Newform orbit 825.2.cv.a

• Label: 825.2.cv.a
• Level: $825$
• Weight: $2$
• Character orbit: 825.cv
• Analytic conductor: $6.588$
• Analytic rank: $0$
• Dimension: $928$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	825.cv (of order \(20\), degree \(8\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(6.58765816676\)
Analytic rank:	\(0\)
Dimension:	\(928\)
Relative dimension:	\(116\) over \(\Q(\zeta_{20})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 928 q - 8 q^{3} - 20 q^{4} - 2 q^{6} - 20 q^{7} - 10 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
38.1	−2.44478	+	1.24568i	−1.61954	+	0.614066i	3.24968	−	4.47280i	−1.97551	+	1.04755i	3.19450	−	3.51869i	−0.197806	+	1.24889i	−1.51462	+	9.56295i	2.24585	−	1.98901i	3.52478	−	5.02189i
38.2	−2.42474	+	1.23547i	0.585344	+	1.63015i	3.17742	−	4.37335i	2.23424	+	0.0904402i	−3.43330	−	3.22951i	−0.205362	+	1.29660i	−1.44987	+	9.15414i	−2.31475	+	1.90839i	−5.52919	+	2.54103i
38.3	−2.41994	+	1.23302i	−0.827007	−	1.52186i	3.16019	−	4.34963i	0.811601	+	2.08358i	3.87779	+	2.66309i	0.267054	−	1.68611i	−1.43454	+	9.05736i	−1.63212	+	2.51718i	−4.53312	−	4.04141i
38.4	−2.40889	+	1.22739i	0.450189	−	1.67252i	3.12070	−	4.29527i	1.71386	−	1.43621i	0.968382	+	4.58148i	−0.250685	+	1.58276i	−1.39958	+	8.83660i	−2.59466	−	1.50590i	−2.36571	+	5.56324i
38.5	−2.28712	+	1.16535i	−1.34816	−	1.08742i	2.69731	−	3.71253i	−1.63132	−	1.52931i	4.35061	+	0.915983i	0.0224301	−	0.141618i	−1.03959	+	6.56372i	0.635051	+	2.93201i	5.51320	+	1.59666i
38.6	−2.27369	+	1.15850i	1.73150	−	0.0435123i	2.65198	−	3.65014i	−0.342188	−	2.20973i	−3.88650	+	2.10489i	−0.0618958	+	0.390795i	−1.00270	+	6.33081i	2.99621	−	0.150684i	3.33801	+	4.62782i
38.7	−2.25231	+	1.14761i	−1.72250	−	0.181618i	2.58032	−	3.55151i	1.83588	−	1.27654i	4.08804	−	1.56770i	0.748612	−	4.72655i	−0.945062	+	5.96689i	2.93403	+	0.625674i	−2.67000	+	4.98203i
38.8	−2.21765	+	1.12995i	1.38785	−	1.03627i	2.46562	−	3.39364i	−0.371993	+	2.20491i	−1.90684	+	3.86630i	−0.340474	+	2.14967i	−0.854544	+	5.39538i	0.852271	−	2.87639i	−1.66649	−	5.31005i
38.9	−2.21490	+	1.12855i	1.56109	+	0.750334i	2.45660	−	3.38122i	−2.23415	+	0.0925858i	−4.30445	+	0.0998496i	−0.553098	+	3.49212i	−0.847511	+	5.35098i	1.87400	+	2.34268i	4.84394	−	2.72642i
38.10	−2.16280	+	1.10200i	−1.60354	+	0.654717i	2.28773	−	3.14879i	2.20077	+	0.395750i	2.74664	−	3.18313i	−0.712174	+	4.49649i	−0.718484	+	4.53633i	2.14269	−	2.09973i	−5.19594	+	1.56932i
38.11	−2.13641	+	1.08856i	−0.933002	+	1.45928i	2.20373	−	3.03317i	0.384502	+	2.20276i	0.404764	−	4.13325i	0.370059	−	2.33646i	−0.656112	+	4.14253i	−1.25902	−	2.72303i	−3.21928	−	4.28745i
