−	2.69017i	−0.247696	−	2.30200i		−	0.0889173i	−1.26539	+	2.52958i		−	0.319711i	5.34946	−	0.575603i
45.18	1.28704	+	0.586108i	0.586507	+	0.586507i	1.31295	+	1.50869i	−1.32116	+	1.32116i	0.411103	+	1.09862i		−	1.42100i	0.805572	+	2.71128i		−	2.31202i	−2.47473	+	0.926044i
45.19	1.28990	−	0.579802i	−1.51913	−	1.51913i	1.32766	−	1.49577i	−1.06305	+	1.06305i	−2.84031	−	1.07872i		−	3.12852i	0.845294	−	2.69916i			1.61549i	−0.754864	+	1.98758i
45.20	1.41102	−	0.0950426i	−0.248483	−	0.248483i	1.98193	−	0.268213i	−0.0434775	+	0.0434775i	−0.374231	−	0.326998i			3.27975i	2.77105	−	0.566821i		−	2.87651i	−0.0572153	+	0.0654797i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
16.e	even	4	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	176.2.j.a	✓	40
4.b	odd	2	1		704.2.j.a		40
8.b	even	2	1		1408.2.j.a		40
8.d	odd	2	1		1408.2.j.b		40
16.e	even	4	1	inner	176.2.j.a	✓	40
16.e	even	4	1		1408.2.j.a		40
16.f	odd	4	1		704.2.j.a		40
16.f	odd	4	1		1408.2.j.b		40

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
176.2.j.a	✓	40	1.a	even	1	1	trivial
176.2.j.a	✓	40	16.e	even	4	1	inner
704.2.j.a		40	4.b	odd	2	1
704.2.j.a		40	16.f	odd	4	1
1408.2.j.a		40	8.b	even	2	1
1408.2.j.a		40	16.e	even	4	1
1408.2.j.b		40	8.d	odd	2	1
1408.2.j.b		40	16.f	odd	4	1

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(176, [\chi])\).