Newform orbit 125.2.g.a

• Label: 125.2.g.a
• Level: $125$
• Weight: $2$
• Character orbit: 125.g
• Analytic conductor: $0.998$
• Analytic rank: $0$
• Dimension: $220$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 125 = 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	125.g (of order \(25\), degree \(20\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(0.998130025266\)
Analytic rank:	\(0\)
Dimension:	\(220\)
Relative dimension:	\(11\) over \(\Q(\zeta_{25})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{25}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 220 q - 20 q^{2} - 20 q^{3} - 20 q^{4} - 15 q^{5} - 20 q^{6} - 15 q^{7} - 5 q^{8} - 20 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
6.1	−2.40956	−	0.618669i	0.245395	−	1.28641i	3.67060	+	2.01793i	−1.14792	−	1.91893i	−1.38715	+	2.94785i	1.60052	−	1.16284i	−3.96915	−	3.72728i	1.19471	+	0.473019i	1.57879	+	5.33394i
6.2	−2.40901	−	0.618528i	−0.622000	+	3.26064i	3.66812	+	2.01657i	−1.51593	+	1.64376i	3.51519	−	7.47017i	0.637759	−	0.463359i	−3.96312	−	3.72162i	−7.45553	−	2.95185i	4.66861	−	3.02218i
6.3	−1.61844	−	0.415545i	−0.244888	+	1.28375i	0.694058	+	0.381562i	1.36515	−	1.77098i	0.929792	−	1.97591i	−1.25281	+	0.910218i	1.47138	+	1.38172i	1.20129	+	0.475623i	−2.94533	+	2.29894i
6.4	−1.17253	−	0.301054i	0.595442	−	3.12142i	−0.468423	−	0.257518i	2.22254	−	0.245569i	−1.63789	+	3.48069i	−0.353637	+	0.256932i	2.23663	+	2.10034i	−6.59936	−	2.61287i	−2.67992	−	0.381170i
6.5	−0.903097	−	0.231876i	−0.0620903	+	0.325489i	−0.990795	−	0.544694i	−1.86049	+	1.24039i	0.131547	−	0.279551i	−3.30296	+	2.39974i	2.12785	+	1.99818i	2.68724	+	1.06395i	1.96782	−	0.688789i
6.6	−0.822898	−	0.211284i	−0.0412084	+	0.216022i	−1.12009	−	0.615777i	0.708288	+	2.12093i	0.0795524	−	0.169058i	3.77476	−	2.74253i	2.03027	+	1.90655i	2.74436	+	1.08657i	−0.134730	−	1.89496i
6.7	0.362552	+	0.0930876i	0.327867	−	1.71874i	−1.62983	−	0.896009i	−1.66215	−	1.49575i	0.278863	−	0.592613i	0.0276395	−	0.0200812i	−1.05322	−	0.989036i	−0.0572451	−	0.0226649i	−0.463380	−	0.697013i
6.8	0.784012	+	0.201300i	−0.488943	+	2.56313i	−1.17846	−	0.647864i	1.66759	+	1.48968i	−0.899294	+	1.91110i	−0.523443	+	0.380304i	−1.97363	−	1.85336i	−3.54123	−	1.40207i	1.00754	+	1.50361i
6.9	1.56052	+	0.400675i	0.408202	−	2.13987i	0.522084	+	0.287018i	0.485910	+	2.18263i	1.49440	−	3.17576i	−0.836629	+	0.607847i	−1.64922	−	1.54872i	−1.62309	−	0.642625i	−0.116252	+	3.60075i
6.10	1.85071	+	0.475182i	−0.137817	+	0.722462i	1.44673	+	0.795344i	1.17007	−	1.90550i	−0.598361	+	1.27158i	−2.81109	+	2.04237i	−0.486202	−	0.456575i	2.28637	+	0.905238i	3.07092	−	2.97055i
