Embedded newform 151.2.k.a.18.6

• Label: 151.2.k.a.18.6
• Level: $151$
• Weight: $2$
• Character: 151.18
• Analytic conductor: $1.206$
• Analytic rank: $0$
• Dimension: $480$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 151 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	151.k (of order \(75\), degree \(40\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(1.20574107052\)
Analytic rank:	\(0\)
Dimension:	\(480\)
Relative dimension:	\(12\) over \(\Q(\zeta_{75})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{75}]$

Embedding invariants

Embedding label			18.6
Character	\(\chi\)	\(=\)	151.18
Dual form			151.2.k.a.42.6

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-0.497907 - 0.552982i) q^{2} +(1.93281 + 2.33637i) q^{3} +(0.151179 - 1.43838i) q^{4} +(0.151228 + 0.130536i) q^{5} +(0.329609 - 2.23211i) q^{6} +(1.65232 - 3.93072i) q^{7} +(-2.07467 + 1.50733i) q^{8} +(-1.16071 + 6.08466i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 480 q - 45 q^{2} - 40 q^{3} + 15 q^{4} - 40 q^{5} - 60 q^{6} - 40 q^{7} - 50 q^{8} - 40 q^{9}+O(q^{10}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/151\mathbb{Z}\right)^\times\).

\(n\)	\(6\)
\(\chi(n)\)	\(e\left(\frac{41}{75}\right)\)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−0.497907	−	0.552982i	−0.352074	−	0.391017i	0.540929	−	0.841068i	\(-0.318073\pi\)
							−0.893003	+	0.450051i	\(0.851406\pi\)
\(3\)	1.93281	+	2.33637i	1.11591	+	1.34890i	0.930521	+	0.366238i	\(0.119354\pi\)
							0.185388	+	0.982665i	\(0.440646\pi\)
\(5\)	0.151228	+	0.130536i	0.0676311	+	0.0583776i	0.686584	−	0.727051i	\(-0.259109\pi\)
							−0.618953	+	0.785428i	\(0.712443\pi\)
\(7\)	1.65232	−	3.93072i	0.624519	−	1.48567i	−0.233658	−	0.972319i	\(-0.575070\pi\)
							0.858177	−	0.513353i	\(-0.171597\pi\)
\(11\)	0.122342	+	0.328967i	0.0368874	+	0.0991872i	0.954413	−	0.298490i	\(-0.0964830\pi\)
							−0.917525	+	0.397677i	\(0.869816\pi\)
\(13\)	1.16583	+	4.17552i	0.323342	+	1.15808i	0.931342	+	0.364145i	\(0.118639\pi\)
							−0.608000	+	0.793937i	\(0.708028\pi\)
\(17\)	−2.47958	+	3.26673i	−0.601387	+	0.792298i	−0.991726	−	0.128373i	\(-0.959024\pi\)
							0.390339	+	0.920671i	\(0.372358\pi\)
\(19\)	−4.21474	−	3.06219i	−0.966928	−	0.702515i	−0.0121788	−	0.999926i	\(-0.503877\pi\)
							−0.954749	+	0.297411i	\(0.903877\pi\)
\(23\)	0.933072	−	0.415431i	0.194559	−	0.0866232i	−0.307145	−	0.951663i	\(-0.599374\pi\)
							0.501704	+	0.865040i	\(0.332707\pi\)
\(29\)	−4.04574	−	6.37507i	−0.751275	−	1.18382i	−0.977744	−	0.209802i	\(-0.932718\pi\)
							0.226469	−	0.974018i	\(-0.427282\pi\)
\(31\)	2.24990	+	3.23718i	0.404094	+	0.581414i	0.970015	−	0.243045i	\(-0.0781462\pi\)
							−0.565922	+	0.824459i	\(0.691479\pi\)
\(37\)	−3.94370	+	4.02717i	−0.648340	+	0.662063i	−0.957328	−	0.289003i	\(-0.906676\pi\)
							0.308989	+	0.951066i	\(0.400010\pi\)
\(41\)	−3.90406	+	1.54573i	−0.609712	+	0.241402i	−0.652630	−	0.757677i	\(-0.726334\pi\)
							0.0429183	+	0.999079i	\(0.486334\pi\)
\(43\)	−1.84524	−	4.38964i	−0.281396	−	0.669414i	0.718257	−	0.695778i	\(-0.244940\pi\)
							−0.999652	+	0.0263641i	\(0.991607\pi\)
\(47\)	6.58543	+	5.21954i	0.960583	+	0.761349i	0.971119	−	0.238596i	\(-0.0766870\pi\)
							−0.0105358	+	0.999944i	\(0.503354\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	151.2.k.a.18.6	✓	480
151.42	even	75	inner	151.2.k.a.42.6	yes	480

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
151.2.k.a.18.6	✓	480	1.1	even	1	trivial
151.2.k.a.42.6	yes	480	151.42	even	75	inner