Newform orbit 368.3.v.a

• Label: 368.3.v.a
• Level: $368$
• Weight: $3$
• Character orbit: 368.v
• Analytic conductor: $10.027$
• Analytic rank: $0$
• Dimension: $1880$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 368 = 2^{4} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	368.v (of order \(44\), degree \(20\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(10.0272737285\)
Analytic rank:	\(0\)
Dimension:	\(1880\)
Relative dimension:	\(94\) over \(\Q(\zeta_{44})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 1880 q - 18 q^{2} - 18 q^{3} - 6 q^{4} - 22 q^{5} - 24 q^{6} - 18 q^{8}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
5.1	−1.99866	+	0.0732790i	0.278870	+	3.89911i	3.98926	−	0.292919i	−3.40401	−	4.54722i	−0.843088	−	7.77254i	−4.72083	−	10.3372i	−7.95170	+	0.877774i	−6.21688	+	0.893852i	7.13666	+	8.83889i
5.2	−1.99574	+	0.130451i	−0.357948	−	5.00476i	3.96597	−	0.520691i	3.32974	+	4.44801i	1.36725	+	9.94152i	1.42980	+	3.13082i	−7.84712	+	1.55653i	−16.0112	+	2.30206i	−7.22555	−	8.44272i
5.3	−1.99447	−	0.148577i	0.388837	+	5.43666i	3.95585	+	0.592668i	−2.80954	−	3.75311i	0.0322389	−	10.9010i	2.99409	+	6.55615i	−7.80178	−	1.76981i	−20.4977	+	2.94712i	5.04593	+	7.90292i
5.4	−1.98354	+	0.256098i	0.0694366	+	0.970850i	3.86883	−	1.01596i	0.750260	+	1.00223i	−0.386362	−	1.90793i	5.35949	+	11.7356i	−7.41377	+	3.00599i	7.97066	−	1.14601i	−1.74484	−	1.79582i
5.5	−1.98194	−	0.268136i	0.328080	+	4.58716i	3.85621	+	1.06286i	4.15253	+	5.54713i	0.579745	−	9.17947i	−0.255004	−	0.558381i	−7.35780	−	3.14051i	−12.0260	+	1.72908i	−6.74270	−	12.1075i
5.6	−1.97867	+	0.291350i	0.0597880	+	0.835945i	3.83023	−	1.15297i	−5.64476	−	7.54052i	−0.361853	−	1.63664i	2.30550	+	5.04835i	−7.24283	+	3.39727i	8.21316	−	1.18087i	13.3660	+	13.2756i
5.7	−1.97474	−	0.316838i	−0.0162966	−	0.227856i	3.79923	+	1.25135i	4.32728	+	5.78056i	−0.0400118	+	0.455120i	−0.345159	−	0.755793i	−7.10603	−	3.67483i	8.85674	−	1.27341i	−6.71376	−	12.7862i
5.8	−1.94271	−	0.475273i	−0.130980	−	1.83134i	3.54823	+	1.84663i	−1.55775	−	2.08091i	−0.615930	+	3.62001i	−0.0509682	−	0.111605i	−6.01553	−	5.27385i	5.57174	−	0.801096i	2.03726	+	4.78296i
5.9	−1.94032	−	0.484923i	−0.269026	−	3.76147i	3.52970	+	1.88181i	−1.63461	−	2.18358i	−1.30203	+	7.42892i	4.31247	+	9.44299i	−5.93622	−	5.36296i	−5.16789	+	0.743030i	2.11280	+	5.02951i
5.10	−1.93627	+	0.500870i	0.0353987	+	0.494938i	3.49826	−	1.93964i	2.44200	+	3.26213i	−0.316441	−	0.940602i	−1.85171	−	4.05469i	−5.80205	+	5.50783i	8.66468	−	1.24579i	−6.36226	−	5.09322i
5.11	−1.92316	+	0.549064i	−0.191786	−	2.68152i	3.39706	−	2.11187i	−3.08310	−	4.11854i	1.84116	+	5.05167i	−3.83439	−	8.39614i	−5.37352	+	5.92666i	1.75464	−	0.252279i	8.19062	+	6.22777i
5.12	−1.90510	+	0.608753i	−0.248509	−	3.47461i	3.25884	−	2.31948i	1.15977	+	1.54927i	2.58861	+	6.46821i	−2.77955	−	6.08636i	−4.79644	+	6.40267i	−3.10275	+	0.446109i	−3.15260	−	2.24551i
5.13	−1.78851	−	0.895113i	0.0320675	+	0.448363i	2.39755	+	3.20184i	0.0158155	+	0.0211270i	0.343982	−	0.830606i	−4.57169	−	10.0106i	−1.42203	−	7.87260i	8.70839	−	1.25208i	−0.00937510	−	0.0519425i
5.14	−1.75697	−	0.955537i	−0.409385	−	5.72396i	2.17390	+	3.35770i	−2.05604	−	2.74655i	−4.75017	+	10.4480i	−4.31601	−	9.45075i	−0.611068	−	7.97663i	−23.6877	+	3.40578i	0.987977	+	6.79024i
5.15	−1.75643	+	0.956526i	0.256408	+	3.58505i	2.17012	−	3.36015i	1.68130	+	2.24596i	−3.87956	−	6.05164i	2.42562	+	5.31138i	−0.597591	+	7.97765i	−3.87845	+	0.557636i	−5.10141	−	2.33666i
5.16	−1.71503	+	1.02891i	−0.396307	−	5.54109i	1.88268	−	3.52924i	−4.30816	−	5.75503i	6.38098	+	9.09539i	3.00404	+	6.57794i	0.402430	+	7.98987i	−21.6383	+	3.11111i	13.3101	+	5.43734i
5.17	−1.71423	−	1.03025i	0.140836	+	1.96914i	1.87716	+	3.53218i	−2.63565	−	3.52082i	1.78729	−	3.52066i	1.22569	+	2.68389i	0.421168	−	7.98891i	5.05071	−	0.726182i	0.890773	+	8.75088i
5.18	−1.69655	−	1.05911i	−0.231368	−	3.23494i	1.75655	+	3.59368i	5.29977	+	7.07966i	−3.03365	+	5.73328i	−1.85050	−	4.05204i	0.826045	−	7.95724i	−1.50294	+	0.216090i	−1.49314	−	17.6241i
5.19	−1.69480	+	1.06191i	0.273850	+	3.82893i	1.74469	−	3.59945i	0.457927	+	0.611718i	−4.53010	−	6.19845i	−3.10616	−	6.80154i	0.865412	+	7.95305i	−5.67729	+	0.816271i	−1.42568	−	0.550462i
5.20	−1.57011	−	1.23885i	0.351961	+	4.92106i	0.930502	+	3.89027i	−1.17883	−	1.57473i	5.54384	−	8.16264i	1.34917	+	2.95427i	3.35846	−	7.26090i	−15.1846	+	2.18321i	−0.0999617	+	3.93288i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
16.e	even	4	1	inner
23.d	odd	22	1	inner
368.v	odd	44	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	368.3.v.a	✓	1880
16.e	even	4	1	inner	368.3.v.a	✓	1880
23.d	odd	22	1	inner	368.3.v.a	✓	1880
368.v	odd	44	1	inner	368.3.v.a	✓	1880

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
368.3.v.a	✓	1880	1.a	even	1	1	trivial
368.3.v.a	✓	1880	16.e	even	4	1	inner
368.3.v.a	✓	1880	23.d	odd	22	1	inner
368.3.v.a	✓	1880	368.v	odd	44	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(368, [\chi])\).