Newform orbit 41.4.d.a

• Label: 41.4.d.a
• Level: $41$
• Weight: $4$
• Character orbit: 41.d
• Analytic conductor: $2.419$
• Analytic rank: $0$
• Dimension: $40$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 41 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	41.d (of order \(5\), degree \(4\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(2.41907831024\)
Analytic rank:	\(0\)
Dimension:	\(40\)
Relative dimension:	\(10\) over \(\Q(\zeta_{5})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 40 q - 3 q^{2} - 6 q^{3} - 43 q^{4} - 5 q^{5} - 95 q^{6} - 3 q^{7} - 38 q^{8} + 350 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
10.1	−3.85741	−	2.80257i	8.20175			4.55306	+	14.0129i	5.68675	+	17.5020i	−31.6375	−	22.9860i	9.31777	−	6.76976i	9.92191	−	30.5365i	40.2686			27.1145	−	83.4499i
10.2	−3.59928	−	2.61503i	−7.16008			3.64430	+	11.2160i	0.649588	+	1.99923i	25.7711	+	18.7238i	16.9425	−	12.3095i	5.21490	−	16.0498i	24.2667			2.88999	−	8.89446i
10.3	−3.16625	−	2.30042i	1.58823			2.26111	+	6.95897i	−4.57744	−	14.0879i	−5.02873	−	3.65358i	−15.3030	+	11.1183i	−0.825907	+	2.54188i	−24.4775			−17.9148	+	55.1360i
10.4	−1.29970	−	0.944286i	−4.38010			−1.67460	−	5.15388i	5.66130	+	17.4237i	5.69280	+	4.13606i	−22.5638	+	16.3935i	−6.66179	+	20.5029i	−7.81475			9.09496	−	27.9914i
10.5	−0.889200	−	0.646042i	3.08580			−2.09883	−	6.45953i	−0.696269	−	2.14289i	−2.74390	−	1.99356i	24.9913	−	18.1572i	−5.02400	+	15.4623i	−17.4778			−0.765277	+	2.35528i
10.6	0.380941	+	0.276770i	9.60274			−2.40362	−	7.39759i	−1.28841	−	3.96532i	3.65807	+	2.65775i	−22.9567	+	16.6790i	2.29584	−	7.06587i	65.2125			0.606673	−	1.86715i
10.7	0.793027	+	0.576168i	−6.08602			−2.17521	−	6.69462i	−3.28465	−	10.1091i	−4.82638	−	3.50657i	1.62568	−	1.18113i	4.55549	−	14.0204i	10.0396			3.21973	−	9.90931i
10.8	2.46224	+	1.78892i	2.36431			0.390251	+	1.20107i	3.59614	+	11.0678i	5.82151	+	4.22957i	5.30102	−	3.85142i	6.33621	−	19.5009i	−21.4100			−10.9449	+	33.6848i
10.9	3.83701	+	2.78775i	2.38319			4.47896	+	13.7848i	−4.56237	−	14.0415i	9.14433	+	6.64374i	−8.16918	+	5.93525i	−9.51798	+	29.2933i	−21.3204			21.6384	−	66.5962i
10.10	4.02961	+	2.92768i	−9.98178			5.19428	+	15.9863i	3.71455	+	11.4322i	−40.2227	−	29.2235i	9.50537	−	6.90606i	−13.5586	+	41.7291i	72.6360			−18.5017	+	56.9424i
16.1	−1.66588	+	5.12707i	−0.206098			−17.0395	−	12.3799i	−10.4942	−	7.62451i	0.343335	−	1.05668i	8.17635	+	25.1642i	56.9678	−	41.3895i	−26.9575			56.5735	−	41.1031i
16.2	−1.25944	+	3.87615i	6.40294			−6.96621	−	5.06125i	12.9896	+	9.43753i	−8.06410	+	24.8187i	−7.86803	−	24.2153i	2.01367	−	1.46301i	13.9976			−52.9409	+	38.4638i
16.3	−0.946578	+	2.91327i	−6.38341			−1.11898	−	0.812985i	−4.90002	−	3.56007i	6.04240	−	18.5966i	−7.43933	−	22.8959i	−16.3977	+	11.9137i	13.7480			15.0097	−	10.9052i
16.4	−0.717401	+	2.20793i	1.13981			2.11183	+	1.53433i	2.32996	+	1.69281i	−0.817703	+	2.51663i	6.12035	+	18.8365i	−19.9282	+	14.4787i	−25.7008			−5.40913	+	3.92996i
16.5	−0.239783	+	0.737978i	8.69666			5.98502	+	4.34837i	−13.9785	−	10.1560i	−2.08532	+	6.41794i	1.09434	+	3.36803i	−9.66620	+	7.02291i	48.6320			10.8467	−	7.88058i
16.6	0.124164	−	0.382138i	−7.20263			6.34152	+	4.60739i	9.53442	+	6.92716i	−0.894308	+	2.75240i	6.78280	+	20.8753i	5.14857	−	3.74065i	24.8779			3.83096	−	2.78336i
16.7	0.571678	−	1.75944i	2.48041			3.70331	+	2.69061i	5.31967	+	3.86497i	1.41800	−	4.36415i	−4.69633	−	14.4538i	18.8245	−	13.6768i	−20.8476			9.84134	−	7.15015i
16.8	0.911418	−	2.80506i	−5.81461			−0.565529	−	0.410881i	−17.8879	−	12.9963i	−5.29955	+	16.3103i	0.685164	+	2.10872i	17.4210	−	12.6571i	6.80974			−52.7589	+	38.3316i
16.9	1.42042	−	4.37159i	5.17677			−10.6211	−	7.71668i	−1.75915	−	1.27810i	7.35317	−	22.6307i	6.53108	+	20.1006i	−19.0710	+	13.8559i	−0.201025			−8.08603	+	5.87485i
16.10	1.61042	−	4.95638i	−6.90788			−15.5001	−	11.2614i	11.4469	+	8.31669i	−11.1246	+	34.2380i	−9.57736	−	29.4761i	−47.0485	+	34.1827i	20.7188			59.6551	−	43.3420i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
41.d	even	5	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	41.4.d.a	✓	40
41.d	even	5	1	inner	41.4.d.a	✓	40
41.d	even	5	1		1681.4.a.h		20
41.f	even	10	1		1681.4.a.i		20

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
41.4.d.a	✓	40	1.a	even	1	1	trivial
41.4.d.a	✓	40	41.d	even	5	1	inner
1681.4.a.h		20	41.d	even	5	1
1681.4.a.i		20	41.f	even	10	1

Hecke kernels

This newform subspace is the entire newspace \(S_{4}^{\mathrm{new}}(41, [\chi])\).