Newform orbit 425.2.p.a

• Label: 425.2.p.a
• Level: $425$
• Weight: $2$
• Character orbit: 425.p
• Analytic conductor: $3.394$
• Analytic rank: $0$
• Dimension: $168$
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 425 = 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	425.p (of order \(10\), degree \(4\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(3.39364208590\)
Analytic rank:	\(0\)
Dimension:	\(168\)
Relative dimension:	\(42\) over \(\Q(\zeta_{10})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

$q$-expansion

The algebraic \(q\)-expansion of this newform has not been computed, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 168 q - 8 q^{2} - 44 q^{4} - 4 q^{8} + 28 q^{9}+O(q^{10}) \)

Embeddings

For each embedding \(\iota_m\) of the coefficient field, the values \(\iota_m(a_n)\) are shown below.

For more information on an embedded modular form you can click on its label.

Label	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
16.1	−2.13901	−	1.55408i	−0.355974	+	0.115663i	1.54215	+	4.74625i	0.624287	−	2.14715i	0.941180	+	0.305808i			1.16016i	2.44332	−	7.51977i	−2.31371	+	1.68101i	−4.67220	+	3.62258i
16.2	−2.13901	−	1.55408i	0.355974	−	0.115663i	1.54215	+	4.74625i	−0.624287	+	2.14715i	−0.941180	−	0.305808i		−	1.16016i	2.44332	−	7.51977i	−2.31371	+	1.68101i	4.67220	−	3.62258i
16.3	−2.10617	−	1.53022i	−2.96838	+	0.964486i	1.47633	+	4.54369i	1.79897	+	1.32805i	7.72779	+	2.51091i		−	1.45026i	2.23447	−	6.87699i	5.45401	−	3.96257i	−1.75672	−	5.54991i
16.4	−2.10617	−	1.53022i	2.96838	−	0.964486i	1.47633	+	4.54369i	−1.79897	−	1.32805i	−7.72779	−	2.51091i			1.45026i	2.23447	−	6.87699i	5.45401	−	3.96257i	1.75672	+	5.54991i
16.5	−1.89741	−	1.37855i	−1.99244	+	0.647384i	1.08173	+	3.32921i	−2.23138	+	0.144731i	4.67293	+	1.51833i			5.09964i	1.08751	−	3.34701i	1.12368	−	0.816399i	4.43335	+	2.80145i
16.6	−1.89741	−	1.37855i	1.99244	−	0.647384i	1.08173	+	3.32921i	2.23138	−	0.144731i	−4.67293	−	1.51833i		−	5.09964i	1.08751	−	3.34701i	1.12368	−	0.816399i	−4.43335	−	2.80145i
16.7	−1.58733	−	1.15326i	−2.60850	+	0.847551i	0.571562	+	1.75909i	−0.656872	−	2.13741i	5.11798	+	1.66293i		−	2.38074i	−0.0911795	+	0.280622i	3.65885	−	2.65831i	−1.42232	+	4.15031i
16.8	−1.58733	−	1.15326i	2.60850	−	0.847551i	0.571562	+	1.75909i	0.656872	+	2.13741i	−5.11798	−	1.66293i			2.38074i	−0.0911795	+	0.280622i	3.65885	−	2.65831i	1.42232	−	4.15031i
16.9	−1.46623	−	1.06528i	−0.575810	+	0.187092i	0.396985	+	1.22179i	−0.705078	+	2.12200i	1.04358	+	0.339079i		−	1.66418i	−0.400621	+	1.23299i	−2.13050	+	1.54790i	3.29433	−	2.36024i
16.10	−1.46623	−	1.06528i	0.575810	−	0.187092i	0.396985	+	1.22179i	0.705078	−	2.12200i	−1.04358	−	0.339079i			1.66418i	−0.400621	+	1.23299i	−2.13050	+	1.54790i	−3.29433	+	2.36024i
16.11	−1.46406	−	1.06370i	−1.47315	+	0.478654i	0.393974	+	1.21253i	2.22243	−	0.246559i	2.66592	+	0.866209i		−	0.242729i	−0.405475	+	1.24792i	−0.486001	+	0.353100i	−3.51604	−	2.00303i
16.12	−1.46406	−	1.06370i	1.47315	−	0.478654i	0.393974	+	1.21253i	−2.22243	+	0.246559i	−2.66592	−	0.866209i			0.242729i	−0.405475	+	1.24792i	−0.486001	+	0.353100i	3.51604	+	2.00303i
16.13	−1.17358	−	0.852653i	−1.92956	+	0.626952i	0.0322299	+	0.0991936i	−1.60043	+	1.56161i	2.79906	+	0.909470i		−	3.65292i	−0.849779	+	2.61535i	0.903084	−	0.656129i	3.20974	−	0.468058i
16.14	−1.17358	−	0.852653i	1.92956	−	0.626952i	0.0322299	+	0.0991936i	1.60043	−	1.56161i	−2.79906	−	0.909470i			3.65292i	−0.849779	+	2.61535i	0.903084	−	0.656129i	−3.20974	+	0.468058i
16.15	−0.770053	−	0.559477i	−1.26213	+	0.410091i	−0.338066	−	1.04046i	−1.81036	−	1.31248i	1.20134	+	0.390341i			2.51296i	−0.910052	+	2.80085i	−1.00225	+	0.728178i	0.659768	+	2.02353i
16.16	−0.770053	−	0.559477i	1.26213	−	0.410091i	−0.338066	−	1.04046i	1.81036	+	1.31248i	−1.20134	−	0.390341i		−	2.51296i	−0.910052	+	2.80085i	−1.00225	+	0.728178i	−0.659768	−	2.02353i
16.17	−0.484961	−	0.352344i	−0.406117	+	0.131955i	−0.506994	−	1.56037i	1.58222	+	1.58005i	0.243445	+	0.0790999i			1.28394i	−0.674391	+	2.07556i	−2.27953	+	1.65618i	−0.210594	−	1.32375i
16.18	−0.484961	−	0.352344i	0.406117	−	0.131955i	−0.506994	−	1.56037i	−1.58222	−	1.58005i	−0.243445	−	0.0790999i		−	1.28394i	−0.674391	+	2.07556i	−2.27953	+	1.65618i	0.210594	+	1.32375i
16.19	−0.372964	−	0.270974i	−2.68354	+	0.871936i	−0.552359	−	1.69999i	1.94832	−	1.09729i	1.23714	+	0.401971i			3.02747i	−0.539562	+	1.66060i	4.01408	−	2.91640i	−1.02399	−	0.118696i
16.20	−0.372964	−	0.270974i	2.68354	−	0.871936i	−0.552359	−	1.69999i	−1.94832	+	1.09729i	−1.23714	−	0.401971i		−	3.02747i	−0.539562	+	1.66060i	4.01408	−	2.91640i	1.02399	+	0.118696i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
17.b	even	2	1	inner
25.d	even	5	1	inner
425.p	even	10	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	425.2.p.a	✓	168
17.b	even	2	1	inner	425.2.p.a	✓	168
25.d	even	5	1	inner	425.2.p.a	✓	168
425.p	even	10	1	inner	425.2.p.a	✓	168

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
425.2.p.a	✓	168	1.a	even	1	1	trivial
425.2.p.a	✓	168	17.b	even	2	1	inner
425.2.p.a	✓	168	25.d	even	5	1	inner
425.2.p.a	✓	168	425.p	even	10	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(425, [\chi])\).