Newform orbit 185.4.c.a

• Label: 185.4.c.a
• Level: $185$
• Weight: $4$
• Character orbit: 185.c
• Analytic conductor: $10.915$
• Analytic rank: $0$
• Dimension: $38$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 185 = 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	185.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(10.9153533511\)
Analytic rank:	\(0\)
Dimension:	\(38\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 38 q - 132 q^{4} - 12 q^{7} + 342 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
36.1		−	5.17832i	−5.27991			−18.8150				−	5.00000i			27.3411i	−10.3558					56.0036i	0.877433			−25.8916
36.2		−	5.12833i	−8.15228			−18.2998					5.00000i			41.8076i	5.56601					52.8208i	39.4597			25.6417
36.3		−	5.02465i	3.10224			−17.2471					5.00000i		−	15.5877i	−6.82934					46.4635i	−17.3761			25.1232
36.4		−	4.58523i	6.29800			−13.0243				−	5.00000i		−	28.8778i	−34.1621					23.0377i	12.6648			−22.9261
36.5		−	4.37775i	9.62482			−11.1647					5.00000i		−	42.1350i	7.38790					13.8542i	65.6371			21.8887
36.6		−	4.32909i	−0.0481568			−10.7410				−	5.00000i			0.208475i	22.7237					11.8660i	−26.9977			−21.6454
36.7		−	3.98006i	−3.98489			−7.84091					5.00000i			15.8601i	33.5488				−	0.633203i	−11.1207			19.9003
36.8		−	3.55953i	−1.91704			−4.67024					5.00000i			6.82376i	−21.1101				−	11.8524i	−23.3250			17.7976
36.9		−	3.54933i	−4.13476			−4.59772				−	5.00000i			14.6756i	−9.11563				−	12.0758i	−9.90378			−17.7466
36.10		−	3.50204i	6.86582			−4.26427				−	5.00000i		−	24.0444i	20.1710				−	13.0827i	20.1395			−17.5102
36.11		−	2.95932i	1.02679			−0.757590					5.00000i		−	3.03859i	−6.58783				−	21.4326i	−25.9457			14.7966
36.12		−	2.79819i	−9.93221			0.170157				−	5.00000i			27.7922i	23.0736				−	22.8616i	71.6489			−13.9909
36.13		−	1.79807i	−6.65261			4.76694					5.00000i			11.9619i	11.0246				−	22.9559i	17.2573			8.99036
36.14		−	1.58475i	−0.464388			5.48858				−	5.00000i			0.735938i	0.488913				−	21.3760i	−26.7843			−7.92373
36.15		−	1.25652i	4.58062			6.42116					5.00000i		−	5.75564i	29.2689				−	18.1205i	−6.01792			6.28259
36.16		−	1.21667i	9.37412			6.51972				−	5.00000i		−	11.4052i	−3.25474				−	17.6657i	60.8740			−6.08333
36.17		−	0.873049i	0.710831			7.23779				−	5.00000i		−	0.620590i	−32.5834				−	13.3033i	−26.4947			−4.36525
36.18		−	0.827610i	6.90400			7.31506					5.00000i		−	5.71382i	−15.3849				−	12.6749i	20.6652			4.13805
36.19		−	0.704803i	−7.92098			7.50325					5.00000i			5.58273i	−19.8697				−	10.9267i	35.7419			3.52402
36.20			0.704803i	−7.92098			7.50325				−	5.00000i		−	5.58273i	−19.8697					10.9267i	35.7419			3.52402

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
37.b	even	2	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	185.4.c.a	✓	38
37.b	even	2	1	inner	185.4.c.a	✓	38

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
185.4.c.a	✓	38	1.a	even	1	1	trivial
185.4.c.a	✓	38	37.b	even	2	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{4}^{\mathrm{new}}(185, [\chi])\).