Newform orbit 176.2.i.a

• Label: 176.2.i.a
• Level: $176$
• Weight: $2$
• Character orbit: 176.i
• Analytic conductor: $1.405$
• Analytic rank: $0$
• Dimension: $44$
• Inner twists: $4$

Newspace parameters

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

Newform invariants

Self dual:	no
Analytic conductor:	\(1.40536707557\)
Analytic rank:	\(0\)
Dimension:	\(44\)
Relative dimension:	\(22\) over \(\Q(i)\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

$q$-expansion

The algebraic \(q\)-expansion of this newform has not been computed, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 44 q - 4 q^{3} - 4 q^{5}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
43.1	−1.39613	−	0.225455i	1.15889	+	1.15889i	1.89834	+	0.629528i	−2.51141	−	2.51141i	−1.35668	−	1.87924i		−	4.37614i	−2.50839	−	1.30689i		−	0.313934i	2.94003	+	4.07245i
43.2	−1.38786	−	0.271723i	−1.64229	−	1.64229i	1.85233	+	0.754228i	1.97065	+	1.97065i	1.83303	+	2.72552i			1.30445i	−2.36585	−	1.55009i			2.39422i	−2.19952	−	3.27046i
43.3	−1.36446	+	0.371814i	−0.766690	−	0.766690i	1.72351	−	1.01465i	−0.946416	−	0.946416i	1.33118	+	0.761052i			0.840189i	−1.97440	+	2.02528i		−	1.82437i	1.64324	+	0.939458i
43.4	−1.13279	−	0.846636i	1.22947	+	1.22947i	0.566413	+	1.91812i	−0.282901	−	0.282901i	−0.351814	−	2.43365i			4.20092i	0.982323	−	2.65237i			0.0232059i	0.0809523	+	0.559981i
43.5	−1.04390	+	0.954084i	0.108192	+	0.108192i	0.179446	−	1.99193i	2.69023	+	2.69023i	−0.216165	−	0.00971706i		−	3.17010i	1.71315	+	2.25058i		−	2.97659i	−5.37502	−	0.241618i
43.6	−0.889668	−	1.09931i	−1.82463	−	1.82463i	−0.416982	+	1.95605i	−2.57632	−	2.57632i	−0.382527	+	3.62916i			2.30642i	2.52129	−	1.28184i			3.65855i	−0.540116	+	5.12426i
43.7	−0.888482	+	1.10027i	2.21950	+	2.21950i	−0.421198	−	1.95515i	−0.858137	−	0.858137i	−4.41404	+	0.470067i			1.49353i	2.52542	+	1.27368i			6.85234i	1.70662	−	0.181745i
43.8	−0.826559	−	1.14752i	−0.429854	−	0.429854i	−0.633599	+	1.89699i	0.703721	+	0.703721i	−0.137966	+	0.848565i		−	3.48768i	2.70053	−	0.840904i		−	2.63045i	0.225866	−	1.38920i
43.9	−0.670735	+	1.24504i	−0.259076	−	0.259076i	−1.10023	−	1.67018i	−1.45525	−	1.45525i	0.496330	−	0.148788i		−	0.413174i	2.81739	−	0.249580i		−	2.86576i	2.78792	−	0.835750i
43.10	−0.378371	+	1.36266i	−2.13264	−	2.13264i	−1.71367	−	1.03118i	0.987102	+	0.987102i	3.71298	−	2.09913i			3.85199i	2.05355	−	1.94498i			6.09629i	−1.71857	+	0.971591i
43.11	−0.181161	−	1.40256i	1.33912	+	1.33912i	−1.93436	+	0.508180i	1.27873	+	1.27873i	1.63560	−	2.12080i			0.148220i	1.06319	+	2.62100i			0.586494i	1.56185	−	2.02516i
43.12	0.181161	+	1.40256i	1.33912	+	1.33912i	−1.93436	+	0.508180i	1.27873	+	1.27873i	−1.63560	+	2.12080i		−	0.148220i	−1.06319	−	2.62100i			0.586494i	−1.56185	+	2.02516i
