Newform orbit 825.2.v.a

• Label: 825.2.v.a
• Level: $825$
• Weight: $2$
• Character orbit: 825.v
• Analytic conductor: $6.588$
• Analytic rank: $0$
• Dimension: $240$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	825.v (of order \(10\), degree \(4\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(6.58765816676\)
Analytic rank:	\(0\)
Dimension:	\(240\)
Relative dimension:	\(60\) over \(\Q(\zeta_{10})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 240 q - 240 q^{4} - 4 q^{5} + 4 q^{6} - 20 q^{7} + 60 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
379.1		−	2.76517i	−0.951057	+	0.309017i	−5.64618			−0.511656	+	2.17674i	0.854486	+	2.62984i	−1.90098	−	2.61647i			10.0823i	0.809017	−	0.587785i	6.01907	+	1.41482i
379.2		−	2.70542i	0.951057	−	0.309017i	−5.31930			−1.72411	−	1.42388i	−0.836021	−	2.57301i	−2.63011	−	3.62003i			8.98009i	0.809017	−	0.587785i	−3.85221	+	4.66444i
379.3		−	2.58202i	−0.951057	+	0.309017i	−4.66681			0.120785	−	2.23280i	0.797887	+	2.45564i	−1.01347	−	1.39492i			6.88574i	0.809017	−	0.587785i	−5.76513	−	0.311869i
379.4		−	2.55494i	0.951057	−	0.309017i	−4.52773			1.22488	−	1.87074i	−0.789521	−	2.42990i	2.78784	+	3.83714i			6.45822i	0.809017	−	0.587785i	−4.77963	−	3.12951i
379.5		−	2.47273i	−0.951057	+	0.309017i	−4.11437			−2.23405	+	0.0949402i	0.764114	+	2.35170i	1.92985	+	2.65621i			5.22827i	0.809017	−	0.587785i	0.234761	+	5.52420i
379.6		−	2.46531i	0.951057	−	0.309017i	−4.07775			−1.61849	+	1.54288i	−0.761822	−	2.34465i	1.80478	+	2.48406i			5.12229i	0.809017	−	0.587785i	3.80367	+	3.99009i
379.7		−	2.45052i	0.951057	−	0.309017i	−4.00503			1.53668	+	1.62438i	−0.757251	−	2.33058i	0.163390	+	0.224887i			4.91336i	0.809017	−	0.587785i	3.98056	−	3.76567i
379.8		−	2.25329i	0.951057	−	0.309017i	−3.07730			−1.65309	+	1.50575i	−0.696304	−	2.14300i	−0.988725	−	1.36086i			2.42747i	0.809017	−	0.587785i	3.39288	+	3.72490i
379.9		−	2.21118i	−0.951057	+	0.309017i	−2.88931			1.63327	−	1.52723i	0.683292	+	2.10296i	−1.35421	−	1.86391i			1.96642i	0.809017	−	0.587785i	−3.37698	−	3.61145i
379.10		−	2.18815i	−0.951057	+	0.309017i	−2.78802			0.0394663	+	2.23572i	0.676177	+	2.08106i	0.879948	+	1.21114i			1.72430i	0.809017	−	0.587785i	4.89210	−	0.0863584i
379.11		−	1.91341i	−0.951057	+	0.309017i	−1.66114			0.171826	−	2.22946i	0.591277	+	1.81976i	2.69745	+	3.71273i		−	0.648375i	0.809017	−	0.587785i	−4.26587	−	0.328774i
379.12		−	1.87868i	0.951057	−	0.309017i	−1.52944			−0.918568	−	2.03868i	−0.580544	−	1.78673i	−0.876577	−	1.20651i		−	0.884028i	0.809017	−	0.587785i	−3.83004	+	1.72570i
379.13		−	1.86648i	0.951057	−	0.309017i	−1.48375			2.08758	−	0.801246i	−0.576774	−	1.77513i	−1.35490	−	1.86487i		−	0.963568i	0.809017	−	0.587785i	−1.49551	−	3.89643i
379.14		−	1.65291i	−0.951057	+	0.309017i	−0.732123			1.22429	+	1.87113i	0.510778	+	1.57201i	−0.542949	−	0.747306i		−	2.09569i	0.809017	−	0.587785i	3.09281	−	2.02364i
379.15		−	1.54435i	−0.951057	+	0.309017i	−0.385030			−2.07009	−	0.845405i	0.477232	+	1.46877i	−2.88816	−	3.97521i		−	2.49409i	0.809017	−	0.587785i	−1.30560	+	3.19696i
379.16		−	1.51414i	−0.951057	+	0.309017i	−0.292615			2.22304	−	0.241016i	0.467895	+	1.44003i	−0.788000	−	1.08459i		−	2.58522i	0.809017	−	0.587785i	−0.364931	−	3.36599i
379.17		−	1.27180i	0.951057	−	0.309017i	0.382519			2.23444	+	0.0853930i	−0.393009	−	1.20956i	1.11081	+	1.52890i		−	3.03009i	0.809017	−	0.587785i	0.108603	−	2.84176i
379.18		−	1.23707i	0.951057	−	0.309017i	0.469655			1.15530	+	1.91449i	−0.382276	−	1.17652i	2.52673	+	3.47774i		−	3.05514i	0.809017	−	0.587785i	2.36836	−	1.42919i
379.19		−	1.19722i	−0.951057	+	0.309017i	0.566663			−1.96576	+	1.06573i	0.369961	+	1.13862i	2.17421	+	2.99254i		−	3.07286i	0.809017	−	0.587785i	1.27591	+	2.35345i
379.20		−	1.19482i	0.951057	−	0.309017i	0.572401			−0.568390	+	2.16262i	−0.369220	−	1.13634i	−1.40869	−	1.93889i		−	3.07356i	0.809017	−	0.587785i	2.58395	+	0.679125i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
275.n	even	10	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	825.2.v.a	✓	240
11.c	even	5	1		825.2.bv.a	yes	240
25.e	even	10	1		825.2.bv.a	yes	240
275.n	even	10	1	inner	825.2.v.a	✓	240

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
825.2.v.a	✓	240	1.a	even	1	1	trivial
825.2.v.a	✓	240	275.n	even	10	1	inner
825.2.bv.a	yes	240	11.c	even	5	1
825.2.bv.a	yes	240	25.e	even	10	1

Hecke kernels

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