Newform orbit 96.3.p.a

• Label: 96.3.p.a
• Level: $96$
• Weight: $3$
• Character orbit: 96.p
• Analytic conductor: $2.616$
• Analytic rank: $0$
• Dimension: $120$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 96 = 2^{5} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	96.p (of order \(8\), degree \(4\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(2.61581053786\)
Analytic rank:	\(0\)
Dimension:	\(120\)
Relative dimension:	\(30\) over \(\Q(\zeta_{8})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 120 q - 4 q^{3} - 8 q^{4} - 4 q^{6} - 8 q^{7} - 4 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
5.1	−1.99935	−	0.0509440i	2.77972	+	1.12834i	3.99481	+	0.203710i	2.35810	−	5.69297i	−5.50016	−	2.39756i	−1.55454	−	1.55454i	−7.97665	−	0.610799i	6.45370	+	6.27294i	−5.00470	+	11.2621i
5.2	−1.99160	−	0.183158i	2.25564	−	1.97790i	3.93291	+	0.729554i	−3.05886	+	7.38474i	−4.85460	+	3.52603i	6.52353	+	6.52353i	−7.69913	−	2.17332i	1.17585	−	8.92286i	7.44458	−	14.1472i
5.3	−1.99034	+	0.196320i	−2.18088	−	2.06004i	3.92292	−	0.781488i	0.400040	−	0.965783i	4.74513	+	3.67202i	−1.74071	−	1.74071i	−7.65452	+	2.32558i	0.512501	+	8.98540i	−0.606614	+	2.00077i
5.4	−1.84984	−	0.760319i	−0.317768	+	2.98312i	2.84383	+	2.81294i	−1.77368	+	4.28204i	2.85595	−	5.27670i	−7.55140	−	7.55140i	−3.12190	−	7.36571i	−8.79805	−	1.89588i	6.53674	−	6.57253i
5.5	−1.76181	+	0.946587i	−2.17853	+	2.06252i	2.20795	−	3.33541i	2.46183	−	5.94339i	1.88580	−	5.69594i	0.814968	+	0.814968i	−0.732725	+	7.96637i	0.491998	−	8.98654i	1.28865	+	12.8015i
5.6	−1.50790	−	1.31386i	−2.99990	+	0.0247672i	0.547547	+	3.96235i	−0.0391005	+	0.0943970i	4.55610	+	3.90410i	2.42911	+	2.42911i	4.38032	−	6.69424i	8.99877	−	0.148598i	0.182984	−	0.0909690i
5.7	−1.50510	+	1.31707i	1.22667	+	2.73775i	0.530655	−	3.96464i	−1.77994	+	4.29715i	−5.45207	−	2.50497i	2.62887	+	2.62887i	4.42302	+	6.66610i	−5.99054	+	6.71665i	−2.98066	−	8.81195i
5.8	−1.44213	+	1.38573i	1.71367	−	2.46239i	0.159500	−	3.99682i	−0.0258289	+	0.0623564i	0.940865	+	5.92577i	−8.71239	−	8.71239i	5.30849	+	5.98497i	−3.12668	−	8.43942i	−0.0491605	−	0.125718i
5.9	−1.43387	−	1.39428i	0.960376	−	2.84213i	0.111984	+	3.99843i	2.53071	−	6.10968i	−5.33977	+	2.73622i	1.09521	+	1.09521i	5.41435	−	5.88938i	−7.15536	−	5.45902i	−12.1473	+	5.23199i
5.10	−1.05135	+	1.70137i	−1.64571	−	2.50831i	−1.78934	−	3.57746i	−1.03584	+	2.50074i	5.99779	−	0.162867i	7.44249	+	7.44249i	7.96782	+	0.716807i	−3.58326	+	8.25592i	−3.16566	−	4.39149i
