Newform orbit 775.2.bj.e

• Label: 775.2.bj.e
• Level: $775$
• Weight: $2$
• Character orbit: 775.bj
• Analytic conductor: $6.188$
• Analytic rank: $0$
• Dimension: $32$
• CM: no
• Inner twists: $8$

Newspace parameters

Level:	\( N \)	\(=\)	\( 775 = 5^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	775.bj (of order \(12\), degree \(4\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(6.18840615665\)
Analytic rank:	\(0\)
Dimension:	\(32\)
Relative dimension:	\(8\) over \(\Q(\zeta_{12})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 32 q - 24 q^{6}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
57.1	−1.80731	−	1.80731i	2.27203	−	0.608789i			4.53275i		0		−5.20654	−	3.00600i	2.24769	−	0.602267i	4.57747	−	4.57747i	2.19343	−	1.26638i		0
57.2	−1.59100	−	1.59100i	−1.94690	+	0.521671i			3.06258i		0		3.92751	+	2.26755i	−0.347023	+	0.0929845i	1.69056	−	1.69056i	0.920219	−	0.531289i		0
57.3	−1.08909	−	1.08909i	1.13152	−	0.303189i			0.372250i		0		−1.56253	−	0.902125i	−1.24059	+	0.332416i	−1.77277	+	1.77277i	−1.40967	+	0.813875i		0
57.4	−0.718478	−	0.718478i	0.173922	−	0.0466024i		−	0.967579i		0		−0.158442	−	0.0914767i	2.69881	−	0.723145i	−2.13214	+	2.13214i	−2.57000	+	1.48379i		0
57.5	0.718478	+	0.718478i	−0.173922	+	0.0466024i		−	0.967579i		0		−0.158442	−	0.0914767i	−2.69881	+	0.723145i	2.13214	−	2.13214i	−2.57000	+	1.48379i		0
57.6	1.08909	+	1.08909i	−1.13152	+	0.303189i			0.372250i		0		−1.56253	−	0.902125i	1.24059	−	0.332416i	1.77277	−	1.77277i	−1.40967	+	0.813875i		0
57.7	1.59100	+	1.59100i	1.94690	−	0.521671i			3.06258i		0		3.92751	+	2.26755i	0.347023	−	0.0929845i	−1.69056	+	1.69056i	0.920219	−	0.531289i		0
57.8	1.80731	+	1.80731i	−2.27203	+	0.608789i			4.53275i		0		−5.20654	−	3.00600i	−2.24769	+	0.602267i	−4.57747	+	4.57747i	2.19343	−	1.26638i		0
68.1	−1.80731	+	1.80731i	2.27203	+	0.608789i		−	4.53275i		0		−5.20654	+	3.00600i	2.24769	+	0.602267i	4.57747	+	4.57747i	2.19343	+	1.26638i		0
68.2	−1.59100	+	1.59100i	−1.94690	−	0.521671i		−	3.06258i		0		3.92751	−	2.26755i	−0.347023	−	0.0929845i	1.69056	+	1.69056i	0.920219	+	0.531289i		0
68.3	−1.08909	+	1.08909i	1.13152	+	0.303189i		−	0.372250i		0		−1.56253	+	0.902125i	−1.24059	−	0.332416i	−1.77277	−	1.77277i	−1.40967	−	0.813875i		0
68.4	−0.718478	+	0.718478i	0.173922	+	0.0466024i			0.967579i		0		−0.158442	+	0.0914767i	2.69881	+	0.723145i	−2.13214	−	2.13214i	−2.57000	−	1.48379i		0
68.5	0.718478	−	0.718478i	−0.173922	−	0.0466024i			0.967579i		0		−0.158442	+	0.0914767i	−2.69881	−	0.723145i	2.13214	+	2.13214i	−2.57000	−	1.48379i		0
68.6	1.08909	−	1.08909i	−1.13152	−	0.303189i		−	0.372250i		0		−1.56253	+	0.902125i	1.24059	+	0.332416i	1.77277	+	1.77277i	−1.40967	−	0.813875i		0
68.7	1.59100	−	1.59100i	1.94690	+	0.521671i		−	3.06258i		0		3.92751	−	2.26755i	0.347023	+	0.0929845i	−1.69056	−	1.69056i	0.920219	+	0.531289i		0
68.8	1.80731	−	1.80731i	−2.27203	−	0.608789i		−	4.53275i		0		−5.20654	+	3.00600i	−2.24769	−	0.602267i	−4.57747	−	4.57747i	2.19343	+	1.26638i		0
243.1	−1.80731	+	1.80731i	0.608789	+	2.27203i		−	4.53275i		0		−5.20654	−	3.00600i	−0.602267	−	2.24769i	4.57747	+	4.57747i	−2.19343	+	1.26638i		0
243.2	−1.59100	+	1.59100i	−0.521671	−	1.94690i		−	3.06258i		0		3.92751	+	2.26755i	0.0929845	+	0.347023i	1.69056	+	1.69056i	−0.920219	+	0.531289i		0
243.3	−1.08909	+	1.08909i	0.303189	+	1.13152i		−	0.372250i		0		−1.56253	−	0.902125i	0.332416	+	1.24059i	−1.77277	−	1.77277i	1.40967	−	0.813875i		0
243.4	−0.718478	+	0.718478i	0.0466024	+	0.173922i			0.967579i		0		−0.158442	−	0.0914767i	−0.723145	−	2.69881i	−2.13214	−	2.13214i	2.57000	−	1.48379i		0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
5.b	even	2	1	inner
5.c	odd	4	2	inner
31.e	odd	6	1	inner
155.i	odd	6	1	inner
155.p	even	12	2	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	775.2.bj.e	✓	32
5.b	even	2	1	inner	775.2.bj.e	✓	32
5.c	odd	4	2	inner	775.2.bj.e	✓	32
31.e	odd	6	1	inner	775.2.bj.e	✓	32
155.i	odd	6	1	inner	775.2.bj.e	✓	32
155.p	even	12	2	inner	775.2.bj.e	✓	32

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
775.2.bj.e	✓	32	1.a	even	1	1	trivial
775.2.bj.e	✓	32	5.b	even	2	1	inner
775.2.bj.e	✓	32	5.c	odd	4	2	inner
775.2.bj.e	✓	32	31.e	odd	6	1	inner
775.2.bj.e	✓	32	155.i	odd	6	1	inner
775.2.bj.e	✓	32	155.p	even	12	2	inner

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(775, [\chi])\):

\( T_{2}^{16} + 75T_{2}^{12} + 1557T_{2}^{8} + 7731T_{2}^{4} + 6561 \)

T3^32 - 49*T3^28 + 1807*T3^24 - 27202*T3^20 + 306187*T3^16 - 565390*T3^12 + 905710*T3^8 - 952*T3^4 + 1

T7^32 - 93*T7^28 + 6615*T7^24 - 179370*T7^20 + 3681747*T7^16 - 9943398*T7^12 + 23806062*T7^8 - 396576*T7^4 + 6561