Newform orbit 273.2.br.b

• Label: 273.2.br.b
• Level: $273$
• Weight: $2$
• Character orbit: 273.br
• 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.br (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.

\(\operatorname{Tr}(f)(q) = \) \( 64 q - 6 q^{3} + 56 q^{4} - 6 q^{7}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
17.1	−2.61237			1.05832	+	1.37112i	4.82446			−0.648305	+	0.374299i	−2.76471	−	3.58186i	−2.10140	+	1.60752i	−7.37851			−0.759929	+	2.90216i	1.69361	−	0.977806i
17.2	−2.61040			−1.58401	−	0.700656i	4.81421			1.65792	−	0.957199i	4.13490	+	1.82900i	0.549406	−	2.58808i	−7.34624			2.01816	+	2.21969i	−4.32784	+	2.49868i
17.3	−2.36811			−1.07288	+	1.35975i	3.60795			−0.0190083	+	0.0109745i	2.54070	−	3.22004i	2.35552	+	1.20478i	−3.80781			−0.697847	−	2.91771i	0.0450138	−	0.0259887i
17.4	−2.28808			1.60560	−	0.649648i	3.23529			3.02328	−	1.74549i	−3.67374	+	1.48644i	2.39720	+	1.11958i	−2.82644			2.15591	−	2.08615i	−6.91750	+	3.99382i
17.5	−2.13558			−1.59741	−	0.669547i	2.56071			−3.07271	+	1.77403i	3.41139	+	1.42987i	−1.82045	+	1.91989i	−1.19745			2.10341	+	2.13908i	6.56202	−	3.78859i
17.6	−1.97083			1.69172	−	0.371591i	1.88419			0.0906165	−	0.0523174i	−3.33410	+	0.732343i	−2.05714	−	1.66379i	0.228249			2.72384	−	1.25726i	−0.178590	+	0.103109i
17.7	−1.76950			0.796103	+	1.53825i	1.13114			−1.27320	+	0.735080i	−1.40871	−	2.72194i	1.84076	−	1.90042i	1.53745			−1.73244	+	2.44921i	2.25292	−	1.30072i
17.8	−1.59822			−0.201046	−	1.72034i	0.554302			−1.21627	+	0.702213i	0.321315	+	2.74948i	0.626391	−	2.57053i	2.31054			−2.91916	+	0.691736i	1.94386	−	1.12229i
17.9	−1.52138			−1.64324	+	0.547514i	0.314598			1.84777	−	1.06681i	2.49999	−	0.832977i	−2.46764	+	0.954340i	2.56414			2.40046	−	1.79939i	−2.81117	+	1.62303i
17.10	−1.27714			−0.939485	−	1.45512i	−0.368921			2.29307	−	1.32390i	1.19985	+	1.85839i	1.96549	+	1.77112i	3.02544			−1.23474	+	2.73412i	−2.92856	+	1.69081i
17.11	−1.27365			1.02504	−	1.39617i	−0.377814			−1.93046	+	1.11455i	−1.30554	+	1.77824i	−0.0252117	+	2.64563i	3.02850			−0.898600	−	2.86226i	2.45873	−	1.41955i
17.12	−0.983060			−0.830478	+	1.51997i	−1.03359			−1.05876	+	0.611275i	0.816410	−	1.49422i	−1.76362	−	1.97222i	2.98220			−1.62061	−	2.52460i	1.04082	−	0.600920i
17.13	−0.732547			1.45763	+	0.935580i	−1.46338			2.08780	−	1.20539i	−1.06778	−	0.685356i	−1.88359	+	1.85798i	2.53708			1.24938	+	2.72746i	−1.52941	+	0.883004i
17.14	−0.419567			−1.72793	+	0.119408i	−1.82396			−3.21070	+	1.85370i	0.724983	−	0.0500996i	2.36714	−	1.18181i	1.60441			2.97148	−	0.412657i	1.34710	−	0.777750i
17.15	−0.367418			−0.167841	+	1.72390i	−1.86500			−0.333187	+	0.192366i	0.0616679	−	0.633392i	0.931377	+	2.47640i	1.42007			−2.94366	−	0.578683i	0.122419	−	0.0706787i
17.16	−0.0763024			0.399573	−	1.68533i	−1.99418			3.58354	−	2.06896i	−0.0304884	+	0.128595i	−2.41424	−	1.08232i	0.304765			−2.68068	−	1.34683i	−0.273433	+	0.157867i
17.17	0.0763024			1.65933	+	0.496625i	−1.99418			−3.58354	+	2.06896i	0.126611	+	0.0378937i	−2.41424	−	1.08232i	−0.304765			2.50673	+	1.64813i	−0.273433	+	0.157867i
17.18	0.367418			−1.57686	−	0.716595i	−1.86500			0.333187	−	0.192366i	−0.579367	−	0.263290i	0.931377	+	2.47640i	−1.42007			1.97298	+	2.25994i	0.122419	−	0.0706787i
17.19	0.419567			−0.967375	+	1.43673i	−1.82396			3.21070	−	1.85370i	−0.405879	+	0.602804i	2.36714	−	1.18181i	−1.60441			−1.12837	−	2.77971i	1.34710	−	0.777750i
17.20	0.732547			−0.0814203	−	1.73014i	−1.46338			−2.08780	+	1.20539i	−0.0596442	−	1.26741i	−1.88359	+	1.85798i	−2.53708			−2.98674	+	0.281736i	−1.52941	+	0.883004i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
3.b	odd	2	1	inner
91.l	odd	6	1	inner
273.br	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.br.b	yes	64
3.b	odd	2	1	inner	273.2.br.b	yes	64
7.d	odd	6	1		273.2.y.b	✓	64
13.e	even	6	1		273.2.y.b	✓	64
21.g	even	6	1		273.2.y.b	✓	64
39.h	odd	6	1		273.2.y.b	✓	64
91.l	odd	6	1	inner	273.2.br.b	yes	64
273.br	even	6	1	inner	273.2.br.b	yes	64

    

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

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T2^32 - 46*T2^30 + 950*T2^28 - 11647*T2^26 + 94449*T2^24 - 534323*T2^22 + 2167391*T2^20 - 6379285*T2^18 + 13630402*T2^16 - 20933043*T2^14 + 22618426*T2^12 - 16585032*T2^10 + 7791329*T2^8 - 2140397*T2^6 + 296869*T2^4 - 16257*T2^2 + 85