Embedded newform 11.10.c.a.3.3

• Label: 11.10.c.a.3.3
• Level: $11$
• Weight: $10$
• Character: 11.3
• Analytic conductor: $5.665$
• Analytic rank: $0$
• Dimension: $32$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 11 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	11.c (of order \(5\), degree \(4\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(5.66539419780\)
Analytic rank:	\(0\)
Dimension:	\(32\)
Relative dimension:	\(8\) over \(\Q(\zeta_{5})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			3.3
Character	\(\chi\)	\(=\)	11.3
Dual form			11.10.c.a.4.3

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-14.4842 + 10.5234i) q^{2} +(-4.17901 - 12.8617i) q^{3} +(-59.1658 + 182.094i) q^{4} +(-591.288 - 429.596i) q^{5} +(195.879 + 142.314i) q^{6} +(2103.13 - 6472.78i) q^{7} +(-3891.91 - 11978.1i) q^{8} +(15775.9 - 11461.9i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 21 q^{2} + 69 q^{3} - 1625 q^{4} + 225 q^{5} + 8173 q^{6} - 10675 q^{7} + 22863 q^{8} - 93587 q^{9}+O(q^{10}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/11\mathbb{Z}\right)^\times\).

\(n\)	\(2\)
\(\chi(n)\)	\(e\left(\frac{4}{5}\right)\)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−14.4842	+	10.5234i	−0.640119	+	0.465074i	−0.859891	−	0.510478i	\(-0.829469\pi\)
							0.219772	+	0.975551i	\(0.429469\pi\)
\(3\)	−4.17901	−	12.8617i	−0.0297871	−	0.0916752i	0.935058	−	0.354495i	\(-0.115347\pi\)
							−0.964845	+	0.262820i	\(0.915347\pi\)
\(5\)	−591.288	−	429.596i	−0.423091	−	0.307394i	0.355789	−	0.934566i	\(-0.384212\pi\)
							−0.778880	+	0.627172i	\(0.784212\pi\)
\(7\)	2103.13	−	6472.78i	0.331074	−	1.01894i	−0.637549	−	0.770410i	\(-0.720052\pi\)
							0.968624	−	0.248533i	\(-0.0799483\pi\)
\(11\)	−32511.1	−	36069.0i	−0.669522	−	0.742792i
							\(13\)	−67450.7	+	49005.8i	−0.655001	+	0.475886i	−0.864971	−	0.501822i	\(-0.832663\pi\)
0.209970	+	0.977708i	\(0.432663\pi\)
\(17\)	12888.1	+	9363.72i	0.0374255	+	0.0271912i	0.606341	−	0.795205i	\(-0.292637\pi\)
							−0.568915	+	0.822396i	\(0.692637\pi\)
\(19\)	−44228.9	−	136123.i	−0.0778602	−	0.239629i	0.904549	−	0.426369i	\(-0.140208\pi\)
							−0.982409	+	0.186741i	\(0.940208\pi\)
\(23\)	−1.08478e6			−0.808289			−0.404144	−	0.914695i	\(-0.632431\pi\)
							−0.404144	+	0.914695i	\(0.632431\pi\)
\(29\)	1.08599e6	−	3.34233e6i	0.285124	−	0.877523i	−0.701237	−	0.712928i	\(-0.747368\pi\)
							0.986361	−	0.164594i	\(-0.0526315\pi\)
\(31\)	−1.91346e6	+	1.39021e6i	−0.372127	+	0.270366i	−0.758092	−	0.652147i	\(-0.773868\pi\)
							0.385966	+	0.922513i	\(0.373868\pi\)
\(37\)	−6.21524e6	+	1.91286e7i	−0.545193	+	1.67793i	0.175337	+	0.984508i	\(0.443898\pi\)
							−0.720530	+	0.693424i	\(0.756102\pi\)
\(41\)	−7.52850e6	−	2.31703e7i	−0.416084	−	1.28057i	−0.911278	−	0.411792i	\(-0.864903\pi\)
							0.495194	−	0.868782i	\(-0.335097\pi\)
\(43\)	1.97074e7			0.879063			0.439532	−	0.898227i	\(-0.355144\pi\)
							0.439532	+	0.898227i	\(0.355144\pi\)
\(47\)	−1.55191e7	−	4.77630e7i	−0.463903	−	1.42775i	−0.860357	−	0.509692i	\(-0.829759\pi\)
							0.396454	−	0.918055i	\(-0.370241\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	11.10.c.a.3.3	✓	32
3.2	odd	2		99.10.f.a.91.6		32
11.2	odd	10		121.10.a.i.1.5		16
11.4	even	5	inner	11.10.c.a.4.3	yes	32
11.9	even	5		121.10.a.h.1.12		16
33.26	odd	10		99.10.f.a.37.6		32

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
11.10.c.a.3.3	✓	32	1.1	even	1	trivial
11.10.c.a.4.3	yes	32	11.4	even	5	inner
99.10.f.a.37.6		32	33.26	odd	10
99.10.f.a.91.6		32	3.2	odd	2
121.10.a.h.1.12		16	11.9	even	5
121.10.a.i.1.5		16	11.2	odd	10