Newform orbit 47.12.c.a

• Label: 47.12.c.a
• Level: $47$
• Weight: $12$
• Character orbit: 47.c
• Analytic conductor: $36.112$
• Analytic rank: $0$
• Dimension: $946$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 47 \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	47.c (of order \(23\), degree \(22\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(36.1121294863\)
Analytic rank:	\(0\)
Dimension:	\(946\)
Relative dimension:	\(43\) over \(\Q(\zeta_{23})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{23}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 946 q - 21 q^{2} + 485 q^{3} - 39073 q^{4} + 749 q^{5} + 15017 q^{6} - 38387 q^{7} - 150905 q^{8} - 2268416 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
2.1	−85.2122	−	11.7122i	−165.508	+	100.647i	5151.90	+	1443.49i	−2351.26	−	6615.81i	15282.1	−	6637.95i	2543.69	−	37187.4i	−260527.	−	113163.i	−64236.2	+	123970.i	122871.	+	591287.i
2.2	−80.7850	−	11.1036i	−655.392	+	398.552i	4430.88	+	1241.47i	1163.26	+	3273.11i	57371.2	−	24919.8i	−1395.95	+	20408.0i	−190987.	−	82957.2i	189195.	−	365130.i	−57630.8	−	277335.i
2.3	−80.1405	−	11.0151i	411.104	−	249.998i	4329.11	+	1212.96i	−1160.10	−	3264.20i	−35699.8	+	15506.6i	−4109.09	+	60072.8i	−181621.	−	78889.0i	25008.5	−	48264.3i	57015.3	+	274373.i
2.4	−79.7283	−	10.9584i	−149.745	+	91.0622i	4264.46	+	1194.85i	4014.86	+	11296.7i	12936.8	−	5619.26i	588.784	−	8607.72i	−175731.	−	76330.8i	−67367.8	+	130014.i	−196304.	−	944666.i
2.5	−76.9666	−	10.5788i	550.181	−	334.573i	3839.88	+	1075.89i	−1625.75	−	4574.42i	−45884.9	+	19930.6i	3773.81	−	55171.1i	−138224.	−	60039.2i	109261.	−	210865.i	76736.4	+	369276.i
2.6	−75.6147	−	10.3930i	430.656	−	261.888i	3637.52	+	1019.18i	3420.27	+	9623.72i	−35285.7	+	15326.8i	689.193	−	10075.6i	−121084.	−	52594.0i	35380.3	−	68280.8i	−158604.	−	763242.i
2.7	−68.7984	−	9.45612i	−175.480	+	106.712i	2671.74	+	748.587i	−134.935	−	379.669i	13081.8	−	5682.23i	−2314.13	+	33831.4i	−46283.4	−	20103.7i	−62093.4	+	119835.i	5693.08	+	27396.6i
2.8	−60.2946	−	8.28730i	−503.426	+	306.140i	1594.70	+	446.814i	−2919.91	−	8215.84i	32890.9	−	14286.5i	−5058.04	+	73945.9i	21876.2	+	9502.17i	78216.6	−	150951.i	107968.	+	519568.i
2.9	−55.2127	−	7.58882i	−555.508	+	337.812i	1018.80	+	285.455i	−1094.43	−	3079.43i	33234.7	−	14435.9i	5735.20	−	83845.6i	50604.8	+	21980.7i	112973.	−	218028.i	37057.2	+	178329.i
2.10	−55.0885	−	7.57175i	55.9835	−	34.0443i	1005.36	+	281.689i	−4557.89	−	12824.7i	−3341.82	+	1451.56i	−128.626	+	1880.45i	51202.9	+	22240.5i	−79524.0	+	153474.i	153982.	+	741003.i
2.11	−52.1846	−	7.17261i	313.615	−	190.713i	699.733	+	196.056i	−76.5256	−	215.322i	−17733.8	+	7702.86i	3849.26	−	56274.2i	63838.7	+	27729.1i	−19516.6	+	37665.3i	2449.03	+	11785.4i
2.12	−50.6090	−	6.95604i	−183.254	+	111.439i	540.827	+	151.533i	1707.75	+	4805.16i	10049.5	−	4365.09i	1617.24	−	23643.2i	69643.5	+	30250.4i	−60335.9	+	116443.i	−53002.8	−	255063.i
2.13	−50.0113	−	6.87389i	332.827	−	202.397i	481.823	+	135.000i	1620.92	+	4560.84i	−18036.4	+	7834.30i	−4668.22	+	68247.0i	71658.2	+	31125.6i	−11689.6	+	22559.9i	−49713.7	−	239236.i
2.14	−38.4209	−	5.28083i	709.738	−	431.601i	−523.776	−	146.755i	−2864.70	−	8060.49i	−29548.0	+	12834.5i	−2027.41	+	29639.7i	92199.2	+	40047.8i	235950.	−	455362.i	67498.3	+	324819.i
2.15	−33.4798	−	4.60169i	−549.385	+	334.088i	−872.336	−	244.417i	3559.74	+	10016.1i	19930.6	−	8657.10i	−1937.46	+	28324.7i	91562.1	+	39771.1i	108709.	−	209800.i	−73088.0	−	351719.i
2.16	−30.7705	−	4.22931i	591.452	−	359.670i	−1043.12	−	292.268i	3539.33	+	9958.72i	−19720.4	+	8565.79i	1320.61	−	19306.6i	89205.4	+	38747.4i	138954.	−	268169.i	−66788.5	−	321404.i
2.17	−23.3641	−	3.21132i	206.580	−	125.624i	−1436.49	−	402.484i	−2507.19	−	7054.56i	−5229.98	+	2271.70i	−73.1768	+	1069.81i	76570.6	+	33259.3i	−54605.3	+	105383.i	35923.8	+	172875.i
2.18	−19.7358	−	2.71262i	−23.3900	+	14.2238i	−1589.91	−	445.472i	1280.94	+	3604.22i	500.204	−	217.269i	−4887.26	+	71449.2i	67591.0	+	29358.9i	−81154.4	+	156621.i	−15503.5	−	74607.0i
2.19	−16.6416	−	2.28734i	−503.778	+	306.354i	−1700.34	−	476.414i	−2082.47	−	5859.50i	9084.41	−	3945.92i	−447.320	+	6539.58i	58761.1	+	25523.5i	78440.0	−	151382.i	21253.0	+	102275.i
2.20	−10.1380	−	1.39343i	−437.073	+	265.790i	−1871.22	−	524.291i	−2715.43	−	7640.48i	4801.39	−	2085.54i	131.533	−	1922.94i	37462.5	+	16272.3i	38889.1	−	75052.5i	16882.4	+	81242.8i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
47.c	even	23	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	47.12.c.a	✓	946
47.c	even	23	1	inner	47.12.c.a	✓	946

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
47.12.c.a	✓	946	1.a	even	1	1	trivial
47.12.c.a	✓	946	47.c	even	23	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{12}^{\mathrm{new}}(47, [\chi])\).