Embedded newform 23.11.d.a.5.5

• Label: 23.11.d.a.5.5
• Level: $23$
• Weight: $11$
• Character: 23.5
• Analytic conductor: $14.613$
• Analytic rank: $0$
• Dimension: $190$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 23 \)
Weight:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	23.d (of order \(22\), degree \(10\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(14.6132168115\)
Analytic rank:	\(0\)
Dimension:	\(190\)
Relative dimension:	\(19\) over \(\Q(\zeta_{22})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			5.5
Character	\(\chi\)	\(=\)	23.5
Dual form			23.11.d.a.14.5

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-28.3423 - 8.32206i) q^{2} +(256.272 - 295.754i) q^{3} +(-127.412 - 81.8829i) q^{4} +(-273.245 - 39.2867i) q^{5} +(-9724.64 + 6249.65i) q^{6} +(-23766.3 + 10853.7i) q^{7} +(22737.8 + 26240.8i) q^{8} +(-13391.4 - 93139.2i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 190 q + 13 q^{2} - 71 q^{3} - 11699 q^{4} - 11 q^{5} + 3346 q^{6} - 11 q^{7} - 50582 q^{8} - 394850 q^{9}+O(q^{10}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/23\mathbb{Z}\right)^\times\).

\(n\)	\(5\)
\(\chi(n)\)	\(e\left(\frac{1}{22}\right)\)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−28.3423	−	8.32206i	−0.885698	−	0.260064i	−0.192919	−	0.981215i	\(-0.561796\pi\)
							−0.692779	+	0.721150i	\(0.743614\pi\)
\(3\)	256.272	−	295.754i	1.05462	−	1.21709i	0.0791716	−	0.996861i	\(-0.474772\pi\)
							0.975447	−	0.220234i	\(-0.0706821\pi\)
\(5\)	−273.245	−	39.2867i	−0.0874385	−	0.0125718i	0.0984567	−	0.995141i	\(-0.468609\pi\)
							−0.185895	+	0.982570i	\(0.559518\pi\)
\(7\)	−23766.3	+	10853.7i	−1.41407	+	0.645784i	−0.968397	−	0.249413i	\(-0.919762\pi\)
							−0.445672	+	0.895197i	\(0.647035\pi\)
\(11\)	−34599.9	−	117837.i	−0.214838	−	0.731672i	−0.994431	−	0.105386i	\(-0.966392\pi\)
							0.779593	−	0.626286i	\(-0.215426\pi\)
\(13\)	−75198.8	+	164662.i	−0.202532	+	0.443484i	−0.983457	−	0.181141i	\(-0.942021\pi\)
							0.780925	+	0.624625i	\(0.214748\pi\)
\(17\)	668210.	+	1.03976e6i	0.470618	+	0.732296i	0.992701	−	0.120599i	\(-0.0384814\pi\)
							−0.522083	+	0.852894i	\(0.674845\pi\)
\(19\)	−518712.	+	807131.i	−0.209487	+	0.325969i	−0.930058	−	0.367413i	\(-0.880244\pi\)
							0.720570	+	0.693382i	\(0.243880\pi\)
\(23\)	−1.27557e6	+	6.30868e6i	−0.198182	+	0.980165i
							\(29\)	1.90824e7	−	1.22635e7i	0.930343	−	0.597895i	0.0147016	−	0.999892i	\(-0.495320\pi\)
0.915641	+	0.401997i	\(0.131684\pi\)
\(31\)	1.83820e7	+	2.12140e7i	0.642073	+	0.740991i	0.979740	−	0.200274i	\(-0.0641833\pi\)
							−0.337667	+	0.941266i	\(0.609638\pi\)
\(37\)	−1.03494e8	+	1.48802e7i	−1.49247	+	0.214585i	−0.839733	−	0.543000i	\(-0.817288\pi\)
							−0.652737	+	0.757585i	\(0.726379\pi\)
\(41\)	−3.47973e6	+	2.42021e7i	−0.0300349	+	0.208898i	−0.999313	−	0.0370714i	\(-0.988197\pi\)
							0.969278	+	0.245969i	\(0.0791062\pi\)
\(43\)	7.31264e7	+	6.33644e7i	0.497430	+	0.431026i	0.867097	−	0.498138i	\(-0.165983\pi\)
							−0.369667	+	0.929164i	\(0.620528\pi\)
\(47\)	−2.98649e8			−1.30218			−0.651092	−	0.758999i	\(-0.725689\pi\)
							−0.651092	+	0.758999i	\(0.725689\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	23.11.d.a.5.5	✓	190
23.14	odd	22	inner	23.11.d.a.14.5	yes	190

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
23.11.d.a.5.5	✓	190	1.1	even	1	trivial
23.11.d.a.14.5	yes	190	23.14	odd	22	inner