Newform orbit 155.2.j.a

• Label: 155.2.j.a
• Level: $155$
• Weight: $2$
• Character orbit: 155.j
• Analytic conductor: $1.238$
• Analytic rank: $0$
• Dimension: $28$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 155 = 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	155.j (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(1.23768123133\)
Analytic rank:	\(0\)
Dimension:	\(28\)
Relative dimension:	\(14\) 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.

\(\operatorname{Tr}(f)(q) = \) \( 28 q - 36 q^{4} - 4 q^{6} + 12 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
129.1		−	2.71952i	−1.10437	−	0.637607i	−5.39577			0.266872	+	2.22009i	−1.73398	+	3.00335i	−2.24157	−	1.29417i			9.23487i	−0.686914	−	1.18977i	6.03756	−	0.725763i
129.2		−	2.45666i	1.68144	+	0.970778i	−4.03517			−0.331217	−	2.21140i	2.38487	−	4.13071i	0.470962	+	0.271910i			4.99972i	0.384819	+	0.666526i	−5.43266	+	0.813686i
129.3		−	2.00510i	−2.72063	−	1.57076i	−2.02044			−1.23835	−	1.86185i	−3.14953	+	5.45514i	2.59556	+	1.49855i			0.0409798i	3.43455	+	5.94882i	−3.73320	+	2.48303i
129.4		−	1.63902i	−0.474794	−	0.274122i	−0.686385			2.22280	−	0.243221i	−0.449292	+	0.778196i	−0.0810635	−	0.0468020i		−	2.15304i	−1.34971	−	2.33777i	−0.398644	−	3.64321i
129.5		−	1.59157i	2.31656	+	1.33747i	−0.533086			−0.853428	+	2.06680i	2.12867	−	3.68696i	−1.59984	−	0.923665i		−	2.33469i	2.07763	+	3.59856i	3.28945	+	1.35829i
129.6		−	0.531807i	−1.14596	−	0.661621i	1.71718			−0.0600405	+	2.23526i	−0.351855	+	0.609430i	3.89827	+	2.25067i		−	1.97682i	−0.624514	−	1.08169i	1.18873	+	0.0319299i
129.7		−	0.215240i	1.37703	+	0.795029i	1.95367			−1.95870	−	1.07865i	0.171122	−	0.296393i	1.58243	+	0.913614i		−	0.850990i	−0.235858	−	0.408518i	−0.232169	+	0.421592i
129.8			0.215240i	−1.37703	−	0.795029i	1.95367			0.0452145	−	2.23561i	0.171122	−	0.296393i	−1.58243	−	0.913614i			0.850990i	−0.235858	−	0.408518i	0.481194	+	0.00973198i
129.9			0.531807i	1.14596	+	0.661621i	1.71718			1.96581	+	1.06563i	−0.351855	+	0.609430i	−3.89827	−	2.25067i			1.97682i	−0.624514	−	1.08169i	−0.566711	+	1.04543i
129.10			1.59157i	−2.31656	−	1.33747i	−0.533086			2.21661	+	0.294310i	2.12867	−	3.68696i	1.59984	+	0.923665i			2.33469i	2.07763	+	3.59856i	−0.468414	+	3.52789i
129.11			1.63902i	0.474794	+	0.274122i	−0.686385			−1.32204	+	1.80339i	−0.449292	+	0.778196i	0.0810635	+	0.0468020i			2.15304i	−1.34971	−	2.33777i	−2.95579	−	2.16684i
129.12			2.00510i	2.72063	+	1.57076i	−2.02044			−0.993231	−	2.00337i	−3.14953	+	5.45514i	−2.59556	−	1.49855i		−	0.0409798i	3.43455	+	5.94882i	4.01696	−	1.99153i
129.13			2.45666i	−1.68144	−	0.970778i	−4.03517			−1.74952	−	1.39254i	2.38487	−	4.13071i	−0.470962	−	0.271910i		−	4.99972i	0.384819	+	0.666526i	3.42100	−	4.29798i
129.14			2.71952i	1.10437	+	0.637607i	−5.39577			1.78921	+	1.34116i	−1.73398	+	3.00335i	2.24157	+	1.29417i		−	9.23487i	−0.686914	−	1.18977i	−3.64731	+	4.86580i
149.1		−	2.71952i	1.10437	−	0.637607i	−5.39577			1.78921	−	1.34116i	−1.73398	−	3.00335i	2.24157	−	1.29417i			9.23487i	−0.686914	+	1.18977i	−3.64731	−	4.86580i
149.2		−	2.45666i	−1.68144	+	0.970778i	−4.03517			−1.74952	+	1.39254i	2.38487	+	4.13071i	−0.470962	+	0.271910i			4.99972i	0.384819	−	0.666526i	3.42100	+	4.29798i
149.3		−	2.00510i	2.72063	−	1.57076i	−2.02044			−0.993231	+	2.00337i	−3.14953	−	5.45514i	−2.59556	+	1.49855i			0.0409798i	3.43455	−	5.94882i	4.01696	+	1.99153i
149.4		−	1.63902i	0.474794	−	0.274122i	−0.686385			−1.32204	−	1.80339i	−0.449292	−	0.778196i	0.0810635	−	0.0468020i		−	2.15304i	−1.34971	+	2.33777i	−2.95579	+	2.16684i
149.5		−	1.59157i	−2.31656	+	1.33747i	−0.533086			2.21661	−	0.294310i	2.12867	+	3.68696i	1.59984	−	0.923665i		−	2.33469i	2.07763	−	3.59856i	−0.468414	−	3.52789i
149.6		−	0.531807i	1.14596	−	0.661621i	1.71718			1.96581	−	1.06563i	−0.351855	−	0.609430i	−3.89827	+	2.25067i		−	1.97682i	−0.624514	+	1.08169i	−0.566711	−	1.04543i

Inner twists

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

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	155.2.j.a	✓	28
5.b	even	2	1	inner	155.2.j.a	✓	28
5.c	odd	4	2		775.2.e.j		28
31.c	even	3	1	inner	155.2.j.a	✓	28
155.j	even	6	1	inner	155.2.j.a	✓	28
155.o	odd	12	2		775.2.e.j		28

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
155.2.j.a	✓	28	1.a	even	1	1	trivial
155.2.j.a	✓	28	5.b	even	2	1	inner
155.2.j.a	✓	28	31.c	even	3	1	inner
155.2.j.a	✓	28	155.j	even	6	1	inner
775.2.e.j		28	5.c	odd	4	2
775.2.e.j		28	155.o	odd	12	2

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(155, [\chi])\).