Newform orbit 203.3.i.a

• Label: 203.3.i.a
• Level: $203$
• Weight: $3$
• Character orbit: 203.i
• Analytic conductor: $5.531$
• Analytic rank: $0$
• Dimension: $76$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 203 = 7 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	203.i (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(5.53134936651\)
Analytic rank:	\(0\)
Dimension:	\(76\)
Relative dimension:	\(38\) over \(\Q(\zeta_{6})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 76 q + 64 q^{4} - 6 q^{5} - 12 q^{7} - 116 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
115.1	−3.36740	+	1.94417i	1.20954	−	2.09498i	5.55960	−	9.62950i	−0.929189	+	0.536468i			9.40621i	4.26365	−	5.55169i			27.6819i	1.57403	+	2.72629i	2.08597	−	3.61300i
115.2	−3.25653	+	1.88016i	−1.80431	+	3.12516i	5.06999	−	8.78148i	−4.47307	+	2.58253i		−	13.5696i	−4.29771	+	5.52537i			23.0882i	−2.01109	−	3.48331i	9.71113	−	16.8202i
115.3	−2.81256	+	1.62383i	−0.770122	+	1.33389i	3.27367	−	5.67017i	3.06569	−	1.76998i		−	5.00220i	−5.85179	−	3.84142i			8.27293i	3.31382	+	5.73971i	−5.74830	+	9.95635i
115.4	−2.81052	+	1.62266i	2.55587	−	4.42689i	3.26603	−	5.65693i	−3.40195	+	1.96412i			16.5892i	−5.02100	+	4.87746i			8.21732i	−8.56491	−	14.8349i	6.37417	−	11.0404i
115.5	−2.79463	+	1.61348i	1.41569	−	2.45205i	3.20664	−	5.55406i	6.94648	−	4.01055i			9.13678i	0.0982754	+	6.99931i			7.78756i	0.491619	+	0.851510i	−12.9419	+	22.4160i
115.6	−2.75567	+	1.59098i	−1.54266	+	2.67196i	3.06246	−	5.30434i	0.876658	−	0.506139i		−	9.81739i	5.64064	+	4.14526i			6.76145i	−0.259596	−	0.449633i	−1.61052	+	2.78950i
115.7	−2.27101	+	1.31117i	−2.54666	+	4.41094i	1.43833	−	2.49126i	−4.29223	+	2.47812i		−	13.3564i	3.88522	−	5.82280i		−	2.94579i	−8.47094	−	14.6721i	6.49847	−	11.2557i
115.8	−2.13772	+	1.23421i	0.485316	−	0.840593i	1.04657	−	1.81272i	−8.09956	+	4.67628i			2.39594i	−6.15229	−	3.33906i		−	4.70694i	4.02894	+	6.97832i	11.5431	−	19.9932i
115.9	−2.10154	+	1.21333i	0.807411	−	1.39848i	0.944318	−	1.63561i	−3.24085	+	1.87110i			3.91861i	6.99488	−	0.267582i		−	5.12354i	3.19618	+	5.53594i	4.54052	−	7.86440i
115.10	−1.79868	+	1.03847i	2.02836	−	3.51323i	0.156836	−	0.271648i	7.14004	−	4.12230i			8.42557i	0.788987	−	6.95539i		−	7.65628i	−3.72851	−	6.45798i	−8.56177	+	14.8294i
115.11	−1.65862	+	0.957602i	−2.97411	+	5.15131i	−0.165997	+	0.287514i	6.17764	−	3.56666i		−	11.3920i	−5.30634	+	4.56538i		−	8.29665i	−13.1906	−	22.8469i	−6.83088	+	11.8314i
115.12	−1.46623	+	0.846526i	−1.13989	+	1.97435i	−0.566789	+	0.981707i	4.48392	−	2.58879i		−	3.85978i	1.02358	−	6.92476i		−	8.69141i	1.90130	+	3.29315i	−4.38295	+	7.59150i
115.13	−1.43454	+	0.828233i	−0.201526	+	0.349054i	−0.628060	+	1.08783i	−0.827501	+	0.477758i		−	0.667643i	−2.43419	+	6.56313i		−	8.70658i	4.41877	+	7.65354i	0.791390	−	1.37073i
115.14	−1.31429	+	0.758805i	2.75518	−	4.77210i	−0.848430	+	1.46952i	−1.66644	+	0.962122i			8.36256i	6.85714	+	1.40701i		−	8.64561i	−10.6820	−	18.5017i	1.46013	−	2.52901i
115.15	−0.982250	+	0.567102i	0.925967	−	1.60382i	−1.35679	+	2.35003i	3.23082	−	1.86532i			2.10047i	−6.57485	+	2.40236i		−	7.61457i	2.78517	+	4.82406i	−2.11565	+	3.66441i
115.16	−0.675154	+	0.389800i	−1.82379	+	3.15889i	−1.69611	+	2.93775i	−6.97734	+	4.02837i		−	2.84365i	1.33070	+	6.87235i		−	5.76298i	−2.15241	−	3.72808i	3.14052	−	5.43953i
115.17	−0.484041	+	0.279461i	−1.31251	+	2.27333i	−1.84380	+	3.19356i	5.24426	−	3.02777i		−	1.46718i	6.40931	+	2.81439i		−	4.29678i	1.05466	+	1.82672i	−1.69229	+	2.93113i
115.18	−0.345652	+	0.199562i	2.20751	−	3.82351i	−1.92035	+	3.32614i	−1.32876	+	0.767159i			1.76214i	−6.23313	−	3.18561i		−	3.12941i	−5.24616	−	9.08662i	0.306192	−	0.530339i
115.19	−0.0532060	+	0.0307185i	−0.989507	+	1.71388i	−1.99811	+	3.46083i	−3.42861	+	1.97951i		−	0.121585i	1.57891	−	6.81961i		−	0.491264i	2.54175	+	4.40245i	0.121615	−	0.210644i
115.20	0.0532060	−	0.0307185i	0.989507	−	1.71388i	−1.99811	+	3.46083i	−3.42861	+	1.97951i		−	0.121585i	1.57891	−	6.81961i			0.491264i	2.54175	+	4.40245i	−0.121615	+	0.210644i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
7.d	odd	6	1	inner
29.b	even	2	1	inner
203.i	odd	6	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	203.3.i.a	✓	76
7.d	odd	6	1	inner	203.3.i.a	✓	76
29.b	even	2	1	inner	203.3.i.a	✓	76
203.i	odd	6	1	inner	203.3.i.a	✓	76

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
203.3.i.a	✓	76	1.a	even	1	1	trivial
203.3.i.a	✓	76	7.d	odd	6	1	inner
203.3.i.a	✓	76	29.b	even	2	1	inner
203.3.i.a	✓	76	203.i	odd	6	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(203, [\chi])\).