Newform orbit 273.2.y.b

• Label: 273.2.y.b
• Level: $273$
• Weight: $2$
• Character orbit: 273.y
• Analytic conductor: $2.180$
• Analytic rank: $0$
• Dimension: $64$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.y (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(2.17991597518\)
Analytic rank:	\(0\)
Dimension:	\(64\)
Relative dimension:	\(32\) 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.

\(\operatorname{Tr}(f)(q) = \) \( 64 q - 28 q^{4} - 12 q^{7}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
101.1	−1.30618	+	2.26238i	−1.71658	+	0.230971i	−2.41223	−	4.17810i	0.648305	−	0.374299i	1.71963	−	4.18524i	−2.44285	−	1.01610i	7.37851			2.89330	−	0.792960i			1.95561i
101.2	−1.30520	+	2.26068i	1.39879	−	1.02146i	−2.40711	−	4.16923i	−1.65792	+	0.957199i	0.483493	+	4.49543i	2.51605	−	0.818240i	7.34624			0.913228	−	2.85762i		−	4.99736i
101.3	−1.18406	+	2.05084i	−0.641138	−	1.60902i	−1.80398	−	3.12458i	0.0190083	−	0.0109745i	4.05899	+	0.590294i	0.134389	+	2.64234i	3.80781			−2.17788	+	2.06321i			0.0519775i
101.4	−1.14404	+	1.98153i	−0.240189	+	1.71532i	−1.61764	−	2.80184i	−3.02328	+	1.74549i	−3.12417	−	2.43833i	0.229018	+	2.63582i	2.82644			−2.88462	−	0.824000i		−	7.98764i
101.5	−1.06779	+	1.84947i	1.37855	−	1.04862i	−1.28036	−	2.21764i	3.07271	−	1.77403i	0.467389	+	3.66929i	−2.57290	−	0.616608i	1.19745			0.800790	−	2.89115i			7.57717i
101.6	−0.985417	+	1.70679i	−0.524054	+	1.65087i	−0.942093	−	1.63175i	−0.0906165	+	0.0523174i	−2.30128	−	2.52124i	0.412313	−	2.61343i	−0.228249			−2.45074	−	1.73029i		−	0.206218i
101.7	−0.884751	+	1.53243i	−1.73022	−	0.0796811i	−0.565569	−	0.979594i	1.27320	−	0.735080i	1.65292	−	2.58094i	2.56619	+	0.643937i	−1.53745			2.98730	+	0.275731i			2.60145i
101.8	−0.799109	+	1.38410i	1.59038	+	0.686061i	−0.277151	−	0.480040i	1.21627	−	0.702213i	−2.22047	+	1.65301i	2.53934	−	0.742795i	−2.31054			2.05864	+	2.18220i			2.24458i
101.9	−0.760690	+	1.31755i	0.347458	−	1.69684i	−0.157299	−	0.272450i	−1.84777	+	1.06681i	1.97137	+	1.74857i	−2.06030	−	1.65987i	−2.56414			−2.75855	−	1.17916i		−	3.24606i
101.10	−0.638569	+	1.10603i	1.72991	−	0.0860586i	0.184460	+	0.319495i	−2.29307	+	1.32390i	−1.00948	+	1.96829i	−0.551092	+	2.58772i	−3.02544			2.98519	−	0.297747i		−	3.38161i
101.11	−0.636825	+	1.10301i	0.696603	+	1.58579i	0.188907	+	0.327197i	1.93046	−	1.11455i	−2.19277	−	0.241511i	−2.30379	+	1.30098i	−3.02850			−2.02949	+	2.20934i			2.83909i
101.12	−0.491530	+	0.851355i	−0.901093	−	1.47920i	0.516796	+	0.895118i	1.05876	−	0.611275i	1.70224	−	0.0400792i	0.826182	−	2.51345i	−2.98220			−1.37606	+	2.66579i			1.20184i
101.13	−0.366273	+	0.634404i	−1.53905	+	0.794556i	0.731688	+	1.26732i	−2.08780	+	1.20539i	0.0596442	−	1.26741i	−2.55085	−	0.702242i	−2.53708			1.73736	−	2.44573i		−	1.76601i
101.14	−0.209784	+	0.363356i	0.760555	−	1.55614i	0.911982	+	1.57960i	3.21070	−	1.85370i	0.405879	+	0.602804i	2.20704	+	1.45910i	−1.60441			−1.84311	−	2.36705i			1.55550i
101.15	−0.183709	+	0.318193i	−1.40902	−	1.00730i	0.932502	+	1.61514i	0.333187	−	0.192366i	0.579367	−	0.263290i	−1.67893	+	2.04479i	−1.42007			0.970675	+	2.83862i			0.141357i
101.16	−0.0381512	+	0.0660798i	1.25975	+	1.18871i	0.997089	+	1.72701i	−3.58354	+	2.06896i	−0.126611	+	0.0378937i	−0.269802	−	2.63196i	−0.304765			0.173957	+	2.99495i		−	0.315733i
101.17	0.0381512	−	0.0660798i	−1.25975	+	1.18871i	0.997089	+	1.72701i	3.58354	−	2.06896i	0.0304884	+	0.128595i	−0.269802	−	2.63196i	0.304765			0.173957	−	2.99495i		−	0.315733i
101.18	0.183709	−	0.318193i	1.40902	−	1.00730i	0.932502	+	1.61514i	−0.333187	+	0.192366i	−0.0616679	−	0.633392i	−1.67893	+	2.04479i	1.42007			0.970675	−	2.83862i			0.141357i
101.19	0.209784	−	0.363356i	−0.760555	−	1.55614i	0.911982	+	1.57960i	−3.21070	+	1.85370i	−0.724983	−	0.0500996i	2.20704	+	1.45910i	1.60441			−1.84311	+	2.36705i			1.55550i
101.20	0.366273	−	0.634404i	1.53905	+	0.794556i	0.731688	+	1.26732i	2.08780	−	1.20539i	1.06778	−	0.685356i	−2.55085	−	0.702242i	2.53708			1.73736	+	2.44573i		−	1.76601i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
3.b	odd	2	1	inner
91.p	odd	6	1	inner
273.y	even	6	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	273.2.y.b	✓	64
3.b	odd	2	1	inner	273.2.y.b	✓	64
7.d	odd	6	1		273.2.br.b	yes	64
13.e	even	6	1		273.2.br.b	yes	64
21.g	even	6	1		273.2.br.b	yes	64
39.h	odd	6	1		273.2.br.b	yes	64
91.p	odd	6	1	inner	273.2.y.b	✓	64
273.y	even	6	1	inner	273.2.y.b	✓	64

