Newform orbit 23.4.c.a

• Label: 23.4.c.a
• Level: $23$
• Weight: $4$
• Character orbit: 23.c
• Analytic conductor: $1.357$
• Analytic rank: $0$
• Dimension: $50$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	23.c (of order \(11\), degree \(10\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(1.35704393013\)
Analytic rank:	\(0\)
Dimension:	\(50\)
Relative dimension:	\(5\) over \(\Q(\zeta_{11})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 50 q - 11 q^{2} - 13 q^{3} - 27 q^{4} - 19 q^{5} - 4 q^{6} - 19 q^{7} + 28 q^{8} + 24 q^{9}+O(q^{10}) \)

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	−3.24175	−	2.08335i	1.21610	+	8.45817i	2.84529	+	6.23031i	12.7969	+	3.75752i	13.6790	−	29.9528i	−11.3462	+	13.0942i	−0.631070	+	4.38919i	−44.1554	+	12.9652i	−33.6563	−	38.8414i
2.2	−2.68394	−	1.72487i	−0.220662	−	1.53474i	0.905070	+	1.98183i	−18.5174	−	5.43720i	−2.05498	+	4.49977i	13.0047	−	15.0082i	−2.64311	+	18.3833i	23.5996	−	6.92946i	40.3212	+	46.5331i
2.3	−0.442460	−	0.284352i	−0.784628	−	5.45721i	−3.20841	−	7.02543i	12.7367	+	3.73985i	−1.20460	+	2.63770i	−5.26652	+	6.07789i	−1.17691	+	8.18558i	−3.25915	+	0.956973i	−4.57207	−	5.27645i
2.4	1.91736	+	1.23221i	0.776967	+	5.40392i	−1.16540	−	2.55188i	−0.907869	−	0.266574i	−5.16905	+	11.3186i	8.82725	−	10.1872i	3.50483	−	24.3766i	−2.69237	+	0.790552i	−1.41223	−	1.62980i
2.5	3.73432	+	2.39990i	−0.655499	−	4.55909i	4.86229	+	10.6469i	−9.99480	−	2.93474i	8.49353	−	18.5982i	−17.7583	+	20.4942i	−2.34036	+	16.2775i	5.55065	−	1.62982i	−30.2807	−	34.9458i
3.1	−0.589312	−	4.09876i	1.03962	−	2.27645i	−8.77657	+	2.57703i	−3.66646	+	4.23132i	−9.94329	−	2.91961i	16.9812	−	10.9132i	1.97323	+	4.32077i	13.5798	+	15.6719i	19.5039	+	12.5344i
3.2	−0.132292	−	0.920110i	0.209861	−	0.459531i	6.84684	−	2.01041i	6.87249	−	7.93128i	−0.450582	−	0.132303i	−25.4560	+	16.3596i	−5.84485	−	12.7984i	17.5141	+	20.2124i	−8.20682	−	5.27420i
3.3	0.0282746	+	0.196654i	−3.66027	+	8.01487i	7.63807	−	2.24274i	−6.59261	+	7.60828i	−1.67965	−	0.493191i	21.3237	−	13.7039i	1.31727	+	2.88443i	−33.1594	−	38.2680i	−1.68261	−	1.08135i
3.4	0.306014	+	2.12837i	3.96829	−	8.68933i	3.23961	−	0.951236i	−11.4648	+	13.2311i	19.7085	+	5.78694i	−2.65189	+	1.70427i	10.1620	+	22.2516i	−42.0760	−	48.5583i	−31.6691	−	20.3525i
3.5	0.619909	+	4.31156i	−0.504759	+	1.10527i	−10.5293	+	3.09169i	4.52322	−	5.22007i	−5.07833	−	1.49113i	2.36872	−	1.52228i	−5.38116	−	11.7831i	16.7144	+	19.2894i	25.3106	+	16.2662i
