Newform orbit 151.2.g.a

• Label: 151.2.g.a
• Level: $151$
• Weight: $2$
• Character orbit: 151.g
• Analytic conductor: $1.206$
• Analytic rank: $0$
• Dimension: $96$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 151 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	151.g (of order \(15\), degree \(8\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(1.20574107052\)
Analytic rank:	\(0\)
Dimension:	\(96\)
Relative dimension:	\(12\) over \(\Q(\zeta_{15})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 96 q - 3 q^{2} - 4 q^{3} - 49 q^{4} - 9 q^{5} + 7 q^{6} - 7 q^{7} + 12 q^{8} - 32 q^{9}+O(q^{10}) \)

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	−1.39854	+	2.42234i	2.05125	−	1.49032i	−2.91182	−	5.04342i	−1.64458	−	1.82650i	0.741310	+	7.05309i	−1.72001	−	1.91027i	10.6950			1.05952	−	3.26086i	6.72440	−	1.42932i
2.2	−1.02524	+	1.77577i	0.211950	−	0.153991i	−1.10223	−	1.90912i	0.787903	+	0.875055i	0.0561521	+	0.534251i	1.60275	+	1.78003i	0.419252			−0.905841	+	2.78789i	−2.36168	+	0.501991i
2.3	−0.709795	+	1.22940i	−0.862342	+	0.626528i	−0.00761718	−	0.0131933i	−2.93840	−	3.26343i	−0.158168	−	1.50487i	−1.87506	−	2.08246i	−2.81755			−0.575954	+	1.77261i	6.09772	−	1.29611i
2.4	−0.579506	+	1.00373i	2.23683	−	1.62515i	0.328346	+	0.568712i	2.59512	+	2.88217i	0.334964	+	3.18697i	−3.20705	−	3.56179i	−3.07914			1.43524	−	4.41720i	−4.39682	+	0.934574i
2.5	−0.465766	+	0.806731i	−2.42147	+	1.75930i	0.566123	+	0.980554i	1.07846	+	1.19776i	−0.291444	−	2.77290i	−0.384809	−	0.427373i	−2.91779			1.84134	−	5.66705i	−1.46858	+	0.312156i
2.6	−0.183451	+	0.317746i	0.0745133	−	0.0541371i	0.932692	+	1.61547i	0.164782	+	0.183009i	0.00353232	+	0.0336078i	0.250565	+	0.278280i	−1.41821			−0.924430	+	2.84510i	−0.0883795	+	0.0187856i
2.7	0.0376638	−	0.0652356i	1.94876	−	1.41586i	0.997163	+	1.72714i	−1.61004	−	1.78814i	−0.0189666	−	0.180455i	1.00235	+	1.11322i	0.300883			0.865968	−	2.66518i	−0.177290	+	0.0376842i
2.8	0.516346	−	0.894338i	−1.72354	+	1.25222i	0.466773	+	0.808475i	−0.972803	−	1.08041i	0.229968	+	2.18800i	3.08940	+	3.43113i	3.02945			0.475465	−	1.46333i	−1.46855	+	0.312150i
2.9	0.702514	−	1.21679i	1.01499	−	0.737432i	0.0129471	+	0.0224250i	−0.315277	−	0.350150i	−0.184257	−	1.75308i	−2.14736	−	2.38489i	2.84644			−0.440657	+	1.35620i	−0.647546	+	0.137640i
2.10	0.729613	−	1.26373i	−1.15094	+	0.836205i	−0.0646694	−	0.112011i	2.41864	+	2.68617i	0.216996	+	2.06458i	−1.66941	−	1.85407i	2.72972			−0.301633	+	0.928330i	5.15925	−	1.09663i
2.11	1.23564	−	2.14019i	0.626432	−	0.455129i	−2.05360	−	3.55694i	0.582934	+	0.647414i	−0.200019	−	1.90306i	1.51631	+	1.68403i	−5.20747			−0.741777	+	2.28295i	2.10588	−	0.447619i
2.12	1.30965	−	2.26838i	−2.50643	+	1.82103i	−2.43037	−	4.20953i	−1.04220	−	1.15748i	0.848240	+	8.07047i	−2.21920	−	2.46467i	−7.49317			2.03901	−	6.27542i	−3.99053	+	0.848214i
4.1	−1.27642	−	2.21083i	−0.959431	+	2.95283i	−2.25852	+	3.91186i	0.321789	−	3.06162i	7.75284	−	1.64792i	0.156584	−	1.48980i	6.42560			−5.37162	−	3.90271i	−7.17947	+	3.19651i
4.2	−1.26450	−	2.19018i	−0.00970562	+	0.0298708i	−2.19793	+	3.80692i	−0.345445	+	3.28669i	0.0776953	−	0.0165146i	−0.112482	+	1.07020i	6.05912			2.42625	+	1.76278i	7.63527	−	3.39944i
4.3	−1.12584	−	1.95002i	0.673537	−	2.07293i	−1.53504	+	2.65877i	0.207318	−	1.97250i	−4.80055	+	1.02039i	−0.0295183	+	0.280848i	2.40949			−1.41635	−	1.02904i	−4.07982	+	1.81645i
4.4	−0.641661	−	1.11139i	−0.136476	+	0.420030i	0.176543	−	0.305782i	−0.124711	+	1.18654i	0.554388	−	0.117839i	0.541472	−	5.15176i	−3.01977			2.26925	+	1.64871i	1.39873	−	0.622755i
4.5	−0.638222	−	1.10543i	−0.628704	+	1.93495i	0.185344	−	0.321026i	−0.135125	+	1.28563i	2.54021	−	0.539939i	−0.402696	+	3.83140i	−3.02605			−0.921718	−	0.669667i	1.50742	−	0.671145i
4.6	−0.179853	−	0.311514i	0.679457	−	2.09115i	0.935306	−	1.62000i	−0.0759530	+	0.722644i	−0.773627	+	0.164440i	−0.0666495	+	0.634128i	−1.39228			−1.48421	−	1.07834i	0.238775	−	0.106309i
4.7	0.0512357	+	0.0887428i	−0.531325	+	1.63525i	0.994750	−	1.72296i	0.397197	−	3.77908i	−0.172339	+	0.0366319i	0.154762	−	1.47246i	0.408809			0.0353152	+	0.0256580i	0.355716	−	0.158375i
4.8	0.495779	+	0.858714i	−0.888421	+	2.73428i	0.508407	−	0.880587i	−0.291406	+	2.77255i	−2.78842	+	0.592697i	0.268466	−	2.55428i	2.99134			−4.25993	−	3.09502i	−2.52530	+	1.12433i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
151.g	even	15	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	151.2.g.a	✓	96
151.g	even	15	1	inner	151.2.g.a	✓	96

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
151.2.g.a	✓	96	1.a	even	1	1	trivial
151.2.g.a	✓	96	151.g	even	15	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(151, [\chi])\).