Embedded newform 273.2.y.b.101.15

• Label: 273.2.y.b.101.15
• Level: $273$
• Weight: $2$
• Character: 273.101
• 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:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			101.15
Character	\(\chi\)	\(=\)	273.101
Dual form			273.2.y.b.173.15

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-0.183709 + 0.318193i) q^{2} +(-1.40902 - 1.00730i) q^{3} +(0.932502 + 1.61514i) q^{4} +(0.333187 - 0.192366i) q^{5} +(0.579367 - 0.263290i) q^{6} +(-1.67893 + 2.04479i) q^{7} -1.42007 q^{8} +(0.970675 + 2.83862i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 28 q^{4} - 12 q^{7}+O(q^{10}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/273\mathbb{Z}\right)^\times\).

\(n\)	\(92\)	\(106\)	\(157\)
\(\chi(n)\)	\(-1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

(See \(a_n\) instead)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−0.183709	+	0.318193i	−0.129902	+	0.224997i	−0.923638	−	0.383265i	\(-0.874800\pi\)
							0.793737	+	0.608262i	\(0.208133\pi\)
\(3\)	−1.40902	−	1.00730i	−0.813498	−	0.581568i
							\(5\)	0.333187	−	0.192366i	0.149006	−	0.0860286i	−0.423643	−	0.905829i	\(-0.639249\pi\)
0.572649	+	0.819800i	\(0.305916\pi\)
\(7\)	−1.67893	+	2.04479i	−0.634577	+	0.772860i
							\(11\)	−3.72762			−1.12392			−0.561960	−	0.827164i	\(-0.689953\pi\)
−0.561960	+	0.827164i	\(0.689953\pi\)
\(13\)	3.56240	+	0.556129i	0.988033	+	0.154242i
							\(17\)	3.01985	+	5.23053i	0.732421	+	1.26859i	0.955846	+	0.293869i	\(0.0949430\pi\)
−0.223425	+	0.974721i	\(0.571724\pi\)
\(19\)	−4.13539			−0.948723			−0.474362	−	0.880330i	\(-0.657321\pi\)
							−0.474362	+	0.880330i	\(0.657321\pi\)
\(23\)	4.37550	+	2.52620i	0.912355	+	0.526748i	0.881188	−	0.472766i	\(-0.156744\pi\)
							0.0311666	+	0.999514i	\(0.490078\pi\)
\(29\)	−5.29576	+	3.05751i	−0.983398	+	0.567765i	−0.903294	−	0.429021i	\(-0.858859\pi\)
							−0.0801039	+	0.996787i	\(0.525525\pi\)
\(31\)	0.464104	−	0.803852i	0.0833556	−	0.144376i	−0.821334	−	0.570448i	\(-0.806770\pi\)
							0.904689	+	0.426072i	\(0.140103\pi\)
\(37\)	−0.475916	−	0.274770i	−0.0782400	−	0.0451719i	0.460370	−	0.887727i	\(-0.347717\pi\)
							−0.538610	+	0.842555i	\(0.681050\pi\)
\(41\)	9.42325	−	5.44051i	1.47166	−	0.849666i	0.472171	−	0.881507i	\(-0.343470\pi\)
							0.999493	+	0.0318414i	\(0.0101371\pi\)
\(43\)	1.64275	−	2.84533i	0.250517	−	0.433908i	−0.713151	−	0.701010i	\(-0.752733\pi\)
							0.963668	+	0.267102i	\(0.0860660\pi\)
\(47\)	7.98492	−	4.61010i	1.16472	−	0.672452i	0.212290	−	0.977207i	\(-0.431908\pi\)
							0.952431	+	0.304755i	\(0.0985746\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.y.b.101.15	✓	64
3.2	odd	2	inner	273.2.y.b.101.18	yes	64
7.5	odd	6		273.2.br.b.257.18	yes	64
13.4	even	6		273.2.br.b.17.15	yes	64
21.5	even	6		273.2.br.b.257.15	yes	64
39.17	odd	6		273.2.br.b.17.18	yes	64
91.82	odd	6	inner	273.2.y.b.173.18	yes	64
273.173	even	6	inner	273.2.y.b.173.15	yes	64

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.y.b.101.15	✓	64	1.1	even	1	trivial
273.2.y.b.101.18	yes	64	3.2	odd	2	inner
273.2.y.b.173.15	yes	64	273.173	even	6	inner
273.2.y.b.173.18	yes	64	91.82	odd	6	inner
273.2.br.b.17.15	yes	64	13.4	even	6
273.2.br.b.17.18	yes	64	39.17	odd	6
273.2.br.b.257.15	yes	64	21.5	even	6
273.2.br.b.257.18	yes	64	7.5	odd	6