Newform orbit 175.4.x.a

• Label: 175.4.x.a
• Level: $175$
• Weight: $4$
• Character orbit: 175.x
• Analytic conductor: $10.325$
• Analytic rank: $0$
• Dimension: $928$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 175 = 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	175.x (of order \(60\), degree \(16\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(10.3253342510\)
Analytic rank:	\(0\)
Dimension:	\(928\)
Relative dimension:	\(58\) over \(\Q(\zeta_{60})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 928 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 24 q^{7} + 84 q^{8} - 10 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
3.1	−2.98654	+	4.59886i	−1.16114	+	3.02487i	−8.97624	−	20.1610i	9.73544	+	5.49738i	−10.4432	−	14.3738i	7.57257	+	16.9014i	76.1974	+	12.0685i	12.2633	+	11.0419i	−54.3569	+	28.3538i
3.2	−2.93952	+	4.52647i	2.08359	−	5.42794i	−8.59424	−	19.3030i	5.69869	−	9.61899i	18.4447	+	25.3869i	−18.5027	−	0.805399i	69.9913	+	11.0855i	−5.05630	−	4.55272i	26.7886	+	54.0702i
3.3	−2.78034	+	4.28135i	0.882639	−	2.29935i	−7.34575	−	16.4988i	−10.5665	+	3.65353i	7.39030	+	10.1719i	−6.43718	−	17.3656i	50.7243	+	8.03394i	15.5569	+	14.0075i	13.7365	−	55.3971i
3.4	−2.76823	+	4.26271i	−3.25777	+	8.48679i	−7.25365	−	16.2920i	−10.0021	+	4.99589i	−27.1584	−	37.3803i	14.5748	−	11.4270i	49.3668	+	7.81893i	−41.3476	−	37.2295i	6.39202	−	56.4656i
3.5	−2.71831	+	4.18582i	3.28166	−	8.54901i	−6.87804	−	15.4483i	−6.26616	+	9.25933i	26.8641	+	36.9752i	12.3275	+	13.8214i	43.9240	+	6.95687i	−42.2513	−	38.0433i	−21.7246	−	51.3987i
3.6	−2.62864	+	4.04775i	0.173128	−	0.451014i	−6.22064	−	13.9718i	−6.75712	−	8.90737i	1.37050	+	1.88633i	16.2876	+	8.81554i	34.7703	+	5.50708i	19.8915	+	17.9104i	53.8168	−	3.93686i
3.7	−2.46147	+	3.79033i	−1.42743	+	3.71858i	−5.05389	−	11.3512i	2.23871	+	10.9539i	−10.5811	−	14.5636i	−18.1267	−	3.79783i	19.7544	+	3.12879i	8.27464	+	7.45052i	−47.0295	−	18.4773i
3.8	−2.44758	+	3.76895i	−2.50628	+	6.52907i	−4.96040	−	11.1412i	−4.07235	−	10.4123i	−18.4734	−	25.4265i	−15.2656	+	10.4863i	18.6227	+	2.94955i	−16.2825	−	14.6608i	49.2108	+	10.1365i
3.9	−2.38969	+	3.67979i	1.74074	−	4.53478i	−4.57638	−	10.2787i	10.9198	+	2.39967i	12.5272	+	17.2422i	14.0149	−	12.1072i	14.0907	+	2.23174i	2.53089	+	2.27882i	−34.9251	+	34.4481i
3.10	−2.26197	+	3.48313i	−1.55172	+	4.04237i	−3.76181	−	8.44916i	8.63834	−	7.09782i	−10.5702	−	14.5486i	3.60941	−	18.1651i	5.12243	+	0.811313i	6.13196	+	5.52124i	5.18297	+	46.1436i
3.11	−1.98207	+	3.05213i	0.456252	−	1.18858i	−2.13297	−	4.79073i	−9.54840	+	5.81619i	2.72336	+	3.74839i	−7.21114	+	17.0587i	−9.90591	−	1.56894i	18.8604	+	16.9819i	1.17388	−	40.6711i
3.12	−1.97283	+	3.03788i	2.51318	−	6.54707i	−2.08281	−	4.67806i	9.50586	+	5.88546i	14.9312	+	20.5510i	−16.0333	+	9.27000i	−10.3009	−	1.63150i	−16.4831	−	14.8414i	−36.6327	+	17.2667i
3.13	−1.96169	+	3.02073i	3.41104	−	8.88607i	−2.02272	−	4.54311i	−3.76740	−	10.5265i	20.1510	+	27.7355i	11.4301	−	14.5724i	−10.7683	−	1.70553i	−47.2621	−	42.5550i	39.1881	+	9.26933i
3.14	−1.78858	+	2.75417i	−3.22364	+	8.39787i	−1.13255	−	2.54375i	11.1404	−	0.944160i	−17.3634	−	23.8987i	13.6862	+	12.4775i	−16.9168	−	2.67935i	−40.0675	−	36.0769i	−17.3251	+	32.3713i
3.15	−1.67008	+	2.57170i	1.53287	−	3.99327i	−0.570578	−	1.28154i	4.62112	−	10.1806i	7.70948	+	10.6112i	5.95919	+	17.5353i	−19.9805	−	3.16461i	6.46837	+	5.82415i	18.4639	+	28.8866i
3.16	−1.55621	+	2.39635i	1.14091	−	2.97218i	−0.0668230	−	0.150087i	−9.96831	−	5.06288i	5.34689	+	7.35936i	−12.1399	−	13.9866i	−22.1135	−	3.50243i	12.5327	+	11.2845i	27.6452	−	16.0087i
3.17	−1.55612	+	2.39621i	−0.0369693	+	0.0963083i	−0.0664387	−	0.149224i	1.07427	+	11.1286i	−0.173247	−	0.238454i	18.4311	−	1.81536i	−22.1149	−	3.50265i	20.0570	+	18.0594i	−28.3382	−	14.7433i
3.18	−1.25359	+	1.93036i	−1.53819	+	4.00713i	1.09910	+	2.46861i	−10.5630	−	3.66383i	−5.80693	−	7.99256i	13.9174	−	12.2190i	−24.3299	−	3.85348i	6.37387	+	5.73906i	20.3141	−	15.7974i
3.19	−1.25167	+	1.92741i	−3.02258	+	7.87409i	1.10568	+	2.48340i	2.53086	+	10.8901i	−11.3933	−	15.6815i	−8.19908	−	16.6065i	−24.3295	−	3.85341i	−32.8005	−	29.5337i	−24.1575	−	8.75286i
3.20	−1.13801	+	1.75238i	−2.76584	+	7.20527i	1.47812	+	3.31992i	−10.3242	+	4.29074i	−9.47881	−	13.0465i	−2.38757	+	18.3657i	−24.0099	−	3.80279i	−24.2011	−	21.7908i	4.23004	−	22.9748i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
7.d	odd	6	1	inner
25.f	odd	20	1	inner
175.x	even	60	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	175.4.x.a	✓	928
7.d	odd	6	1	inner	175.4.x.a	✓	928
25.f	odd	20	1	inner	175.4.x.a	✓	928
175.x	even	60	1	inner	175.4.x.a	✓	928

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
175.4.x.a	✓	928	1.a	even	1	1	trivial
175.4.x.a	✓	928	7.d	odd	6	1	inner
175.4.x.a	✓	928	25.f	odd	20	1	inner
175.4.x.a	✓	928	175.x	even	60	1	inner

Hecke kernels

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