43.13	0.378371	−	1.36266i	−2.13264	−	2.13264i	−1.71367	−	1.03118i	0.987102	+	0.987102i	−3.71298	+	2.09913i		−	3.85199i	−2.05355	+	1.94498i			6.09629i	1.71857	−	0.971591i
43.14	0.670735	−	1.24504i	−0.259076	−	0.259076i	−1.10023	−	1.67018i	−1.45525	−	1.45525i	−0.496330	+	0.148788i			0.413174i	−2.81739	+	0.249580i		−	2.86576i	−2.78792	+	0.835750i
43.15	0.826559	+	1.14752i	−0.429854	−	0.429854i	−0.633599	+	1.89699i	0.703721	+	0.703721i	0.137966	−	0.848565i			3.48768i	−2.70053	+	0.840904i		−	2.63045i	−0.225866	+	1.38920i
43.16	0.888482	−	1.10027i	2.21950	+	2.21950i	−0.421198	−	1.95515i	−0.858137	−	0.858137i	4.41404	−	0.470067i		−	1.49353i	−2.52542	−	1.27368i			6.85234i	−1.70662	+	0.181745i
43.17	0.889668	+	1.09931i	−1.82463	−	1.82463i	−0.416982	+	1.95605i	−2.57632	−	2.57632i	0.382527	−	3.62916i		−	2.30642i	−2.52129	+	1.28184i			3.65855i	0.540116	−	5.12426i
43.18	1.04390	−	0.954084i	0.108192	+	0.108192i	0.179446	−	1.99193i	2.69023	+	2.69023i	0.216165	+	0.00971706i			3.17010i	−1.71315	−	2.25058i		−	2.97659i	5.37502	+	0.241618i
43.19	1.13279	+	0.846636i	1.22947	+	1.22947i	0.566413	+	1.91812i	−0.282901	−	0.282901i	0.351814	+	2.43365i		−	4.20092i	−0.982323	+	2.65237i			0.0232059i	−0.0809523	−	0.559981i
43.20	1.36446	−	0.371814i	−0.766690	−	0.766690i	1.72351	−	1.01465i	−0.946416	−	0.946416i	−1.33118	−	0.761052i		−	0.840189i	1.97440	−	2.02528i		−	1.82437i	−1.64324	−	0.939458i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
11.b	odd	2	1	inner
16.f	odd	4	1	inner
176.i	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.i.a	✓	44
4.b	odd	2	1		704.2.i.a		44
8.b	even	2	1		1408.2.i.b		44
8.d	odd	2	1		1408.2.i.a		44
11.b	odd	2	1	inner	176.2.i.a	✓	44
16.e	even	4	1		704.2.i.a		44
16.e	even	4	1		1408.2.i.a		44
16.f	odd	4	1	inner	176.2.i.a	✓	44
16.f	odd	4	1		1408.2.i.b		44
44.c	even	2	1		704.2.i.a		44
88.b	odd	2	1		1408.2.i.b		44
88.g	even	2	1		1408.2.i.a		44
176.i	even	4	1	inner	176.2.i.a	✓	44
176.i	even	4	1		1408.2.i.b		44
176.l	odd	4	1		704.2.i.a		44
176.l	odd	4	1		1408.2.i.a		44

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
176.2.i.a	✓	44	1.a	even	1	1	trivial
176.2.i.a	✓	44	11.b	odd	2	1	inner
176.2.i.a	✓	44	16.f	odd	4	1	inner
176.2.i.a	✓	44	176.i	even	4	1	inner
704.2.i.a		44	4.b	odd	2	1
704.2.i.a		44	16.e	even	4	1
704.2.i.a		44	44.c	even	2	1
704.2.i.a		44	176.l	odd	4	1
1408.2.i.a		44	8.d	odd	2	1
1408.2.i.a		44	16.e	even	4	1
1408.2.i.a		44	88.g	even	2	1
1408.2.i.a		44	176.l	odd	4	1
1408.2.i.b		44	8.b	even	2	1
1408.2.i.b		44	16.f	odd	4	1
1408.2.i.b		44	88.b	odd	2	1
1408.2.i.b		44	176.i	even	4	1

Hecke kernels

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