5.11	−0.896196	−	1.78797i	2.31396	+	1.90935i	−2.39366	+	3.20474i	−0.794982	+	1.91926i	1.34009	−	5.84843i	4.69711	+	4.69711i	7.87517	+	1.40772i	1.70880	+	8.83629i	4.14403	−	0.298628i
5.12	−0.576838	−	1.91501i	−0.719266	−	2.91250i	−3.33452	+	2.20930i	−3.63719	+	8.78095i	−5.16256	+	3.05744i	−5.54083	−	5.54083i	6.15430	+	5.11122i	−7.96531	+	4.18972i	18.9137	+	1.90006i
5.13	−0.503078	+	1.93569i	2.97132	−	0.413808i	−3.49383	−	1.94761i	2.54567	−	6.14580i	−0.693801	+	5.95975i	7.32134	+	7.32134i	5.52764	−	5.78318i	8.65753	−	2.45911i	10.6157	+	8.01946i
5.14	−0.369569	+	1.96556i	−2.74887	+	1.20154i	−3.72684	−	1.45282i	−0.710186	+	1.71454i	−1.34580	−	5.84712i	−3.31956	−	3.31956i	4.23292	−	6.78840i	6.11260	−	6.60576i	−3.10757	−	2.02955i
5.15	−0.310806	−	1.97570i	−1.34666	+	2.68076i	−3.80680	+	1.22812i	2.72057	−	6.56803i	5.71494	+	1.82741i	−5.53321	−	5.53321i	3.60958	+	7.13939i	−5.37299	−	7.22018i	−13.8221	−	3.33365i
5.16	0.310806	+	1.97570i	2.84782	+	0.943351i	−3.80680	+	1.22812i	−2.72057	+	6.56803i	−0.978660	+	5.91965i	−5.53321	−	5.53321i	−3.60958	−	7.13939i	7.22018	+	5.37299i	−13.8221	−	3.33365i
5.17	0.369569	−	1.96556i	2.79336	−	1.09413i	−3.72684	−	1.45282i	0.710186	−	1.71454i	−1.11823	−	5.89488i	−3.31956	−	3.31956i	−4.23292	+	6.78840i	6.60576	−	6.11260i	−3.10757	−	2.02955i
5.18	0.503078	−	1.93569i	−2.39365	+	1.80844i	−3.49383	−	1.94761i	−2.54567	+	6.14580i	2.29639	+	5.54316i	7.32134	+	7.32134i	−5.52764	+	5.78318i	2.45911	−	8.65753i	10.6157	+	8.01946i
5.19	0.576838	+	1.91501i	−1.55085	−	2.56805i	−3.33452	+	2.20930i	3.63719	−	8.78095i	4.02324	−	4.45124i	−5.54083	−	5.54083i	−6.15430	−	5.11122i	−4.18972	+	7.96531i	18.9137	+	1.90006i
5.20	0.896196	+	1.78797i	−0.286103	+	2.98633i	−2.39366	+	3.20474i	0.794982	−	1.91926i	−5.59586	+	2.16479i	4.69711	+	4.69711i	−7.87517	−	1.40772i	−8.83629	−	1.70880i	4.14403	−	0.298628i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
3.b	odd	2	1	inner
32.g	even	8	1	inner
96.p	odd	8	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	96.3.p.a	✓	120
3.b	odd	2	1	inner	96.3.p.a	✓	120
4.b	odd	2	1		384.3.p.a		120
12.b	even	2	1		384.3.p.a		120
32.g	even	8	1	inner	96.3.p.a	✓	120
32.h	odd	8	1		384.3.p.a		120
96.o	even	8	1		384.3.p.a		120
96.p	odd	8	1	inner	96.3.p.a	✓	120

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
96.3.p.a	✓	120	1.a	even	1	1	trivial
96.3.p.a	✓	120	3.b	odd	2	1	inner
96.3.p.a	✓	120	32.g	even	8	1	inner
96.3.p.a	✓	120	96.p	odd	8	1	inner
384.3.p.a		120	4.b	odd	2	1
384.3.p.a		120	12.b	even	2	1
384.3.p.a		120	32.h	odd	8	1
384.3.p.a		120	96.o	even	8	1

Hecke kernels

This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(96, [\chi])\).