Embedded newform 633.2.v.b.13.11

• Label: 633.2.v.b.13.11
• Level: $633$
• Weight: $2$
• Character: 633.13
• Analytic conductor: $5.055$
• Analytic rank: $0$
• Dimension: $456$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 633 = 3 \cdot 211 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	633.v (of order \(35\), degree \(24\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(5.05453044795\)
Analytic rank:	\(0\)
Dimension:	\(456\)
Relative dimension:	\(19\) over \(\Q(\zeta_{35})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{35}]$

Embedding invariants

Embedding label			13.11
Character	\(\chi\)	\(=\)	633.13
Dual form			633.2.v.b.487.11

$q$-expansion

\(f(q)\)	\(=\)	\(q+(0.264523 - 0.400735i) q^{2} +(-0.0448648 - 0.998993i) q^{3} +(0.695434 + 1.62705i) q^{4} +(0.148575 - 3.30828i) q^{5} +(-0.412200 - 0.246278i) q^{6} +(1.38356 + 2.09600i) q^{7} +(1.78088 + 0.323181i) q^{8} +(-0.995974 + 0.0896393i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 456 q - 3 q^{2} + 19 q^{3} + 9 q^{4} + 2 q^{5} - 3 q^{6} - 10 q^{7} - 9 q^{8} + 19 q^{9}+O(q^{10}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/633\mathbb{Z}\right)^\times\).

\(n\)	\(212\)	\(424\)
\(\chi(n)\)	\(1\)	\(e\left(\frac{24}{35}\right)\)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	0.264523	−	0.400735i	0.187046	−	0.283363i	−0.728936	−	0.684582i	\(-0.759985\pi\)
							0.915982	+	0.401219i	\(0.131413\pi\)
\(3\)	−0.0448648	−	0.998993i	−0.0259027	−	0.576769i
							\(5\)	0.148575	−	3.30828i	0.0664447	−	1.47951i	−0.638158	−	0.769905i	\(-0.720303\pi\)
0.704603	−	0.709602i	\(-0.251125\pi\)
\(7\)	1.38356	+	2.09600i	0.522936	+	0.792215i	0.996051	−	0.0887863i	\(-0.0282988\pi\)
							−0.473114	+	0.881001i	\(0.656870\pi\)
\(11\)	4.26780	+	1.17784i	1.28679	+	0.355131i	0.841501	−	0.540256i	\(-0.181672\pi\)
							0.445289	+	0.895387i	\(0.353101\pi\)
\(13\)	0.309436	−	0.323644i	0.0858220	−	0.0897628i	−0.678489	−	0.734610i	\(-0.737365\pi\)
							0.764311	+	0.644848i	\(0.223079\pi\)
\(17\)	0.798084	+	5.89169i	0.193564	+	1.42894i	0.783448	+	0.621457i	\(0.213459\pi\)
							−0.589884	+	0.807488i	\(0.700827\pi\)
\(19\)	1.57538	−	4.84852i	0.361417	−	1.11233i	−0.590778	−	0.806834i	\(-0.701179\pi\)
							0.952195	−	0.305492i	\(-0.0988209\pi\)
\(23\)	−2.30338	−	7.08907i	−0.480288	−	1.47817i	−0.838692	−	0.544606i	\(-0.816679\pi\)
							0.358404	−	0.933567i	\(-0.383321\pi\)
\(29\)	6.41452	−	6.70906i	1.19115	−	1.24584i	0.228965	−	0.973435i	\(-0.426466\pi\)
							0.962182	−	0.272407i	\(-0.0878197\pi\)
\(31\)	−9.69439	+	4.66857i	−1.74116	+	0.838500i	−0.758847	+	0.651268i	\(0.774237\pi\)
							−0.982316	+	0.187232i	\(0.940049\pi\)
\(37\)	4.19374	−	1.15740i	0.689446	−	0.190275i	0.0962790	−	0.995354i	\(-0.469306\pi\)
							0.593167	+	0.805079i	\(0.297877\pi\)
\(41\)	−0.222610	+	0.413679i	−0.0347658	+	0.0646058i	−0.897386	−	0.441247i	\(-0.854536\pi\)
							0.862620	+	0.505853i	\(0.168822\pi\)
\(43\)	0.209192	−	0.100742i	0.0319015	−	0.0153629i	−0.417865	−	0.908509i	\(-0.637221\pi\)
							0.449766	+	0.893146i	\(0.351507\pi\)
\(47\)	−2.37917	−	0.214129i	−0.347038	−	0.0312340i	−0.0852505	−	0.996360i	\(-0.527169\pi\)
							−0.261787	+	0.965126i	\(0.584312\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	633.2.v.b.13.11	✓	456
211.65	even	35	inner	633.2.v.b.487.11	yes	456

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
633.2.v.b.13.11	✓	456	1.1	even	1	trivial
633.2.v.b.487.11	yes	456	211.65	even	35	inner