Newform orbit 11.18.c.a

• Label: 11.18.c.a
• Level: $11$
• Weight: $18$
• Character orbit: 11.c
• Analytic conductor: $20.154$
• Analytic rank: $0$
• Dimension: $64$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 11 \)
Weight:	\( k \)	\(=\)	\( 18 \)
Character orbit:	\([\chi]\)	\(=\)	11.c (of order \(5\), degree \(4\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(20.1544296079\)
Analytic rank:	\(0\)
Dimension:	\(64\)
Relative dimension:	\(16\) 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.

\(\operatorname{Tr}(f)(q) = \) \( 64 q + 795 q^{2} - 6360 q^{3} - 1037785 q^{4} - 91530 q^{5} + 11140861 q^{6} + 49560700 q^{7} + 9544335 q^{8} - 151892774 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
3.1	−562.713	+	408.835i	−2738.01	−	8426.72i	108996.	−	335456.i	864407.	+	628029.i	4.98585e6	+	3.62243e6i	7.02691e6	−	2.16266e7i	4.76403e7	+	1.46622e8i	4.09637e7	−	2.97619e7i	−7.43173e8
3.2	−473.906	+	344.313i	2496.11	+	7682.24i	65532.0	−	201687.i	−538471.	−	391222.i	−3.82801e6	−	2.78122e6i	−2.10383e6	+	6.47492e6i	1.46612e7	+	4.51226e7i	5.16904e7	−	3.75552e7i	3.89887e8
3.3	−386.011	+	280.453i	−4209.80	−	12956.4i	29846.8	−	91859.0i	−163840.	−	119037.i	5.25871e6	+	3.82067e6i	−8.75750e6	+	2.69528e7i	−5.08468e6	−	1.56490e7i	−4.56705e7	+	3.31815e7i	9.66281e7
3.4	−329.817	+	239.626i	5133.68	+	15799.8i	10855.0	−	33408.3i	530211.	+	385221.i	−5.47922e6	−	3.98089e6i	2.00658e6	−	6.17563e6i	−1.20870e7	−	3.71998e7i	−1.18803e8	+	8.63158e7i	−2.67181e8
3.5	−282.167	+	205.006i	−4663.18	−	14351.8i	−2912.84	+	8964.81i	−587500.	−	426844.i	4.25800e6	+	3.09362e6i	7.41842e6	−	2.28315e7i	−1.51426e7	−	4.66043e7i	−7.97520e7	+	5.79432e7i	2.53279e8
3.6	−187.138	+	135.964i	−651.935	−	2006.45i	−23969.0	+	73769.0i	1.34755e6	+	979050.i	394806.	+	286843.i	−867362.	+	2.66947e6i	−1.49135e7	−	4.58989e7i	1.00876e8	−	7.32905e7i	−3.85292e8
3.7	−90.8118	+	65.9786i	1830.07	+	5632.38i	−36609.9	+	112674.i	−884974.	−	642971.i	−537809.	−	390741.i	2.95566e6	−	9.09658e6i	−8.65594e6	−	2.66402e7i	7.61020e7	−	5.52914e7i	1.22788e8
3.8	21.1618	−	15.3750i	−1775.25	−	5463.67i	−40292.0	+	124006.i	45099.8	+	32766.9i	−121571.	−	88326.7i	−2.81268e6	+	8.65653e6i	2.11340e6	+	6.50439e6i	7.77764e7	−	5.65079e7i	1.45818e6
3.9	82.4939	−	59.9353i	5715.48	+	17590.5i	−37290.5	+	114768.i	−195114.	−	141759.i	1.52578e6	+	1.10855e6i	−7.38758e6	+	2.27366e7i	7.93250e6	+	2.44137e7i	−1.72281e8	+	1.25169e8i	−2.45921e7