6.11	1.93284	+	0.496268i	−0.289066	+	1.51534i	1.73696	+	0.954900i	−2.21785	+	0.284821i	−1.31073	+	2.78545i	2.58545	−	1.87844i	−0.0259901	−	0.0244063i	0.576636	+	0.228306i	−4.42809	−	0.550137i
11.1	−1.97173	+	1.85157i	3.22832e−5	0	5.08701e-5i	0.333796	−	5.30554i	2.21278	−	0.321903i	−0.000157843	0	4.05273e-5i	0.678693	−	2.08880i	5.71721	+	6.91092i	1.27734	−	2.71448i	−3.76696	+	4.73182i
11.2	−1.60644	+	1.50855i	0.822947	+	1.29676i	0.179354	−	2.85076i	−2.23260	−	0.124575i	−3.27824	−	0.841710i	−1.28662	+	3.95980i	1.20298	+	1.45415i	0.273000	−	0.580155i	3.77447	−	3.16786i
11.3	−1.26877	+	1.19146i	−1.66333	−	2.62099i	0.0646335	−	1.02732i	0.461407	+	2.18795i	5.23318	+	1.34365i	−0.283105	+	0.871308i	−1.07687	−	1.30172i	−2.82557	+	6.00465i	−3.19226	−	2.22626i
11.4	−1.01409	+	0.952292i	1.42906	+	2.25184i	−0.00406678	+	0.0646397i	0.248313	+	2.22224i	−3.59359	−	0.922678i	1.42081	−	4.37282i	−1.83091	−	2.21319i	−1.75122	+	3.72153i	−2.36803	−	2.01708i
11.5	−0.992063	+	0.931610i	−0.836274	−	1.31776i	−0.00928759	+	0.147622i	−0.216983	−	2.22552i	2.05727	+	0.528217i	0.230945	−	0.710774i	−1.86327	−	2.25231i	0.240210	−	0.510472i	2.28857	+	2.00571i
11.6	0.0548468	−	0.0515046i	−0.203470	−	0.320618i	−0.125226	+	1.99040i	−0.553871	+	2.16639i	−0.0276730	−	0.00710521i	−1.02685	+	3.16032i	0.191565	+	0.231562i	1.21594	−	2.58401i	0.0812007	+	0.147346i
11.7	0.436521	−	0.409921i	1.22515	+	1.93053i	−0.103065	+	1.63818i	−1.37573	−	1.76278i	1.32617	+	0.340503i	0.159126	−	0.489740i	1.38994	+	1.68015i	−0.948615	+	2.01591i	−1.32313	−	0.205550i
11.8	0.444774	−	0.417671i	−0.468839	−	0.738773i	−0.102206	+	1.62452i	2.19457	+	0.428772i	−0.517091	−	0.132766i	0.739388	−	2.27560i	1.41089	+	1.70548i	0.951363	−	2.02175i	1.15518	−	0.725902i
11.9	1.03453	−	0.971489i	−1.68964	−	2.66244i	0.000881745	−	0.0140149i	−2.20603	+	0.365290i	−4.33451	−	1.11291i	1.16348	−	3.58083i	1.79652	+	2.17162i	−2.95638	+	6.28262i	−1.92733	+	2.52104i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
125.g	even	25	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	125.2.g.a	✓	220
5.b	even	2	1		625.2.g.a		220
5.c	odd	4	2		625.2.h.b		440
125.g	even	25	1	inner	125.2.g.a	✓	220
125.h	even	50	1		625.2.g.a		220
125.i	odd	100	2		625.2.h.b		440

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
125.2.g.a	✓	220	1.a	even	1	1	trivial
125.2.g.a	✓	220	125.g	even	25	1	inner
625.2.g.a		220	5.b	even	2	1
625.2.g.a		220	125.h	even	50	1
625.2.h.b		440	5.c	odd	4	2
625.2.h.b		440	125.i	odd	100	2

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(125, [\chi])\).