Newform orbit 175.4.q.a

• Label: 175.4.q.a
• Level: $175$
• Weight: $4$
• Character orbit: 175.q
• Analytic conductor: $10.325$
• Analytic rank: $0$
• Dimension: $464$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 175 = 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	175.q (of order \(15\), degree \(8\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(10.3253342510\)
Analytic rank:	\(0\)
Dimension:	\(464\)
Relative dimension:	\(58\) 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.

\(\operatorname{Tr}(f)(q) = \) \( 464 q - 3 q^{2} - 3 q^{3} + 221 q^{4} - 8 q^{5} - 92 q^{6} - 8 q^{7} - 170 q^{8} + 483 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
11.1	−5.13667	−	2.28699i	−4.27234	−	4.74491i	15.8020	+	17.5499i	−6.02017	−	9.42112i	11.0940	+	34.1438i	−15.3318	+	10.3892i	−27.1329	−	83.5065i	−1.43905	+	13.6916i	9.37761	+	62.1613i
11.2	−4.77001	−	2.12374i	3.63348	+	4.03539i	12.8896	+	14.3154i	4.50971	−	10.2305i	−8.76159	−	26.9654i	18.3584	+	2.44320i	−18.1734	−	55.9319i	−0.259912	+	2.47290i	−43.2382	+	39.2220i
11.3	−4.71180	−	2.09783i	0.215044	+	0.238831i	12.4472	+	13.8240i	−5.59557	+	9.67934i	−0.512220	−	1.57645i	−1.55774	−	18.4546i	−16.8976	−	52.0056i	2.81147	−	26.7494i	46.6708	−	33.8686i
11.4	−4.66480	−	2.07690i	2.55912	+	2.84219i	12.0938	+	13.4316i	10.6420	+	3.42737i	−6.03482	−	18.5733i	−18.5102	−	0.609764i	−15.8959	−	48.9225i	1.29332	−	12.3051i	−42.5247	−	38.0905i
11.5	−4.63629	−	2.06421i	−6.51143	−	7.23167i	11.8812	+	13.1954i	8.36735	+	7.41535i	15.2612	+	46.9691i	11.9392	−	14.1582i	−15.3003	−	47.0896i	−7.07614	+	67.3250i	−23.4866	−	51.6517i
11.6	−4.61510	−	2.05477i	6.22022	+	6.90826i	11.7240	+	13.0208i	−8.77373	+	6.92976i	−14.5120	−	44.6634i	0.0735614	+	18.5201i	−14.8636	−	45.7455i	−6.21058	+	59.0897i	54.7307	−	13.9535i
11.7	−4.26963	−	1.90096i	−2.18621	−	2.42804i	9.26303	+	10.2876i	11.1767	−	0.285058i	4.71872	+	14.5227i	4.42756	+	17.9832i	−8.43931	−	25.9735i	1.70644	−	16.2357i	−48.2623	−	20.0294i
11.8	−4.06416	−	1.80948i	−1.15071	−	1.27800i	7.89014	+	8.76289i	−10.6928	−	3.26556i	2.36417	+	7.27617i	18.1900	−	3.48189i	−5.21254	−	16.0425i	2.51313	−	23.9109i	37.5483	+	32.6202i
11.9	−3.87642	−	1.72589i	4.29915	+	4.77469i	6.69488	+	7.43541i	−3.75598	−	10.5306i	−8.42470	−	25.9286i	−12.0051	−	14.1024i	−2.62948	−	8.09271i	−1.49270	+	14.2021i	−3.61488	+	47.3033i
11.10	−3.78724	−	1.68619i	−3.15856	−	3.50793i	6.14689	+	6.82681i	−4.40247	+	10.2771i	6.04718	+	18.6113i	−0.166192	+	18.5195i	−1.51985	−	4.67760i	0.493155	−	4.69206i	34.0023	−	31.4983i
11.11	−3.38103	−	1.50533i	−2.86637	−	3.18343i	3.81227	+	4.23396i	4.50015	−	10.2347i	4.89917	+	15.0781i	−17.1933	−	6.88404i	2.63347	+	8.10499i	0.904137	−	8.60228i	−30.6217	+	27.8295i
11.12	−3.24664	−	1.44550i	3.85991	+	4.28687i	3.09815	+	3.44084i	6.24593	+	9.27299i	−6.33509	−	19.4974i	18.5174	+	0.325734i	3.70085	+	11.3901i	−0.656037	+	6.24177i	−6.87420	−	39.1345i
11.13	−3.24093	−	1.44296i	−1.74960	−	1.94313i	3.06847	+	3.40789i	10.9410	−	2.30086i	2.86650	+	8.82216i	3.11888	−	18.2558i	3.74297	+	11.5197i	2.10762	−	20.0527i	−38.7792	−	8.33049i
11.14	−3.13970	−	1.39788i	−5.69617	−	6.32624i	2.55058	+	2.83270i	−11.0817	+	1.48202i	9.04091	+	27.8251i	−14.2610	−	11.8163i	4.44805	+	13.6897i	−4.75266	+	45.2185i	36.8648	+	10.8378i
11.15	−2.91514	−	1.29791i	1.75793	+	1.95238i	1.46046	+	1.62201i	−8.34239	−	7.44343i	−2.59062	−	7.97312i	−3.63552	+	18.1599i	5.73640	+	17.6548i	2.10080	−	19.9878i	14.6584	+	32.5263i
11.16	−2.75998	−	1.22882i	−6.11021	−	6.78607i	0.754430	+	0.837879i	0.0177564	−	11.1803i	8.52516	+	26.2378i	17.3544	+	6.46731i	6.41614	+	19.7469i	−5.89388	+	56.0765i	−13.7876	+	30.8356i
11.17	−2.74035	−	1.22008i	2.09512	+	2.32686i	0.667859	+	0.741732i	2.65881	+	10.8596i	−2.90239	−	8.93263i	−17.8762	+	4.84182i	6.49043	+	19.9755i	1.79749	−	17.1020i	5.96352	−	33.0030i
11.18	−2.56820	−	1.14344i	5.52121	+	6.13193i	−0.0648233	−	0.0719935i	−10.4854	+	3.88019i	−7.16812	−	22.0612i	1.27946	−	18.4760i	7.03395	+	21.6483i	−4.29449	+	40.8593i	31.3655	+	2.02433i
11.19	−2.24078	−	0.997659i	6.35574	+	7.05877i	−1.32728	−	1.47409i	9.95753	−	5.08406i	−7.19957	−	22.1580i	−11.9903	+	14.1150i	7.56724	+	23.2896i	−6.60846	+	62.8753i	−27.3848	+	1.45804i
11.20	−1.70952	−	0.761126i	3.40919	+	3.78629i	−3.00991	−	3.34284i	8.72808	−	6.98718i	−2.94623	−	9.06755i	13.1917	−	12.9992i	7.22727	+	22.2433i	0.108855	−	1.03569i	−20.2389	+	5.30154i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
7.c	even	3	1	inner
25.d	even	5	1	inner
175.q	even	15	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	175.4.q.a	✓	464
7.c	even	3	1	inner	175.4.q.a	✓	464
25.d	even	5	1	inner	175.4.q.a	✓	464
175.q	even	15	1	inner	175.4.q.a	✓	464

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
175.4.q.a	✓	464	1.a	even	1	1	trivial
175.4.q.a	✓	464	7.c	even	3	1	inner
175.4.q.a	✓	464	25.d	even	5	1	inner
175.4.q.a	✓	464	175.q	even	15	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{4}^{\mathrm{new}}(175, [\chi])\).