4.1	−2.10729	−	4.61431i	8.43369	−	2.47635i	−11.6123	+	13.4013i	−5.02341	−	3.22835i	−29.1989	−	33.6973i	3.12135	+	21.7095i	47.3705	+	13.9092i	42.2809	−	27.1723i	−4.31085	+	29.9826i
4.2	−1.58245	−	3.46509i	−7.04544	+	2.06873i	−4.26380	+	4.92069i	−4.88780	−	3.14120i	18.3174	+	21.1394i	−2.25200	−	15.6630i	−5.44232	−	1.59801i	22.6448	−	14.5529i	−3.14982	+	21.9075i
4.3	−0.308069	−	0.674576i	1.68484	−	0.494713i	4.87874	−	5.63037i	3.36936	+	2.16536i	−0.852766	−	0.984145i	0.387311	+	2.69380i	−10.9935	−	3.22799i	−20.1199	+	12.9303i	0.422704	−	2.93997i
4.4	1.49850	+	3.28126i	−7.64281	+	2.24413i	−3.28227	+	3.78794i	15.0482	+	9.67090i	−18.8163	−	21.7152i	−2.56161	−	17.8164i	10.3412	+	3.03646i	30.6625	−	19.7056i	−9.18297	+	63.8690i
4.5	1.61009	+	3.52560i	3.27467	−	0.961529i	−4.59861	+	5.30707i	−10.7624	−	6.91659i	8.66248	+	9.99703i	−0.249078	−	1.73238i	3.63606	+	1.06764i	−12.9149	+	8.29992i	7.05669	−	49.0804i
6.1	−2.10729	+	4.61431i	8.43369	+	2.47635i	−11.6123	−	13.4013i	−5.02341	+	3.22835i	−29.1989	+	33.6973i	3.12135	−	21.7095i	47.3705	−	13.9092i	42.2809	+	27.1723i	−4.31085	−	29.9826i
6.2	−1.58245	+	3.46509i	−7.04544	−	2.06873i	−4.26380	−	4.92069i	−4.88780	+	3.14120i	18.3174	−	21.1394i	−2.25200	+	15.6630i	−5.44232	+	1.59801i	22.6448	+	14.5529i	−3.14982	−	21.9075i
6.3	−0.308069	+	0.674576i	1.68484	+	0.494713i	4.87874	+	5.63037i	3.36936	−	2.16536i	−0.852766	+	0.984145i	0.387311	−	2.69380i	−10.9935	+	3.22799i	−20.1199	−	12.9303i	0.422704	+	2.93997i
6.4	1.49850	−	3.28126i	−7.64281	−	2.24413i	−3.28227	−	3.78794i	15.0482	−	9.67090i	−18.8163	+	21.7152i	−2.56161	+	17.8164i	10.3412	−	3.03646i	30.6625	+	19.7056i	−9.18297	−	63.8690i
6.5	1.61009	−	3.52560i	3.27467	+	0.961529i	−4.59861	−	5.30707i	−10.7624	+	6.91659i	8.66248	−	9.99703i	−0.249078	+	1.73238i	3.63606	−	1.06764i	−12.9149	−	8.29992i	7.05669	+	49.0804i

Inner twists

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

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	23.4.c.a	✓	50
3.b	odd	2	1		207.4.i.a		50
23.c	even	11	1	inner	23.4.c.a	✓	50
23.c	even	11	1		529.4.a.n		25
23.d	odd	22	1		529.4.a.m		25
69.h	odd	22	1		207.4.i.a		50

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
23.4.c.a	✓	50	1.a	even	1	1	trivial
23.4.c.a	✓	50	23.c	even	11	1	inner
207.4.i.a		50	3.b	odd	2	1
207.4.i.a		50	69.h	odd	22	1
529.4.a.m		25	23.d	odd	22	1
529.4.a.n		25	23.c	even	11	1

Hecke kernels

This newform subspace is the entire newspace \(S_{4}^{\mathrm{new}}(23, [\chi])\).