Newform orbit 463.2.a.b

• Label: 463.2.a.b
• Level: $463$
• Weight: $2$
• Character orbit: 463.a
• Self dual: yes
• Analytic conductor: $3.697$
• Analytic rank: $0$
• Dimension: $22$
• CM: no
• Inner twists: $1$

Newspace parameters

Level:	\( N \)	\(=\)	\( 463 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	463.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	\(3.69707361359\)
Analytic rank:	\(0\)
Dimension:	\(22\)
Twist minimal:	yes
Fricke sign:	\(-1\)
Sato-Tate group:	$\mathrm{SU}(2)$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 22 q + 8 q^{2} + 4 q^{3} + 22 q^{4} + 14 q^{5} + 2 q^{7} + 21 q^{8} + 30 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
1.1	−2.49893			1.34061			4.24463			1.30386			−3.35009			−1.67630			−5.60917			−1.20276			−3.25826
1.2	−2.02032			3.06294			2.08171			1.66689			−6.18813			2.34658			−0.165073			6.38162			−3.36766
1.3	−1.99949			−2.56041			1.99796			3.97888			5.11951			0.473364			0.00408482			3.55569			−7.95574
1.4	−1.86304			−2.25465			1.47092			−1.04714			4.20049			0.00401867			0.985700			2.08343			1.95086
1.5	−1.65028			0.828656			0.723423			−3.55479			−1.36751			−2.11374			2.10671			−2.31333			5.86640
1.6	−1.22193			1.56250			−0.506889			2.09878			−1.90926			2.18049			3.06324			−0.558603			−2.56456
1.7	−0.777910			−1.18956			−1.39486			−0.711191			0.925373			−3.88299			2.64089			−1.58494			0.553243
1.8	−0.311178			−0.854543			−1.90317			3.79485			0.265915			4.27394			1.21458			−2.26976			−1.18087
1.9	−0.195384			3.11207			−1.96182			−1.99950			−0.608049			1.00227			0.774078			6.68495			0.390671
1.10	−0.143675			2.36203			−1.97936			4.14060			−0.339365			−4.11895			0.571736			2.57917			−0.594903
1.11	0.392048			−1.41186			−1.84630			−2.40315			−0.553518			3.14707			−1.50793			−1.00664			−0.942149
1.12	0.447079			−3.14242			−1.80012			−2.87600			−1.40491			−2.88479			−1.69895			6.87478			−1.28580
1.13	0.957229			−2.50835			−1.08371			2.94752			−2.40107			−1.34740			−2.95182			3.29184			2.82146
1.14	1.22088			1.99866			−0.509442			0.962728			2.44013			3.67766			−3.06374			0.994644			1.17538
1.15	1.31959			1.29950			−0.258670			1.62917			1.71482			2.29508			−2.98053			−1.31129			2.14985
1.16	1.82765			2.88805			1.34032			0.997077			5.27836			−2.38656			−1.20567			5.34084			1.82231
1.17	2.18364			0.187092			2.76830			4.18769			0.408542			−0.967874			1.67768			−2.96500			9.14442
1.18	2.20743			2.68149			2.87274			−3.26515			5.91920			1.06721			1.92652			4.19040			−7.20760
1.19	2.31997			−1.45090			3.38227			−0.241750			−3.36606			1.78073			3.20683			−0.894877			−0.560854
1.20	2.47153			0.128527			4.10846			0.260576			0.317657			3.19970			5.21112			−2.98348			0.644022

Atkin-Lehner signs

\( p \)	Sign
\(463\)	\(-1\)

Inner twists

This newform does not admit any (nontrivial) inner twists.

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	463.2.a.b	✓	22
3.b	odd	2	1		4167.2.a.i		22
4.b	odd	2	1		7408.2.a.i		22

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
463.2.a.b	✓	22	1.a	even	1	1	trivial
4167.2.a.i		22	3.b	odd	2	1
7408.2.a.i		22	4.b	odd	2	1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T2^22 - 8*T2^21 - T2^20 + 161*T2^19 - 281*T2^18 - 1216*T2^17 + 3523*T2^16 + 3859*T2^15 - 19383*T2^14 - 1030*T2^13 + 56835*T2^12 - 26406*T2^11 - 90387*T2^10 + 71356*T2^9 + 71796*T2^8 - 76057*T2^7 - 22452*T2^6 + 32959*T2^5 + 1404*T2^4 - 4772*T2^3 - 174*T2^2 + 237*T2 + 25