Newform orbit 55.5.i.c

• Label: 55.5.i.c
• Level: $55$
• Weight: $5$
• Character orbit: 55.i
• Analytic conductor: $5.685$
• Analytic rank: $0$
• Dimension: $32$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 55 = 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	55.i (of order \(10\), degree \(4\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(5.68534796961\)
Analytic rank:	\(0\)
Dimension:	\(32\)
Relative dimension:	\(8\) over \(\Q(\zeta_{10})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 32 q + 3 q^{3} + 40 q^{4} + 200 q^{5} + 60 q^{6} - 60 q^{7} + 240 q^{8} - 333 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
6.1	−6.51152	+	2.11572i	−5.57602	−	4.05121i	24.9793	−	18.1485i	3.45492	−	10.6331i	44.8796	+	14.5823i	35.9576	+	49.4914i	−59.8666	+	82.3993i	−10.3507	−	31.8563i			76.5475i
6.2	−5.33134	+	1.73226i	4.18265	+	3.03888i	12.4782	−	9.06595i	3.45492	−	10.6331i	−27.5633	−	8.95585i	−8.84881	−	12.1793i	1.89819	−	2.61264i	−16.7706	−	51.6145i			62.6737i
6.3	−1.13026	+	0.367245i	−12.1907	−	8.85708i	−11.8016	+	8.57440i	3.45492	−	10.6331i	17.0314	+	5.53385i	8.86736	+	12.2049i	21.3667	−	29.4087i	45.1356	+	138.913i			13.2870i
6.4	−1.08647	+	0.353014i	0.967832	+	0.703171i	−11.8885	+	8.63749i	3.45492	−	10.6331i	−1.29975	−	0.422313i	−11.5117	−	15.8444i	20.6108	−	28.3684i	−24.5881	−	75.6745i			12.7722i
6.5	1.47701	−	0.479911i	7.72989	+	5.61609i	−10.9930	+	7.98689i	3.45492	−	10.6331i	14.1124	+	4.58539i	48.0319	+	66.1102i	−27.0094	+	37.1752i	3.18032	+	9.78802i		−	17.3633i
6.6	4.09361	−	1.33010i	−8.24143	−	5.98775i	2.04423	−	1.48522i	3.45492	−	10.6331i	−41.7015	−	13.5496i	−31.1710	−	42.9032i	−34.0871	+	46.9168i	7.03767	+	21.6597i		−	48.1233i
6.7	5.26648	−	1.71118i	12.5492	+	9.11756i	11.8634	−	8.61925i	3.45492	−	10.6331i	81.6921	+	26.5434i	−50.3543	−	69.3068i	−4.34867	+	5.98543i	49.3232	+	151.801i		−	61.9112i
6.8	6.57658	−	2.13686i	−0.348489	−	0.253192i	25.7410	−	18.7019i	3.45492	−	10.6331i	−2.83290	−	0.920466i	27.5700	+	37.9469i	64.2916	−	88.4898i	−24.9730	−	76.8591i		−	77.3124i
41.1	−4.33964	−	5.97300i	−5.15176	−	15.8555i	−11.9000	+	36.6244i	9.04508	+	6.57164i	−72.3481	+	99.5786i	−34.5328	−	11.2204i	158.053	−	51.3544i	−159.326	+	115.757i		−	82.5449i
41.2	−3.52979	−	4.85833i	0.882567	+	2.71626i	−6.19975	+	19.0809i	9.04508	+	6.57164i	10.0812	−	13.8756i	53.1572	+	17.2718i	23.2040	−	7.53944i	58.9312	−	42.8160i		−	67.1405i
41.3	−3.23013	−	4.44589i	3.83090	+	11.7903i	−4.38793	+	13.5047i	9.04508	+	6.57164i	40.0440	−	55.1159i	−83.1841	−	27.0282i	−9.40947	+	3.05732i	−58.8049	+	42.7242i		−	61.4407i
