Newform orbit 230.4.e.a

• Label: 230.4.e.a
• Level: $230$
• Weight: $4$
• Character orbit: 230.e
• Analytic conductor: $13.570$
• Analytic rank: $0$
• Dimension: $72$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	230.e (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(13.5704393013\)
Analytic rank:	\(0\)
Dimension:	\(72\)
Relative dimension:	\(36\) over \(\Q(i)\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 72 q - 16 q^{3} - 16 q^{6}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
137.1	−1.41421	−	1.41421i	−7.12210	+	7.12210i			4.00000i	−1.63222	−	11.0606i	20.1443			−16.1147	+	16.1147i	5.65685	−	5.65685i		−	74.4485i	−13.3337	+	17.9503i
137.2	−1.41421	−	1.41421i	−7.12210	+	7.12210i			4.00000i	1.63222	+	11.0606i	20.1443			16.1147	−	16.1147i	5.65685	−	5.65685i		−	74.4485i	13.3337	−	17.9503i
137.3	−1.41421	−	1.41421i	−4.47764	+	4.47764i			4.00000i	−11.1722	+	0.427507i	12.6647			−6.97055	+	6.97055i	5.65685	−	5.65685i		−	13.0984i	16.4044	+	15.1952i
137.4	−1.41421	−	1.41421i	−4.47764	+	4.47764i			4.00000i	11.1722	−	0.427507i	12.6647			6.97055	−	6.97055i	5.65685	−	5.65685i		−	13.0984i	−16.4044	−	15.1952i
137.5	−1.41421	−	1.41421i	−3.58924	+	3.58924i			4.00000i	−11.1634	−	0.614616i	10.1519			16.2976	−	16.2976i	5.65685	−	5.65685i			1.23476i	14.9183	+	16.6567i
137.6	−1.41421	−	1.41421i	−3.58924	+	3.58924i			4.00000i	11.1634	+	0.614616i	10.1519			−16.2976	+	16.2976i	5.65685	−	5.65685i			1.23476i	−14.9183	−	16.6567i
137.7	−1.41421	−	1.41421i	−2.02411	+	2.02411i			4.00000i	−2.14096	+	10.9734i	5.72506			−1.46247	+	1.46247i	5.65685	−	5.65685i			18.8059i	18.5466	−	12.4910i
137.8	−1.41421	−	1.41421i	−2.02411	+	2.02411i			4.00000i	2.14096	−	10.9734i	5.72506			1.46247	−	1.46247i	5.65685	−	5.65685i			18.8059i	−18.5466	+	12.4910i
137.9	−1.41421	−	1.41421i	0.422683	−	0.422683i			4.00000i	−11.1421	+	0.923475i	−1.19553			−23.7633	+	23.7633i	5.65685	−	5.65685i			26.6427i	17.0634	+	14.4514i
137.10	−1.41421	−	1.41421i	0.422683	−	0.422683i			4.00000i	11.1421	−	0.923475i	−1.19553			23.7633	−	23.7633i	5.65685	−	5.65685i			26.6427i	−17.0634	−	14.4514i
137.11	−1.41421	−	1.41421i	0.933603	−	0.933603i			4.00000i	−4.48554	−	10.2411i	−2.64063			−3.80706	+	3.80706i	5.65685	−	5.65685i			25.2568i	−8.13958	+	20.8266i
137.12	−1.41421	−	1.41421i	0.933603	−	0.933603i			4.00000i	4.48554	+	10.2411i	−2.64063			3.80706	−	3.80706i	5.65685	−	5.65685i			25.2568i	8.13958	−	20.8266i
137.13	−1.41421	−	1.41421i	3.25915	−	3.25915i			4.00000i	−7.62223	+	8.17934i	−9.21827			22.5290	−	22.5290i	5.65685	−	5.65685i			5.75586i	22.3468	−	0.787870i
137.14	−1.41421	−	1.41421i	3.25915	−	3.25915i			4.00000i	7.62223	−	8.17934i	−9.21827			−22.5290	+	22.5290i	5.65685	−	5.65685i			5.75586i	−22.3468	+	0.787870i
137.15	−1.41421	−	1.41421i	5.03526	−	5.03526i			4.00000i	−6.80528	−	8.87064i	−14.2419			11.1481	−	11.1481i	5.65685	−	5.65685i		−	23.7076i	−2.92086	+	22.1691i
137.16	−1.41421	−	1.41421i	5.03526	−	5.03526i			4.00000i	6.80528	+	8.87064i	−14.2419			−11.1481	+	11.1481i	5.65685	−	5.65685i		−	23.7076i	2.92086	−	22.1691i
137.17	−1.41421	−	1.41421i	6.26949	−	6.26949i			4.00000i	−8.82273	+	6.86728i	−17.7328			−11.5218	+	11.5218i	5.65685	−	5.65685i		−	51.6130i	22.1890	+	2.76543i
137.18	−1.41421	−	1.41421i	6.26949	−	6.26949i			4.00000i	8.82273	−	6.86728i	−17.7328			11.5218	−	11.5218i	5.65685	−	5.65685i		−	51.6130i	−22.1890	−	2.76543i
137.19	1.41421	+	1.41421i	−6.86623	+	6.86623i			4.00000i	−11.1776	+	0.245509i	−19.4206			21.1410	−	21.1410i	−5.65685	+	5.65685i		−	67.2901i	−16.1548	−	15.4604i
137.20	1.41421	+	1.41421i	−6.86623	+	6.86623i			4.00000i	11.1776	−	0.245509i	−19.4206			−21.1410	+	21.1410i	−5.65685	+	5.65685i		−	67.2901i	16.1548	+	15.4604i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
5.c	odd	4	1	inner
23.b	odd	2	1	inner
115.e	even	4	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	230.4.e.a	✓	72
5.c	odd	4	1	inner	230.4.e.a	✓	72
23.b	odd	2	1	inner	230.4.e.a	✓	72
115.e	even	4	1	inner	230.4.e.a	✓	72

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
230.4.e.a	✓	72	1.a	even	1	1	trivial
230.4.e.a	✓	72	5.c	odd	4	1	inner
230.4.e.a	✓	72	23.b	odd	2	1	inner
230.4.e.a	✓	72	115.e	even	4	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{4}^{\mathrm{new}}(230, [\chi])\).