Newform orbit 23.6.c.a

• Label: 23.6.c.a
• Level: $23$
• Weight: $6$
• Character orbit: 23.c
• Analytic conductor: $3.689$
• Analytic rank: $0$
• Dimension: $90$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 23 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	23.c (of order \(11\), degree \(10\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(3.68882785570\)
Analytic rank:	\(0\)
Dimension:	\(90\)
Relative dimension:	\(9\) 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.

\(\operatorname{Tr}(f)(q) = \) \( 90 q - 11 q^{2} - 7 q^{3} - 139 q^{4} + 5 q^{5} - 148 q^{6} - 29 q^{7} - 44 q^{8} - 894 q^{9}+O(q^{10}) \)

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	−8.49747	−	5.46100i	1.17717	+	8.18741i	29.0913	+	63.7011i	−4.12458	−	1.21109i	34.7084	−	76.0009i	66.5045	−	76.7503i	54.6681	−	380.225i	167.509	−	49.1850i	28.4348	+	32.8155i
2.2	−5.98228	−	3.84458i	−4.25176	−	29.5716i	7.71364	+	16.8905i	10.2972	+	3.02354i	−88.2553	+	193.252i	60.9133	−	70.2977i	−13.5930	+	94.5412i	−623.247	+	183.002i	−49.9767	−	57.6762i
2.3	−5.01311	−	3.22173i	−0.293619	−	2.04217i	1.45843	+	3.19351i	−10.1657	−	2.98491i	−5.10736	+	11.1836i	−159.381	+	183.936i	−24.1608	+	168.042i	229.073	−	67.2618i	41.3450	+	47.7146i
2.4	−2.21730	−	1.42497i	4.20469	+	29.2443i	−10.4074	−	22.7890i	−83.1134	−	24.4043i	32.3492	−	70.8350i	22.1618	−	25.5761i	−21.4006	+	148.845i	−604.392	+	177.466i	149.512	+	172.546i
2.5	−1.85052	−	1.18926i	1.12337	+	7.81321i	−11.2832	−	24.7067i	82.9428	+	24.3542i	7.21310	−	15.7945i	98.7062	−	113.913i	−18.5206	+	128.813i	173.372	−	50.9067i	−124.524	−	143.708i
2.6	1.87482	+	1.20487i	−1.73793	−	12.0876i	−11.2301	−	24.5904i	−45.2299	−	13.2807i	11.3057	−	24.7560i	13.6774	−	15.7845i	18.7232	−	130.223i	90.0673	−	26.4461i	−68.7963	−	79.3951i
2.7	5.39264	+	3.46564i	2.36907	+	16.4773i	3.77666	+	8.26972i	27.3965	+	8.04434i	−44.3288	+	97.0664i	−81.9154	+	94.5354i	20.8990	−	145.356i	−32.7312	+	9.61074i	119.861	+	138.327i
2.8	6.83356	+	4.39166i	−3.42127	−	23.7955i	14.1176	+	30.9132i	81.6604	+	23.9777i	81.1223	−	177.633i	−26.6137	+	30.7138i	−2.29389	+	15.9544i	−321.363	+	94.3608i	452.730	+	522.478i
2.9	8.74318	+	5.61890i	0.603375	+	4.19657i	31.5779	+	69.1460i	−63.3504	−	18.6013i	−18.3047	+	40.0817i	143.409	−	165.503i	−65.1024	+	452.797i	215.910	−	63.3968i	−449.365	−	518.594i
3.1	−1.56617	−	10.8929i	3.45588	−	7.56732i	−85.4995	+	25.1049i	43.9262	−	50.6935i	−87.8428	−	25.7930i	−42.6312	+	27.3974i	261.081	+	571.688i	113.810	+	131.344i	−620.998	−	399.091i
3.2	−1.13164	−	7.87071i	−6.81486	+	14.9225i	−29.9637	+	8.79812i	−54.8415	+	63.2904i	125.162	+	36.7510i	−3.45670	+	2.22148i	−2.54800	−	5.57934i	−17.1066	−	19.7421i	560.201	+	360.019i
3.3	−0.696058	−	4.84119i	8.29077	−	18.1543i	7.75116	−	2.27595i	−11.8362	+	13.6597i	−93.6590	−	27.5008i	−29.6881	+	19.0794i	−81.4306	−	178.308i	−101.709	−	117.378i	74.3679	+	47.7933i
3.4	−0.608938	−	4.23525i	−6.59663	+	14.4446i	13.1372	−	3.85743i	52.7594	−	60.8875i	65.1935	+	19.1425i	55.4232	−	35.6183i	−81.2163	−	177.839i	−5.99980	−	6.92413i	−290.001	−	186.373i
3.5	0.330150	+	2.29625i	−5.46335	+	11.9631i	25.5400	−	7.49923i	−32.3567	+	37.3416i	−29.2739	−	8.59559i	−167.445	+	107.610i	56.4907	+	123.697i	45.8643	+	52.9303i	−96.4282	−	61.9706i
3.6	0.364275	+	2.53359i	3.17904	−	6.96113i	24.4174	−	7.16960i	−2.80660	+	3.23899i	18.7947	+	5.51861i	130.259	−	83.7125i	61.0854	+	133.758i	120.780	+	139.388i	−9.22864	−	5.93088i
3.7	0.991600	+	6.89673i	9.66731	−	21.1685i	−15.8778	+	4.66215i	66.8592	−	77.1597i	155.579	+	45.6822i	−163.317	+	104.958i	44.7249	+	97.9339i	−195.515	−	225.637i	598.447	+	384.598i
3.8	1.13144	+	7.86930i	−9.75312	+	21.3564i	−29.9420	+	8.79177i	30.9167	−	35.6798i	−179.095	−	52.5869i	34.5697	−	22.2166i	2.62201	+	5.74140i	−201.839	−	232.935i	315.756	+	202.924i
3.9	1.41793	+	9.86195i	2.99089	−	6.54914i	−64.5437	+	18.9517i	−49.3449	+	56.9471i	68.8281	+	20.2098i	37.4214	−	24.0493i	−145.974	−	319.639i	125.185	+	144.472i	−631.577	−	405.890i
4.1	−4.47298	−	9.79445i	−7.03817	+	2.06659i	−54.9683	+	63.4367i	15.8872	+	10.2101i	51.7227	+	59.6912i	−16.2855	−	113.268i	536.597	+	157.559i	−159.160	+	102.286i	28.9391	−	201.276i
4.2	−2.60966	−	5.71435i	−0.942040	+	0.276608i	−4.88796	+	5.64100i	−66.5354	−	42.7597i	4.03903	+	4.66129i	20.2510	+	140.849i	−147.892	−	43.4250i	−203.614	+	130.855i	−70.7094	+	491.795i

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	23.6.c.a	✓	90
23.c	even	11	1	inner	23.6.c.a	✓	90
23.c	even	11	1		529.6.a.j		45
23.d	odd	22	1		529.6.a.k		45

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
23.6.c.a	✓	90	1.a	even	1	1	trivial
23.6.c.a	✓	90	23.c	even	11	1	inner
529.6.a.j		45	23.c	even	11	1
529.6.a.k		45	23.d	odd	22	1

Hecke kernels

This newform subspace is the entire newspace \(S_{6}^{\mathrm{new}}(23, [\chi])\).