Newform orbit 495.2.u.a

• Label: 495.2.u.a
• Level: $495$
• Weight: $2$
• Character orbit: 495.u
• Analytic conductor: $3.953$
• Analytic rank: $0$
• Dimension: $52$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 495 = 3^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	495.u (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(3.95259490005\)
Analytic rank:	\(0\)
Dimension:	\(52\)
Relative dimension:	\(26\) over \(\Q(\zeta_{6})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

$q$-expansion

The dimension is sufficiently large that we do not compute an algebraic \(q\)-expansion, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 52 q + 20 q^{4} + q^{5} + 4 q^{6} + 6 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
34.1	−2.27037	−	1.31080i	1.27895	−	1.16803i	2.43639	+	4.21996i	2.23146	+	0.143525i	−4.43474	+	0.975412i	2.09033	+	1.20686i		−	7.53129i	0.271421	−	2.98770i	−4.87810	−	3.25085i
34.2	−2.08956	−	1.20641i	−1.33315	+	1.10577i	1.91084	+	3.30968i	−1.72394	−	1.42409i	4.11970	−	0.702243i	−0.128806	−	0.0743661i		−	4.39540i	0.554566	−	2.94830i	1.88425	+	5.05549i
34.3	−2.02226	−	1.16755i	−0.597351	−	1.62578i	1.72636	+	2.99014i	−2.08543	+	0.806825i	−0.690190	+	3.98520i	1.18589	+	0.684674i		−	3.39225i	−2.28634	+	1.94233i	5.15930	+	0.803244i
34.4	−1.97685	−	1.14134i	1.39742	+	1.02334i	1.60530	+	2.78045i	0.758244	+	2.10358i	−1.59452	−	3.61791i	−0.899784	−	0.519491i		−	2.76338i	0.905564	+	2.86006i	0.901959	−	5.02388i
34.5	−1.72676	−	0.996944i	−1.72536	+	0.152056i	0.987794	+	1.71091i	2.01495	−	0.969522i	3.13088	+	1.45753i	−2.38803	−	1.37873i			0.0486743i	2.95376	−	0.524705i	−4.44589	−	0.334665i
34.6	−1.32180	−	0.763144i	−0.144418	+	1.72602i	0.164778	+	0.285404i	2.06762	−	0.851443i	1.50809	−	2.17125i	3.72773	+	2.15221i			2.54958i	−2.95829	−	0.498536i	−3.38276	−	0.452450i
34.7	−1.18072	−	0.681687i	1.20439	−	1.24477i	−0.0706068	−	0.122295i	−2.20536	−	0.369286i	−2.27058	+	0.648705i	−1.74985	−	1.01028i			2.91927i	−0.0989033	−	2.99837i	2.35217	+	1.93939i
34.8	−1.15150	−	0.664820i	−0.589124	+	1.62878i	−0.116029	−	0.200968i	−0.592642	+	2.15610i	1.76122	−	1.48388i	−1.03524	−	0.597694i			2.96783i	−2.30587	−	1.91911i	2.11585	−	2.08876i
34.9	−0.923436	−	0.533146i	−1.70778	−	0.288947i	−0.431510	−	0.747398i	−1.23891	−	1.86148i	1.42297	+	1.17732i	3.88800	+	2.24474i			3.05282i	2.83302	+	0.986917i	0.151608	+	2.37948i
34.10	−0.760142	−	0.438868i	1.56106	−	0.750387i	−0.614789	−	1.06485i	2.21225	+	0.325527i	−1.51595	−	0.114701i	−3.20764	−	1.85193i			2.83472i	1.87384	−	2.34280i	−1.53876	−	1.21833i
34.11	−0.556414	−	0.321246i	1.67181	+	0.452826i	−0.793602	−	1.37456i	−2.03962	+	0.916491i	−0.784750	−	0.789021i	1.85099	+	1.06867i			2.30475i	2.58990	+	1.51408i	1.42929	+	0.145270i
