Newform orbit 11.16.c.a

• Label: 11.16.c.a
• Level: $11$
• Weight: $16$
• Character orbit: 11.c
• Analytic conductor: $15.696$
• Analytic rank: $0$
• Dimension: $56$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 11 \)
Weight:	\( k \)	\(=\)	\( 16 \)
Character orbit:	\([\chi]\)	\(=\)	11.c (of order \(5\), degree \(4\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(15.6962855610\)
Analytic rank:	\(0\)
Dimension:	\(56\)
Relative dimension:	\(14\) 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.

\(\operatorname{Tr}(f)(q) = \) \( 56 q - 309 q^{2} + 5973 q^{3} - 261945 q^{4} + 152073 q^{5} - 772739 q^{6} - 7602707 q^{7} + 10151679 q^{8} - 87187685 q^{9}+O(q^{10}) \)

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	−277.051	+	201.289i	1749.55	+	5384.55i	26113.9	−	80370.4i	176509.	+	128241.i	−1.56856e6	−	1.13963e6i	−538687.	+	1.65791e6i	5.47517e6	+	1.68508e7i	−1.43239e7	+	1.04069e7i	−7.47156e7
3.2	−253.298	+	184.032i	−327.889	−	1009.14i	20166.3	−	62065.6i	−268522.	−	195093.i	268768.	+	195271.i	361718.	−	1.11325e6i	3.14361e6	+	9.67504e6i	1.06977e7	−	7.77230e6i	1.03919e8
3.3	−213.826	+	155.354i	−1820.29	−	5602.28i	11460.9	−	35273.0i	109531.	+	79578.7i	1.25956e6	+	915123.i	−194947.	+	599985.i	352851.	+	1.08596e6i	−1.64635e7	+	1.19615e7i	−3.57833e7
3.4	−165.778	+	120.445i	279.199	+	859.286i	2849.59	−	8770.14i	62426.8	+	45355.7i	−149782.	−	108823.i	157496.	−	484722.i	−1.49101e6	−	4.58884e6i	1.09481e7	−	7.95425e6i	−1.58119e7
3.5	−107.587	+	78.1665i	2192.64	+	6748.26i	−4660.92	+	14344.8i	−188428.	−	136901.i	−763387.	−	554633.i	788945.	−	2.42812e6i	−1.96642e6	−	6.05201e6i	−2.91228e7	+	2.11590e7i	3.09735e7
3.6	−57.2981	+	41.6295i	507.864	+	1563.04i	−8575.81	+	26393.6i	−25417.0	−	18466.5i	−94168.4	−	68417.3i	−1.09423e6	+	3.36769e6i	−1.32453e6	−	4.07650e6i	9.42333e6	−	6.84645e6i	2.22510e6
3.7	−19.2607	+	13.9937i	−1826.07	−	5620.06i	−9950.72	+	30625.2i	−225607.	−	163913.i	113817.	+	82692.7i	−633513.	+	1.94975e6i	−477973.	−	1.47105e6i	−1.66420e7	+	1.20911e7i	6.63909e6
3.8	−15.2767	+	11.0992i	−1209.73	−	3723.16i	−10015.7	+	30825.1i	92109.6	+	66921.6i	59804.5	+	43450.5i	1.03122e6	−	3.17377e6i	−380333.	−	1.17055e6i	−789941.	+	573926.i	−2.14990e6
3.9	53.8977	−	39.1590i	1716.66	+	5283.35i	−8754.33	+	26943.1i	246015.	+	178740.i	299415.	+	217538.i	263323.	−	810423.i	1.25782e6	+	3.87118e6i	−1.33583e7	+	9.70540e6i	2.02589e7
3.10	102.038	−	74.1351i	73.1475	+	225.125i	−5210.09	+	16035.0i	−75699.5	−	54998.9i	24153.5	+	17548.5i	582256.	−	1.79200e6i	1.93426e6	+	5.95306e6i	1.15632e7	−	8.40114e6i	−1.18016e7
3.11	145.376	−	105.622i	−1295.51	−	3987.17i	−147.608	+	454.292i	253124.	+	183906.i	−609470.	−	442806.i	−1.01402e6	+	3.12083e6i	1.84609e6	+	5.68169e6i	−2.61066e6	+	1.89676e6i	5.62228e7
3.12	164.192	−	119.293i	1338.90	+	4120.71i	2602.47	−	8009.59i	−142395.	−	103456.i	711407.	+	516867.i	−560331.	+	1.72452e6i	1.52689e6	+	4.69929e6i	−3.57908e6	+	2.60036e6i	−3.57216e7
3.13	231.765	−	168.387i	−1332.91	−	4102.29i	15234.9	−	46888.3i	−77837.3	−	56552.1i	−999696.	−	726321.i	180035.	−	554092.i	−1.46364e6	−	4.50461e6i	−3.44359e6	+	2.50191e6i	−2.75626e7
3.14	262.743	−	190.894i	1046.87	+	3221.93i	22467.4	−	69147.7i	100198.	+	72798.2i	890104.	+	646698.i	209213.	−	643893.i	−4.00814e6	−	1.23358e7i	2.32360e6	−	1.68819e6i	4.02230e7
4.1	−277.051	−	201.289i	1749.55	−	5384.55i	26113.9	+	80370.4i	176509.	−	128241.i	−1.56856e6	+	1.13963e6i	−538687.	−	1.65791e6i	5.47517e6	−	1.68508e7i	−1.43239e7	−	1.04069e7i	−7.47156e7
4.2	−253.298	−	184.032i	−327.889	+	1009.14i	20166.3	+	62065.6i	−268522.	+	195093.i	268768.	−	195271.i	361718.	+	1.11325e6i	3.14361e6	−	9.67504e6i	1.06977e7	+	7.77230e6i	1.03919e8
4.3	−213.826	−	155.354i	−1820.29	+	5602.28i	11460.9	+	35273.0i	109531.	−	79578.7i	1.25956e6	−	915123.i	−194947.	−	599985.i	352851.	−	1.08596e6i	−1.64635e7	−	1.19615e7i	−3.57833e7
4.4	−165.778	−	120.445i	279.199	−	859.286i	2849.59	+	8770.14i	62426.8	−	45355.7i	−149782.	+	108823.i	157496.	+	484722.i	−1.49101e6	+	4.58884e6i	1.09481e7	+	7.95425e6i	−1.58119e7
4.5	−107.587	−	78.1665i	2192.64	−	6748.26i	−4660.92	−	14344.8i	−188428.	+	136901.i	−763387.	+	554633.i	788945.	+	2.42812e6i	−1.96642e6	+	6.05201e6i	−2.91228e7	−	2.11590e7i	3.09735e7
4.6	−57.2981	−	41.6295i	507.864	−	1563.04i	−8575.81	−	26393.6i	−25417.0	+	18466.5i	−94168.4	+	68417.3i	−1.09423e6	−	3.36769e6i	−1.32453e6	+	4.07650e6i	9.42333e6	+	6.84645e6i	2.22510e6

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	11.16.c.a	✓	56
11.c	even	5	1	inner	11.16.c.a	✓	56
11.c	even	5	1		121.16.a.j		28
11.d	odd	10	1		121.16.a.i		28

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
11.16.c.a	✓	56	1.a	even	1	1	trivial
11.16.c.a	✓	56	11.c	even	5	1	inner
121.16.a.i		28	11.d	odd	10	1
121.16.a.j		28	11.c	even	5	1

Hecke kernels

This newform subspace is the entire newspace \(S_{16}^{\mathrm{new}}(11, [\chi])\).