Newform orbit 96.3.m.a

• Label: 96.3.m.a
• Level: $96$
• Weight: $3$
• Character orbit: 96.m
• Analytic conductor: $2.616$
• Analytic rank: $0$
• Dimension: $64$
• CM: no
• Inner twists: $2$

Newspace parameters

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

Newform invariants

Self dual:	no
Analytic conductor:	\(2.61581053786\)
Analytic rank:	\(0\)
Dimension:	\(64\)
Relative dimension:	\(16\) 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.

\(\operatorname{Tr}(f)(q) = \) \( 64 q+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
19.1	−1.97063	−	0.341475i	−1.60021	−	0.662827i	3.76679	+	1.34584i	−2.29382	+	0.950132i	2.92708	+	1.85262i	3.26583	+	3.26583i	−6.96339	−	3.93843i	2.12132	+	2.12132i	4.84473	−	1.08908i
19.2	−1.92437	−	0.544810i	1.60021	+	0.662827i	3.40636	+	2.09683i	−8.76568	+	3.63086i	−2.71827	−	2.14733i	−4.20494	−	4.20494i	−5.41272	−	5.89088i	2.12132	+	2.12132i	18.8465	−	2.21148i
19.3	−1.84914	+	0.762031i	1.60021	+	0.662827i	2.83862	−	2.81820i	6.06733	−	2.51317i	−3.46410	−	0.00625081i	−9.25703	−	9.25703i	−3.10143	+	7.37436i	2.12132	+	2.12132i	−9.30421	+	9.27069i
19.4	−1.49565	−	1.32779i	−1.60021	−	0.662827i	0.473939	+	3.97182i	5.66092	−	2.34483i	1.51325	+	3.11610i	−8.77775	−	8.77775i	4.56491	−	6.56975i	2.12132	+	2.12132i	−11.5802	−	4.00947i
19.5	−1.46158	+	1.36521i	1.60021	+	0.662827i	0.272417	−	3.99071i	−1.99171	+	0.824993i	−3.24372	+	1.21584i	8.28172	+	8.28172i	5.04999	+	6.20464i	2.12132	+	2.12132i	1.78475	−	3.92489i
19.6	−1.19507	−	1.60369i	1.60021	+	0.662827i	−1.14363	+	3.83303i	2.44597	−	1.01315i	−0.849386	−	3.35835i	3.89082	+	3.89082i	7.51370	−	2.74670i	2.12132	+	2.12132i	−4.54788	−	2.71179i
19.7	−0.795895	+	1.83482i	−1.60021	−	0.662827i	−2.73310	−	2.92064i	6.54910	−	2.71273i	2.48976	−	2.40854i	1.95699	+	1.95699i	7.53410	−	2.69022i	2.12132	+	2.12132i	−0.235042	+	14.1754i
19.8	−0.712728	−	1.86869i	−1.60021	−	0.662827i	−2.98404	+	2.66374i	−4.75081	+	1.96785i	−0.0981101	+	3.46271i	5.89664	+	5.89664i	7.10452	+	3.67773i	2.12132	+	2.12132i	7.06335	+	7.47527i
19.9	0.408652	+	1.95781i	−1.60021	−	0.662827i	−3.66601	+	1.60012i	−4.62667	+	1.91643i	0.643760	−	3.40376i	−2.45923	−	2.45923i	−4.63085	−	6.52344i	2.12132	+	2.12132i	−5.64269	−	8.27497i
19.10	0.729010	+	1.86240i	1.60021	+	0.662827i	−2.93709	+	2.71542i	8.33737	−	3.45345i	−0.0678852	+	3.46344i	1.00716	+	1.00716i	−7.19837	−	3.49048i	2.12132	+	2.12132i	12.5098	+	13.0099i
19.11	0.948970	−	1.76053i	−1.60021	−	0.662827i	−2.19891	−	3.34138i	−4.89089	+	2.02587i	−2.68547	+	2.18820i	−6.40097	−	6.40097i	−7.96928	+	0.700377i	2.12132	+	2.12132i	−1.07471	+	10.5330i
19.12	1.02518	+	1.71727i	1.60021	+	0.662827i	−1.89801	+	3.52102i	−7.00900	+	2.90322i	0.502250	+	3.42750i	2.35957	+	2.35957i	−7.99233	+	0.350291i	2.12132	+	2.12132i	−12.1711	−	9.05999i
19.13	1.32170	−	1.50104i	1.60021	+	0.662827i	−0.506212	−	3.96784i	2.17599	−	0.901324i	3.10992	−	1.52591i	0.825541	+	0.825541i	−6.62493	−	4.48446i	2.12132	+	2.12132i	1.52309	−	4.45751i
19.14	1.64362	+	1.13952i	−1.60021	−	0.662827i	1.40297	+	3.74589i	0.838363	−	0.347262i	−1.87482	−	2.91291i	8.29065	+	8.29065i	−1.96258	+	7.75553i	2.12132	+	2.12132i	1.77366	+	0.384569i
19.15	1.92938	−	0.526758i	−1.60021	−	0.662827i	3.44505	−	2.03264i	3.51382	−	1.45547i	−3.43656	−	0.435928i	−1.77216	−	1.77216i	5.57613	−	5.73645i	2.12132	+	2.12132i	6.01282	−	4.65909i
19.16	1.98432	+	0.249937i	1.60021	+	0.662827i	3.87506	+	0.991913i	−1.26028	+	0.522023i	3.00966	+	1.71521i	−2.90283	−	2.90283i	7.44145	+	2.93680i	2.12132	+	2.12132i	−2.63126	+	0.720872i
43.1	−1.99199	−	0.178809i	0.662827	+	1.60021i	3.93605	+	0.712374i	−1.28772	+	3.10884i	−1.03421	−	3.30612i	0.299204	−	0.299204i	−7.71320	−	2.12285i	−2.12132	+	2.12132i	3.12102	−	5.96252i
43.2	−1.99038	−	0.195968i	−0.662827	−	1.60021i	3.92319	+	0.780100i	−0.862642	+	2.08260i	1.00569	+	3.31491i	6.00123	−	6.00123i	−7.65575	−	2.32151i	−2.12132	+	2.12132i	2.12510	−	3.97611i
43.3	−1.48044	+	1.34472i	−0.662827	−	1.60021i	0.383430	−	3.98158i	−0.872612	+	2.10667i	3.13312	+	1.47770i	−6.43807	+	6.43807i	4.78648	+	6.41012i	−2.12132	+	2.12132i	−1.54104	−	4.29223i
43.4	−1.37677	−	1.45069i	−0.662827	−	1.60021i	−0.209027	+	3.99453i	−1.48548	+	3.58626i	−1.40885	+	3.16467i	−7.09685	+	7.09685i	6.08263	−	5.19631i	−2.12132	+	2.12132i	7.24772	−	2.78247i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
32.h	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.m.a	✓	64
3.b	odd	2	1		288.3.u.b		64
4.b	odd	2	1		384.3.m.a		64
32.g	even	8	1		384.3.m.a		64
32.h	odd	8	1	inner	96.3.m.a	✓	64
96.o	even	8	1		288.3.u.b		64

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
96.3.m.a	✓	64	1.a	even	1	1	trivial
96.3.m.a	✓	64	32.h	odd	8	1	inner
288.3.u.b		64	3.b	odd	2	1
288.3.u.b		64	96.o	even	8	1
384.3.m.a		64	4.b	odd	2	1
384.3.m.a		64	32.g	even	8	1

Hecke kernels

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