Newform orbit 224.3.w.a

• Label: 224.3.w.a
• Level: $224$
• Weight: $3$
• Character orbit: 224.w
• Analytic conductor: $6.104$
• Analytic rank: $0$
• Dimension: $192$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 224 = 2^{5} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	224.w (of order \(8\), degree \(4\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(6.10355792167\)
Analytic rank:	\(0\)
Dimension:	\(192\)
Relative dimension:	\(48\) 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.

\(\operatorname{Tr}(f)(q) = \) \( 192 q+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
43.1	−1.99992	−	0.0176912i	−0.954366	−	2.30404i	3.99937	+	0.0707620i	−0.872291	+	2.10590i	1.86790	+	4.62479i	−1.87083	+	1.87083i	−7.99718	−	0.212272i	1.96616	−	1.96616i	1.78177	−	4.19620i
43.2	−1.99845	−	0.0786486i	1.73419	+	4.18671i	3.98763	+	0.314351i	−2.33059	+	5.62654i	−3.13642	−	8.50332i	−1.87083	+	1.87083i	−7.94437	−	0.941838i	−8.15712	+	8.15712i	5.10010	−	11.0611i
43.3	−1.99185	−	0.180328i	0.825363	+	1.99260i	3.93496	+	0.718374i	0.360772	−	0.870982i	−1.28468	−	4.11781i	1.87083	−	1.87083i	−7.70833	−	2.14048i	3.07472	−	3.07472i	−0.875668	+	1.66981i
43.4	−1.92658	+	0.536908i	−0.340996	−	0.823236i	3.42346	−	2.06880i	−1.83063	+	4.41953i	1.09896	+	1.40295i	1.87083	−	1.87083i	−5.48483	+	5.82380i	5.80252	−	5.80252i	1.15398	−	9.49749i
43.5	−1.86971	−	0.710051i	0.216404	+	0.522445i	2.99165	+	2.65518i	2.53768	−	6.12651i	−0.0336503	−	1.13048i	1.87083	−	1.87083i	−3.70822	−	7.08866i	6.13784	−	6.13784i	−9.09487	+	9.65293i
43.6	−1.86483	−	0.722783i	−1.45943	−	3.52338i	2.95517	+	2.69573i	−3.21097	+	7.75196i	0.174951	+	7.62534i	1.87083	−	1.87083i	−3.56245	−	7.16302i	−3.92028	+	3.92028i	11.5909	−	12.1352i
43.7	−1.80532	+	0.860701i	1.98167	+	4.78418i	2.51839	−	3.10769i	1.28939	−	3.11286i	−7.69530	−	6.93136i	1.87083	−	1.87083i	−1.87171	+	7.77796i	−12.5974	+	12.5974i	0.351479	+	6.72950i
43.8	−1.75066	−	0.967050i	−1.86844	−	4.51082i	2.12963	+	3.38595i	0.599529	−	1.44739i	−1.09118	+	9.70379i	−1.87083	+	1.87083i	−0.453865	−	7.98712i	−10.4924	+	10.4924i	−2.44927	+	1.95412i
43.9	−1.72313	+	1.01530i	0.819473	+	1.97838i	1.93834	−	3.49898i	1.60646	−	3.87835i	−3.42071	−	2.57700i	−1.87083	+	1.87083i	0.212503	+	7.99718i	3.12150	−	3.12150i	1.16954	+	8.31393i
43.10	−1.70535	−	1.04488i	0.502742	+	1.21373i	1.81645	+	3.56377i	−0.0438594	+	0.105886i	0.410845	−	2.59514i	−1.87083	+	1.87083i	0.626019	−	7.97547i	5.14358	−	5.14358i	0.185434	−	0.134745i
43.11	−1.55094	+	1.26277i	−1.89928	−	4.58527i	0.810816	−	3.91696i	−2.09096	+	5.04803i	8.73581	+	4.71311i	−1.87083	+	1.87083i	3.68870	+	7.09884i	−11.0535	+	11.0535i	−3.13156	−	10.4696i
43.12	−1.49125	−	1.33273i	−1.51777	−	3.66421i	0.447645	+	3.97487i	2.18754	−	5.28118i	−2.62005	+	7.48703i	1.87083	−	1.87083i	4.62989	−	6.52412i	−4.75887	+	4.75887i	−10.3006	+	4.96015i
43.13	−1.40435	+	1.42401i	−1.23085	−	2.97155i	−0.0555981	−	3.99961i	0.908665	−	2.19371i	5.96006	+	2.42035i	1.87083	−	1.87083i	5.77356	+	5.53769i	−0.951124	+	0.951124i	1.84778	+	4.37468i
43.14	−1.34412	−	1.48100i	1.15434	+	2.78683i	−0.386709	+	3.98126i	−3.15510	+	7.61708i	2.57571	−	5.45539i	1.87083	−	1.87083i	6.41602	−	4.77856i	−0.0699303	+	0.0699303i	15.5217	−	5.56554i
43.15	−1.03112	+	1.71371i	0.406888	+	0.982314i	−1.87359	−	3.53407i	0.691237	−	1.66879i	−2.10295	−	0.315595i	−1.87083	+	1.87083i	7.98826	+	0.433260i	5.56458	−	5.56458i	2.14708	+	2.90530i
43.16	−1.00544	−	1.72890i	−0.343872	−	0.830180i	−1.97818	+	3.47661i	−1.68929	+	4.07830i	−1.08955	+	1.42922i	−1.87083	+	1.87083i	7.99964	−	0.0754426i	5.79301	−	5.79301i	8.74944	−	1.17988i
43.17	−0.703873	−	1.87205i	0.0651792	+	0.157357i	−3.00913	+	2.63537i	3.56366	−	8.60344i	0.248701	−	0.232778i	−1.87083	+	1.87083i	7.05157	+	3.77827i	6.34345	−	6.34345i	−18.6144	−	0.615620i
43.18	−0.521176	+	1.93090i	1.24651	+	3.00935i	−3.45675	−	2.01268i	3.27130	−	7.89762i	−6.46041	+	0.838495i	1.87083	−	1.87083i	5.68785	−	5.62569i	−1.13845	+	1.13845i	13.5446	+	10.4326i
43.19	−0.518278	+	1.93168i	−0.266183	−	0.642623i	−3.46277	−	2.00230i	−0.747592	+	1.80485i	1.37930	−	0.181123i	1.87083	−	1.87083i	5.66248	−	5.65123i	6.02185	−	6.02185i	−3.09892	−	2.37952i
43.20	−0.491313	+	1.93871i	−1.80355	−	4.35417i	−3.51722	−	1.90503i	3.60551	−	8.70447i	9.32759	−	1.35732i	−1.87083	+	1.87083i	5.42137	−	5.88292i	−9.34199	+	9.34199i	15.1040	+	11.2667i

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	224.3.w.a	✓	192
32.h	odd	8	1	inner	224.3.w.a	✓	192

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
224.3.w.a	✓	192	1.a	even	1	1	trivial
224.3.w.a	✓	192	32.h	odd	8	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(224, [\chi])\).