Newform orbit 23.3.d.a

• Label: 23.3.d.a
• Level: $23$
• Weight: $3$
• Character orbit: 23.d
• Analytic conductor: $0.627$
• Analytic rank: $0$
• Dimension: $30$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	23.d (of order \(22\), degree \(10\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(0.626704608029\)
Analytic rank:	\(0\)
Dimension:	\(30\)
Relative dimension:	\(3\) over \(\Q(\zeta_{22})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 30 q - 11 q^{2} - 11 q^{3} - 23 q^{4} - 11 q^{5} + 22 q^{6} - 11 q^{7} + 10 q^{8} - 38 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
5.1	−3.10125	−	0.910608i	−3.16934	+	3.65762i	5.42352	+	3.48548i	−5.40865	−	0.777647i	13.1596	−	8.45714i	−0.889564	+	0.406250i	−5.17926	−	5.97719i	−2.05259	−	14.2761i	16.0654	+	7.33684i
5.2	−1.80062	−	0.528710i	2.35762	−	2.72084i	−0.402313	−	0.258551i	5.05070	+	0.726181i	−5.68372	+	3.65270i	−8.85488	+	4.04389i	5.50346	+	6.35133i	−0.563759	−	3.92103i	−8.71046	−	3.97793i
5.3	1.44626	+	0.424661i	−0.590042	+	0.680945i	−1.45368	−	0.934223i	−1.77862	−	0.255727i	−1.14252	+	0.734256i	2.68734	−	1.22727i	−5.65401	−	6.52507i	1.16530	+	8.10482i	−2.46375	−	1.12516i
7.1	−1.38322	+	1.59632i	−3.80315	+	2.44414i	−0.0656849	−	0.456848i	6.26010	−	2.85889i	1.35897	−	9.45184i	2.54176	+	8.65643i	−6.28757	−	4.04078i	4.75142	−	10.4042i	−4.09539	+	13.9476i
7.2	−0.881085	+	1.01683i	2.64748	−	1.70143i	0.311634	+	2.16747i	−2.08252	+	0.951056i	−0.602595	+	4.19114i	−2.90589	−	9.89656i	−7.00598	−	4.50247i	0.375553	−	0.822346i	0.867820	−	2.95552i
7.3	1.59301	−	1.83844i	−1.87410	+	1.20441i	−0.272894	−	1.89802i	−2.69128	+	1.22907i	−0.771235	+	5.36406i	−1.33225	−	4.53722i	4.26162	+	2.73877i	−1.67709	+	3.67232i	−2.02769	+	6.90566i
10.1	−1.38322	−	1.59632i	−3.80315	−	2.44414i	−0.0656849	+	0.456848i	6.26010	+	2.85889i	1.35897	+	9.45184i	2.54176	−	8.65643i	−6.28757	+	4.04078i	4.75142	+	10.4042i	−4.09539	−	13.9476i
10.2	−0.881085	−	1.01683i	2.64748	+	1.70143i	0.311634	−	2.16747i	−2.08252	−	0.951056i	−0.602595	−	4.19114i	−2.90589	+	9.89656i	−7.00598	+	4.50247i	0.375553	+	0.822346i	0.867820	+	2.95552i
10.3	1.59301	+	1.83844i	−1.87410	−	1.20441i	−0.272894	+	1.89802i	−2.69128	−	1.22907i	−0.771235	−	5.36406i	−1.33225	+	4.53722i	4.26162	−	2.73877i	−1.67709	−	3.67232i	−2.02769	−	6.90566i
11.1	−1.94274	+	1.24852i	−0.365090	+	2.53926i	0.553766	−	1.21258i	0.682875	+	2.32566i	−2.46105	−	5.38894i	6.72814	−	5.82996i	−0.876504	−	6.09622i	2.32089	+	0.681474i	−4.23029	−	3.66556i