38.12	−2.09165	+	1.06575i	1.73189	+	0.0235223i	2.06361	−	2.84032i	2.22769	+	0.193327i	−3.64758	+	1.79656i	0.541889	−	3.42136i	−0.554823	+	3.50301i	2.99889	+	0.0814762i	−4.86560	+	1.96979i
38.13	−2.07571	+	1.05763i	1.08379	+	1.35107i	2.01444	−	2.77263i	−0.344707	+	2.20934i	−3.67857	−	1.65819i	0.0739128	−	0.466667i	−0.520107	+	3.28383i	−0.650799	+	2.92856i	−1.62115	−	4.95053i
38.14	−2.05172	+	1.04540i	−0.248863	+	1.71408i	1.94111	−	2.67170i	−1.57343	−	1.58881i	−1.28131	−	3.77697i	−0.670968	+	4.23632i	−0.469154	+	2.96212i	−2.87613	−	0.853141i	4.88918	+	1.61492i
38.15	−1.93149	+	0.984142i	−1.02179	+	1.39855i	1.58654	−	2.18368i	0.926837	−	2.03494i	0.597212	−	3.70687i	0.171202	−	1.08093i	−0.237100	+	1.49699i	−0.911874	−	2.85806i	0.212493	+	4.84260i
38.16	−1.92531	+	0.980995i	0.755789	−	1.55846i	1.56890	−	2.15940i	−0.953410	−	2.02262i	0.0737082	+	3.74193i	0.505668	−	3.19266i	−0.226198	+	1.42816i	−1.85757	−	2.35573i	3.81979	+	2.95889i
38.17	−1.90864	+	0.972500i	−0.646038	−	1.60706i	1.52158	−	2.09427i	−2.10156	+	0.763835i	2.79592	+	2.43902i	0.486510	−	3.07170i	−0.197261	+	1.24546i	−2.16527	+	2.07644i	3.26829	−	3.50165i
38.18	−1.89125	+	0.963640i	−1.33586	−	1.10248i	1.47265	−	2.02693i	−0.0520351	−	2.23546i	3.58885	+	0.797778i	−0.523626	+	3.30604i	−0.167826	+	1.05961i	0.569064	+	2.94553i	2.25259	+	4.17767i
38.19	−1.88133	+	0.958585i	−0.609839	+	1.62114i	1.44495	−	1.98880i	−2.18014	+	0.496987i	−0.406693	−	3.63448i	0.331686	−	2.09418i	−0.151375	+	0.955745i	−2.25619	−	1.97727i	3.62516	−	3.02484i
38.20	−1.79864	+	0.916453i	−0.105008	−	1.72886i	1.21965	−	1.67870i	−0.703354	+	2.12257i	1.77329	+	3.01337i	−0.558251	+	3.52466i	−0.0236817	+	0.149520i	−2.97795	+	0.363090i	−0.680153	−	4.46233i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
3.b	odd	2	1	inner
275.bj	odd	20	1	inner
825.cv	even	20	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	825.2.cv.a	✓	928
3.b	odd	2	1	inner	825.2.cv.a	✓	928
11.c	even	5	1		825.2.df.a	yes	928
25.f	odd	20	1		825.2.df.a	yes	928
33.h	odd	10	1		825.2.df.a	yes	928
75.l	even	20	1		825.2.df.a	yes	928
275.bj	odd	20	1	inner	825.2.cv.a	✓	928
825.cv	even	20	1	inner	825.2.cv.a	✓	928

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
825.2.cv.a	✓	928	1.a	even	1	1	trivial
825.2.cv.a	✓	928	3.b	odd	2	1	inner
825.2.cv.a	✓	928	275.bj	odd	20	1	inner
825.2.cv.a	✓	928	825.cv	even	20	1	inner
825.2.df.a	yes	928	11.c	even	5	1
825.2.df.a	yes	928	25.f	odd	20	1
825.2.df.a	yes	928	33.h	odd	10	1
825.2.df.a	yes	928	75.l	even	20	1

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(825, [\chi])\).