3.10	143.607	−	104.337i	−6712.54	−	20659.1i	−30766.6	+	94689.8i	397499.	+	288800.i	−3.11948e6	−	2.26643e6i	27247.8	−	83860.2i	1.26510e7	+	3.89359e7i	−2.77263e8	+	2.01443e8i	8.72162e7
3.11	239.423	−	173.951i	4094.89	+	12602.8i	−13439.0	+	41361.1i	529060.	+	384385.i	3.17267e6	+	2.30508e6i	6.22941e6	−	1.91722e7i	1.59639e7	+	4.91319e7i	−3.75851e7	+	2.73071e7i	1.93533e8
3.12	320.806	−	233.079i	−1270.61	−	3910.53i	8087.20	−	24889.8i	357094.	+	259444.i	−1.31908e6	−	958370.i	3.52515e6	−	1.08493e7i	1.28543e7	+	3.95615e7i	9.07988e7	−	6.59692e7i	1.75029e8
3.13	333.640	−	242.403i	−2567.10	−	7900.73i	12052.5	−	37093.7i	−1.31349e6	−	954305.i	−2.77165e6	−	2.01372e6i	−3.59130e6	+	1.10529e7i	1.17332e7	+	3.61111e7i	4.86451e7	−	3.53427e7i	−6.69558e8
3.14	465.387	−	338.123i	2231.14	+	6866.73i	61754.0	−	190059.i	688990.	+	500581.i	3.36014e6	+	2.44129e6i	−8.17849e6	+	2.51708e7i	−1.22244e7	−	3.76228e7i	6.23025e7	−	4.52654e7i	4.89905e8
3.15	505.741	−	367.442i	4955.93	+	15252.8i	80256.5	−	247004.i	−1.06502e6	−	773784.i	8.11093e6	+	5.89294e6i	5.21144e6	−	1.60392e7i	−2.48508e7	−	7.64829e7i	−1.03610e8	+	7.52768e7i	−8.22946e8
3.16	541.603	−	393.497i	−4465.10	−	13742.2i	97989.8	−	301582.i	259422.	+	188481.i	−7.82581e6	−	5.68579e6i	2.58175e6	−	7.94582e6i	−3.84847e7	−	1.18444e8i	−6.44333e7	+	4.68135e7i	2.14670e8
4.1	−562.713	−	408.835i	−2738.01	+	8426.72i	108996.	+	335456.i	864407.	−	628029.i	4.98585e6	−	3.62243e6i	7.02691e6	+	2.16266e7i	4.76403e7	−	1.46622e8i	4.09637e7	+	2.97619e7i	−7.43173e8
4.2	−473.906	−	344.313i	2496.11	−	7682.24i	65532.0	+	201687.i	−538471.	+	391222.i	−3.82801e6	+	2.78122e6i	−2.10383e6	−	6.47492e6i	1.46612e7	−	4.51226e7i	5.16904e7	+	3.75552e7i	3.89887e8
4.3	−386.011	−	280.453i	−4209.80	+	12956.4i	29846.8	+	91859.0i	−163840.	+	119037.i	5.25871e6	−	3.82067e6i	−8.75750e6	−	2.69528e7i	−5.08468e6	+	1.56490e7i	−4.56705e7	−	3.31815e7i	9.66281e7
4.4	−329.817	−	239.626i	5133.68	−	15799.8i	10855.0	+	33408.3i	530211.	−	385221.i	−5.47922e6	+	3.98089e6i	2.00658e6	+	6.17563e6i	−1.20870e7	+	3.71998e7i	−1.18803e8	−	8.63158e7i	−2.67181e8

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
11.c	even	5	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	11.18.c.a	✓	64
11.c	even	5	1	inner	11.18.c.a	✓	64
11.c	even	5	1		121.18.a.i		32
11.d	odd	10	1		121.18.a.j		32

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
11.18.c.a	✓	64	1.a	even	1	1	trivial
11.18.c.a	✓	64	11.c	even	5	1	inner
121.18.a.i		32	11.c	even	5	1
121.18.a.j		32	11.d	odd	10	1

Hecke kernels

This newform subspace is the entire newspace \(S_{18}^{\mathrm{new}}(11, [\chi])\).