Newform orbit 71.11.e.a

• Label: 71.11.e.a
• Level: $71$
• Weight: $11$
• Character orbit: 71.e
• Analytic conductor: $45.110$
• Analytic rank: $0$
• Dimension: $236$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 71 \)
Weight:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	71.e (of order \(10\), degree \(4\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(45.1103649398\)
Analytic rank:	\(0\)
Dimension:	\(236\)
Relative dimension:	\(59\) 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.

\(\operatorname{Tr}(f)(q) = \) \( 236 q + 30 q^{2} + 59 q^{3} - 27818 q^{4} + 3303 q^{5} + 27866 q^{6} - 5 q^{7} - 145199 q^{8} - 973354 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
14.1	−19.4061	+	59.7258i	−57.1788	+	175.978i	−2362.14	−	1716.19i	4315.55	−	3135.43i	−9400.82	−	6830.09i	−28113.6	−	9134.68i	96315.7	−	69977.4i	20072.7	+	14583.7i	103518.	+	318596.i
14.2	−19.1843	+	59.0433i	43.4464	−	133.714i	−2289.64	−	1663.52i	−2061.92	+	1498.07i	7061.45	+	5130.44i	8882.57	+	2886.12i	90714.1	−	65907.6i	31779.7	+	23089.3i	−48894.6	−	150482.i
14.3	−17.8742	+	55.0110i	128.622	−	395.859i	−1878.29	−	1364.66i	1093.06	−	794.153i	19477.6	+	14151.3i	−23046.9	−	7488.40i	60726.0	−	44120.0i	−92389.2	−	67124.7i	24149.7	+	74325.1i
14.4	−17.2112	+	52.9705i	−114.392	+	352.063i	−1681.22	−	1221.48i	1506.05	−	1094.21i	−16680.1	−	12118.8i	27121.9	+	8812.45i	47497.3	−	34508.8i	−63090.9	−	45838.2i	32040.1	+	98609.2i
14.5	−16.9675	+	52.2207i	−115.583	+	355.729i	−1610.67	−	1170.22i	−1923.64	+	1397.61i	−16615.2	−	12071.7i	−10586.9	−	3439.88i	42950.9	−	31205.6i	−65412.1	−	47524.7i	−40344.5	−	124168.i
14.6	−16.3176	+	50.2204i	−22.1552	+	68.1867i	−1427.39	−	1037.06i	1741.82	−	1265.51i	−3062.85	−	2225.29i	15542.3	+	5049.99i	31628.0	−	22979.1i	43613.1	+	31686.7i	35132.0	+	108125.i
14.7	−16.2580	+	50.0371i	91.1363	−	280.489i	−1410.95	−	1025.12i	3491.28	−	2536.56i	12553.1	+	9120.39i	13870.2	+	4506.69i	30647.5	−	22266.7i	−22596.4	−	16417.3i	70160.8	+	215933.i
14.8	−15.9892	+	49.2096i	−30.5114	+	93.9043i	−1337.50	−	971.750i	−2860.83	+	2078.51i	−4133.14	−	3002.90i	−9806.61	−	3186.36i	26340.1	−	19137.2i	39884.6	+	28977.8i	−56540.5	−	174014.i
14.9	−14.5101	+	44.6575i	89.1609	−	274.409i	−955.316	−	694.078i	−1858.54	+	1350.31i	10960.7	+	7963.40i	−26393.8	−	8575.85i	5957.87	−	4328.65i	−19578.9	−	14224.9i	−33333.9	−	102591.i
14.10	−14.3907	+	44.2899i	129.754	−	399.343i	−926.074	−	672.832i	−2983.26	+	2167.47i	15819.6	+	11493.6i	16429.5	+	5338.25i	4547.03	−	3303.61i	−94866.7	−	68924.7i	−53065.8	−	163320.i
14.11	−14.2576	+	43.8803i	45.5545	−	140.202i	−893.767	−	649.360i	2253.52	−	1637.28i	5502.62	+	3997.89i	−2008.05	−	652.456i	3014.41	−	2190.10i	30190.2	+	21934.5i	39714.5	+	122229.i
14.12	−12.6064	+	38.7984i	−20.2167	+	62.2205i	−517.962	−	376.321i	2383.11	−	1731.43i	−2159.20	−	1568.75i	−15990.5	−	5195.62i	−12665.7	+	9202.18i	44309.0	+	32192.3i	37134.3	+	114288.i
14.13	−11.9937	+	36.9127i	−45.4052	+	139.743i	−390.269	−	283.547i	−4400.17	+	3196.91i	−4613.72	−	3352.06i	21654.4	+	7035.96i	−17006.2	+	12355.7i	30305.2	+	22018.0i	−65232.6	−	200765.i
14.14	−10.5179	+	32.3708i	−120.793	+	371.764i	−108.812	−	79.0562i	5009.33	−	3639.49i	−10763.8	−	7820.36i	−2792.72	−	907.408i	−24493.6	+	17795.6i	−75845.5	−	55105.0i	65125.6	+	200436.i
14.15	−10.4826	+	32.2621i	−120.705	+	371.492i	−102.526	−	74.4892i	377.768	−	274.465i	−10719.8	−	7788.41i	−11301.8	−	3672.16i	−24624.5	+	17890.8i	−75665.2	−	54974.0i	4894.82	+	15064.7i
14.16	−10.1921	+	31.3682i	67.6837	−	208.309i	−51.6491	−	37.5253i	−4366.28	+	3172.29i	5844.43	+	4246.23i	−14591.8	−	4741.18i	−25620.2	+	18614.2i	8960.12	+	6509.91i	−55007.2	−	169295.i
14.17	−10.0133	+	30.8177i	−75.4503	+	232.212i	−21.0331	−	15.2814i	733.505	−	532.923i	−6400.75	−	4650.42i	3903.64	+	1268.37i	−26162.7	+	19008.3i	−458.144	−	332.861i	9078.67	+	27941.3i
14.18	−8.92442	+	27.4665i	48.0631	−	147.923i	153.668	+	111.647i	−920.054	+	668.459i	3633.99	+	2640.25i	26817.8	+	8713.62i	−28363.1	+	20607.0i	28200.5	+	20488.9i	−10149.3	−	31236.3i
14.19	−8.56871	+	26.3718i	54.5128	−	167.773i	206.386	+	149.948i	−500.546	+	363.668i	3957.37	+	2875.20i	−2395.92	−	778.482i	−28694.4	+	20847.7i	22595.5	+	16416.6i	−5301.54	−	16316.5i
14.20	−7.96819	+	24.5236i	139.395	−	429.014i	290.519	+	211.075i	2978.78	−	2164.21i	9410.24	+	6836.94i	15236.1	+	4950.52i	−28852.9	+	20962.9i	−116851.	−	84896.9i	29338.7	+	90295.3i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
71.e	odd	10	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	71.11.e.a	✓	236
71.e	odd	10	1	inner	71.11.e.a	✓	236

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
71.11.e.a	✓	236	1.a	even	1	1	trivial
71.11.e.a	✓	236	71.e	odd	10	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{11}^{\mathrm{new}}(71, [\chi])\).