34.12	−0.508451	−	0.293555i	−1.19597	−	1.25286i	−0.827651	−	1.43353i	0.706562	+	2.12150i	0.240311	+	0.988100i	−2.13965	−	1.23533i			2.14606i	−0.139304	+	2.99676i	0.263524	−	1.28609i
34.13	−0.184631	−	0.106597i	0.391562	+	1.68721i	−0.977274	−	1.69269i	−1.06711	−	1.96501i	0.107557	−	0.353251i	0.0767866	+	0.0443328i			0.843084i	−2.69336	+	1.32129i	−0.0124418	+	0.476553i
34.14	0.184631	+	0.106597i	−0.391562	−	1.68721i	−0.977274	−	1.69269i	−1.16819	−	1.90665i	0.107557	−	0.353251i	−0.0767866	−	0.0443328i		−	0.843084i	−2.69336	+	1.32129i	−0.0124418	−	0.476553i
34.15	0.508451	+	0.293555i	1.19597	+	1.25286i	−0.827651	−	1.43353i	1.48399	+	1.67265i	0.240311	+	0.988100i	2.13965	+	1.23533i		−	2.14606i	−0.139304	+	2.99676i	0.263524	+	1.28609i
34.16	0.556414	+	0.321246i	−1.67181	−	0.452826i	−0.793602	−	1.37456i	1.81351	−	1.30812i	−0.784750	−	0.789021i	−1.85099	−	1.06867i		−	2.30475i	2.58990	+	1.51408i	1.42929	−	0.145270i
34.17	0.760142	+	0.438868i	−1.56106	+	0.750387i	−0.614789	−	1.06485i	−0.824208	+	2.07862i	−1.51595	−	0.114701i	3.20764	+	1.85193i		−	2.83472i	1.87384	−	2.34280i	−1.53876	+	1.21833i
34.18	0.923436	+	0.533146i	1.70778	+	0.288947i	−0.431510	−	0.747398i	−0.992638	−	2.00366i	1.42297	+	1.17732i	−3.88800	−	2.24474i		−	3.05282i	2.83302	+	0.986917i	0.151608	−	2.37948i
34.19	1.15150	+	0.664820i	0.589124	−	1.62878i	−0.116029	−	0.200968i	2.16356	+	0.564808i	1.76122	−	1.48388i	1.03524	+	0.597694i		−	2.96783i	−2.30587	−	1.91911i	2.11585	+	2.08876i
34.20	1.18072	+	0.681687i	−1.20439	+	1.24477i	−0.0706068	−	0.122295i	0.782871	−	2.09454i	−2.27058	+	0.648705i	1.74985	+	1.01028i		−	2.91927i	−0.0989033	−	2.99837i	2.35217	−	1.93939i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
5.b	even	2	1	inner
9.c	even	3	1	inner
45.j	even	6	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	495.2.u.a	✓	52
5.b	even	2	1	inner	495.2.u.a	✓	52
9.c	even	3	1	inner	495.2.u.a	✓	52
45.j	even	6	1	inner	495.2.u.a	✓	52

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
495.2.u.a	✓	52	1.a	even	1	1	trivial
495.2.u.a	✓	52	5.b	even	2	1	inner
495.2.u.a	✓	52	9.c	even	3	1	inner
495.2.u.a	✓	52	45.j	even	6	1	inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T2^52 - 36*T2^50 + 732*T2^48 - 10190*T2^46 + 107310*T2^44 - 891650*T2^42 + 6019501*T2^40 - 33518040*T2^38 + 155688647*T2^36 - 606424346*T2^34 + 1988880491*T2^32 - 5495670472*T2^30 + 12800930992*T2^28 - 25076890121*T2^26 + 41218126191*T2^24 - 56519482074*T2^22 + 64281512813*T2^20 - 60006961049*T2^18 + 45538316438*T2^16 - 27601593985*T2^14 + 13179134060*T2^12 - 4797994195*T2^10 + 1306176393*T2^8 - 243798948*T2^6 + 29282220*T2^4 - 1228528*T2^2 + 38416