Newform orbit 273.2.r.b

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

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

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
68.1		−	2.73146i	−1.52761	+	0.816332i	−5.46085			0.121221	−	0.209960i	2.22977	+	4.17261i	−2.13335	+	1.56488i			9.45317i	1.66721	−	2.49408i	−0.573498	−	0.331109i
68.2		−	2.60090i	0.206727	−	1.71967i	−4.76468			1.54658	−	2.67876i	−4.47269	−	0.537676i	1.09877	+	2.40680i			7.19066i	−2.91453	−	0.711004i	−6.96719	−	4.02251i
68.3		−	2.39671i	1.60287	+	0.656371i	−3.74420			1.10064	−	1.90637i	1.57313	−	3.84160i	−1.62460	−	2.08822i			4.18035i	2.13835	+	2.10415i	−4.56901	−	2.63792i
68.4		−	2.39579i	0.452516	+	1.67189i	−3.73983			−1.50632	+	2.60901i	4.00551	−	1.08414i	2.64172	−	0.145950i			4.16828i	−2.59046	+	1.51312i	6.25066	+	3.60882i
68.5		−	1.97104i	1.69142	−	0.372976i	−1.88498			−0.272603	+	0.472162i	−0.735148	−	3.33384i	2.35644	+	1.20299i		−	0.226699i	2.72178	−	1.26171i	0.930648	+	0.537310i
68.6		−	1.92371i	−1.08390	−	1.35099i	−1.70067			−1.94643	+	3.37132i	−2.59891	+	2.08510i	−0.630216	+	2.56960i		−	0.575834i	−0.650341	+	2.92866i	6.48544	+	3.74437i
68.7		−	1.85355i	−1.03215	+	1.39092i	−1.43566			−0.852778	+	1.47706i	2.57815	+	1.91315i	−1.51863	−	2.16651i		−	1.04604i	−0.869331	−	2.87128i	2.73780	+	1.58067i
68.8		−	1.85049i	−1.73048	+	0.0736936i	−1.42433			1.21731	−	2.10844i	0.136370	+	3.20225i	2.52177	−	0.800422i		−	1.06527i	2.98914	−	0.255051i	−3.90166	−	2.25263i
68.9		−	1.53974i	−1.04458	−	1.38161i	−0.370785			0.956175	−	1.65614i	−2.12732	+	1.60838i	−2.63109	−	0.278191i		−	2.50856i	−0.817709	+	2.88641i	−2.55002	−	1.47226i
68.10		−	1.40538i	−0.386542	+	1.68837i	0.0248937			1.48377	−	2.56997i	2.37281	+	0.543240i	0.0176221	+	2.64569i		−	2.84575i	−2.70117	−	1.30525i	−3.61180	−	2.08527i
68.11		−	1.05456i	1.46610	−	0.922247i	0.887893			−0.000964697		0.00167090i	−0.972570	−	1.54610i	−2.64511	+	0.0584461i		−	3.04547i	1.29892	−	2.70422i	0.00176208	+	0.00101734i
68.12		−	0.883413i	1.41202	+	1.00309i	1.21958			−1.72131	+	2.98140i	0.886146	−	1.24740i	−2.26618	+	1.36544i		−	2.84422i	0.987606	+	2.83278i	2.63381	+	1.52063i
68.13		−	0.843135i	0.346738	−	1.69699i	1.28912			−1.06280	+	1.84082i	−1.43079	−	0.292347i	2.34470	−	1.22572i		−	2.77318i	−2.75955	−	1.17682i	1.55206	+	0.896082i
68.14		−	0.771110i	0.714765	+	1.57769i	1.40539			0.907647	−	1.57209i	1.21657	−	0.551162i	0.574285	−	2.58267i		−	2.62593i	−1.97822	+	2.25536i	−1.21225	−	0.699896i
68.15		−	0.546208i	−1.72803	+	0.117898i	1.70166			−1.25657	+	2.17644i	0.0643970	+	0.943866i	−0.612705	−	2.57383i		−	2.02188i	2.97220	−	0.407464i	1.18879	+	0.686349i
68.16		−	0.0504397i	−1.05075	+	1.37693i	1.99746			−1.19579	+	2.07117i	0.0694519	+	0.0529993i	0.00656452	+	2.64574i		−	0.201631i	−0.791866	−	2.89360i	0.104469	+	0.0603154i
68.17			0.0504397i	0.667082	−	1.59844i	1.99746			1.19579	−	2.07117i	0.0806247	+	0.0336474i	0.00656452	+	2.64574i			0.201631i	−2.11000	−	2.13258i	0.104469	+	0.0603154i
68.18			0.546208i	−0.761914	−	1.55547i	1.70166			1.25657	−	2.17644i	0.849611	−	0.416164i	−0.612705	−	2.57383i			2.02188i	−1.83897	+	2.37027i	1.18879	+	0.686349i
68.19			0.771110i	1.72370	−	0.169842i	1.40539			−0.907647	+	1.57209i	0.130967	+	1.32917i	0.574285	−	2.58267i			2.62593i	2.94231	−	0.585513i	−1.21225	−	0.699896i
68.20			0.843135i	−1.29627	+	1.14878i	1.28912			1.06280	−	1.84082i	−0.968576	−	1.09293i	2.34470	−	1.22572i			2.77318i	0.360617	−	2.97825i	1.55206	+	0.896082i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
3.b	odd	2	1	inner
91.v	odd	6	1	inner
273.r	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.r.b	✓	64
3.b	odd	2	1	inner	273.2.r.b	✓	64
7.d	odd	6	1		273.2.bf.b	yes	64
13.c	even	3	1		273.2.bf.b	yes	64
21.g	even	6	1		273.2.bf.b	yes	64
39.i	odd	6	1		273.2.bf.b	yes	64
91.v	odd	6	1	inner	273.2.r.b	✓	64
273.r	even	6	1	inner	273.2.r.b	✓	64

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
273.2.r.b	✓	64	1.a	even	1	1	trivial
273.2.r.b	✓	64	3.b	odd	2	1	inner
273.2.r.b	✓	64	91.v	odd	6	1	inner
273.2.r.b	✓	64	273.r	even	6	1	inner
273.2.bf.b	yes	64	7.d	odd	6	1
273.2.bf.b	yes	64	13.c	even	3	1
273.2.bf.b	yes	64	21.g	even	6	1
273.2.bf.b	yes	64	39.i	odd	6	1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T2^32 + 48*T2^30 + 1036*T2^28 + 13303*T2^26 + 113325*T2^24 + 676187*T2^22 + 2908599*T2^20 + 9145849*T2^18 + 21096866*T2^16 + 35519813*T2^14 + 43068692*T2^12 + 36750070*T2^10 + 21268707*T2^8 + 7852455*T2^6 + 1648423*T2^4 + 148395*T2^2 + 367