41.4	−0.539548	−	0.742624i	2.14850	+	6.61241i	4.68389	−	14.4155i	9.04508	+	6.57164i	3.75132	−	5.16324i	14.7007	+	4.77655i	−27.2006	+	8.83802i	26.4224	−	19.1970i		−	10.2628i
41.5	−0.336982	−	0.463816i	−3.12765	−	9.62592i	4.84270	−	14.9043i	9.04508	+	6.57164i	−3.41069	+	4.69441i	−32.4398	−	10.5403i	−17.2687	+	5.61095i	−17.3458	+	12.6025i		−	6.40978i
41.6	2.17816	+	2.99798i	4.85120	+	14.9304i	0.700761	−	2.15672i	9.04508	+	6.57164i	−34.1945	+	47.0647i	29.0809	+	9.44896i	64.3816	−	20.9189i	−133.854	+	97.2504i			41.4311i
41.7	2.31182	+	3.18195i	−1.98676	−	6.11462i	0.163986	−	0.504697i	9.04508	+	6.57164i	14.8634	−	20.4577i	18.0365	+	5.86042i	61.8347	−	20.0913i	32.0890	−	23.3141i			43.9735i
41.8	4.13200	+	5.68721i	0.980059	+	3.01631i	−10.3266	+	31.7821i	9.04508	+	6.57164i	−13.1048	+	18.0372i	−13.3596	−	4.34081i	−116.450	+	37.8369i	57.3928	−	41.6983i			78.5953i
46.1	−6.51152	−	2.11572i	−5.57602	+	4.05121i	24.9793	+	18.1485i	3.45492	+	10.6331i	44.8796	−	14.5823i	35.9576	−	49.4914i	−59.8666	−	82.3993i	−10.3507	+	31.8563i		−	76.5475i
46.2	−5.33134	−	1.73226i	4.18265	−	3.03888i	12.4782	+	9.06595i	3.45492	+	10.6331i	−27.5633	+	8.95585i	−8.84881	+	12.1793i	1.89819	+	2.61264i	−16.7706	+	51.6145i		−	62.6737i
46.3	−1.13026	−	0.367245i	−12.1907	+	8.85708i	−11.8016	−	8.57440i	3.45492	+	10.6331i	17.0314	−	5.53385i	8.86736	−	12.2049i	21.3667	+	29.4087i	45.1356	−	138.913i		−	13.2870i
46.4	−1.08647	−	0.353014i	0.967832	−	0.703171i	−11.8885	−	8.63749i	3.45492	+	10.6331i	−1.29975	+	0.422313i	−11.5117	+	15.8444i	20.6108	+	28.3684i	−24.5881	+	75.6745i		−	12.7722i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
11.d	odd	10	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	55.5.i.c	✓	32
11.d	odd	10	1	inner	55.5.i.c	✓	32

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
55.5.i.c	✓	32	1.a	even	1	1	trivial
55.5.i.c	✓	32	11.d	odd	10	1	inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T2^32 - 84*T2^30 - 240*T2^29 + 5741*T2^28 + 20160*T2^27 - 325174*T2^26 - 1161610*T2^25 + 16821451*T2^24 + 60212470*T2^23 - 555077870*T2^22 - 3006592530*T2^21 + 16753466795*T2^20 + 84458673110*T2^19 - 383018262150*T2^18 - 1761117043690*T2^17 + 8623942879405*T2^16 + 30800878516280*T2^15 - 153756238747340*T2^14 - 562121148762200*T2^13 + 3765085610403580*T2^12 - 2261892682681600*T2^11 - 20538547153377600*T2^10 + 27176203359420000*T2^9 + 107705398407414800*T2^8 + 5733829448048000*T2^7 - 222792101797664000*T2^6 - 208732504641040000*T2^5 + 117438840891672000*T2^4 + 379758807901440000*T2^3 + 332625039383200000*T2^2 + 144738278216000000*T2 + 30702749284000000