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
273.2.y.b	✓	64	1.a	even	1	1	trivial
273.2.y.b	✓	64	3.b	odd	2	1	inner
273.2.y.b	✓	64	91.p	odd	6	1	inner
273.2.y.b	✓	64	273.y	even	6	1	inner
273.2.br.b	yes	64	7.d	odd	6	1
273.2.br.b	yes	64	13.e	even	6	1
273.2.br.b	yes	64	21.g	even	6	1
273.2.br.b	yes	64	39.h	odd	6	1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T2^64 + 46*T2^62 + 1166*T2^60 + 20406*T2^58 + 272289*T2^56 + 2909665*T2^54 + 25681983*T2^52 + 190913074*T2^50 + 1211595988*T2^48 + 6624520229*T2^46 + 31405848771*T2^44 + 129628056147*T2^42 + 466986679456*T2^40 + 1469721086403*T2^38 + 4040064579103*T2^36 + 9684581726794*T2^34 + 20190317494068*T2^32 + 36455511496312*T2^30 + 56695793379151*T2^28 + 75377651356596*T2^26 + 84875363641672*T2^24 + 79932727406078*T2^22 + 62019660932995*T2^20 + 38829494986515*T2^18 + 19171003716275*T2^16 + 7198860548134*T2^14 + 2002517535904*T2^12 + 383499973607*T2^10 + 52672506167*T2^8 + 4462331843*T2^6 + 239056184*T2^4 + 1381845*T2^2 + 7225