11.2	0.0163142	−	0.0104845i	0.749667	−	5.21405i	−1.66150	+	3.63819i	1.45779	+	4.96477i	−0.0424364	−	0.0929228i	−1.27914	+	1.10838i	0.0220779	+	0.153555i	−17.9889	−	5.28201i	0.0758357	+	0.0657120i
11.3	1.20995	−	0.777587i	−0.238691	+	1.66013i	−0.802326	+	1.75685i	−2.65558	−	9.04406i	1.00209	+	2.19428i	−5.31379	+	4.60443i	1.21408	+	8.44409i	5.93637	+	1.74307i	−10.2457	−	8.87791i
14.1	−3.10125	+	0.910608i	−3.16934	−	3.65762i	5.42352	−	3.48548i	−5.40865	+	0.777647i	13.1596	+	8.45714i	−0.889564	−	0.406250i	−5.17926	+	5.97719i	−2.05259	+	14.2761i	16.0654	−	7.33684i
14.2	−1.80062	+	0.528710i	2.35762	+	2.72084i	−0.402313	+	0.258551i	5.05070	−	0.726181i	−5.68372	−	3.65270i	−8.85488	−	4.04389i	5.50346	−	6.35133i	−0.563759	+	3.92103i	−8.71046	+	3.97793i
14.3	1.44626	−	0.424661i	−0.590042	−	0.680945i	−1.45368	+	0.934223i	−1.77862	+	0.255727i	−1.14252	−	0.734256i	2.68734	+	1.22727i	−5.65401	+	6.52507i	1.16530	−	8.10482i	−2.46375	+	1.12516i
15.1	−0.387684	+	2.69640i	−0.141551	−	0.309954i	−3.28232	−	0.963778i	−0.353921	+	0.306674i	0.890639	−	0.261515i	4.93105	−	7.67286i	−0.655341	+	1.43500i	5.81771	−	6.71400i	−0.689708	−	1.07321i
15.2	0.123822	−	0.861198i	−1.04228	−	2.28229i	3.11164	+	0.913660i	−1.80972	+	1.56813i	−2.09456	+	0.615017i	−6.61670	+	10.2958i	2.61786	−	5.73232i	1.77128	−	2.04416i	1.12639	+	1.75270i
15.3	0.496456	−	3.45293i	1.53764	+	3.36695i	−7.83827	−	2.30152i	−4.84192	+	4.19555i	12.3892	−	3.63780i	3.55260	−	5.52795i	−6.04175	+	13.2296i	−3.07830	+	3.55255i	12.0831	+	18.8017i
17.1	−1.55977	+	3.41542i	0.201951	+	0.0592983i	−6.61275	−	7.63152i	2.90325	+	4.51755i	−0.517526	+	0.597257i	7.13192	+	1.02541i	21.9686	−	6.45058i	−7.53401	−	4.84182i	−19.9577	+	2.86949i
17.2	−0.282292	+	0.618133i	0.844537	+	0.247978i	2.31704	+	2.67401i	−3.24760	−	5.05336i	−0.391690	+	0.452034i	−3.20136	−	0.460286i	−4.91504	+	1.44319i	−6.91953	−	4.44691i	4.04042	−	0.580925i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
23.d	odd	22	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	23.3.d.a	✓	30
3.b	odd	2	1		207.3.j.a		30
4.b	odd	2	1		368.3.p.a		30
23.c	even	11	1		529.3.b.b		30
23.d	odd	22	1	inner	23.3.d.a	✓	30
23.d	odd	22	1		529.3.b.b		30
69.g	even	22	1		207.3.j.a		30
92.h	even	22	1		368.3.p.a		30

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
23.3.d.a	✓	30	1.a	even	1	1	trivial
23.3.d.a	✓	30	23.d	odd	22	1	inner
207.3.j.a		30	3.b	odd	2	1
207.3.j.a		30	69.g	even	22	1
368.3.p.a		30	4.b	odd	2	1
368.3.p.a		30	92.h	even	22	1
529.3.b.b		30	23.c	even	11	1
529.3.b.b		30	23.d	odd	22	1

Hecke kernels

This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(23, [\chi])\).