Newform orbit 3808.1.e.d

• Label: 3808.1.e.d
• Level: $3808$
• Weight: $1$
• Character orbit: 3808.e
• Analytic conductor: $1.900$
• Analytic rank: $0$
• Dimension: $4$
• Projective image: $D_{10}$
• CM discriminant: -119
• Inner twists: $4$

Newspace parameters

Level:	$N$	$=$	$3808 = 2^{5} \cdot 7 \cdot 17$
Weight:	$k$	$=$	$1$
Character orbit:	$[\chi]$	$=$	3808.e (of order $2$, degree $1$, not minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$1.90043956811$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
Defining polynomial:	$x^{4} - x^{3} + x^{2} - x + 1$
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$2^{2}$
Twist minimal:	no (minimal twist has level 952)
Projective image:	$D_{10}$
Projective field:	Galois closure of 10.2.6571095523328.1

$q$-expansion

The $q$-expansion and trace form are shown below.

$f(q)$	$=$	q + (z^4 + z) * q^3 + (z^3 + z^2) * q^5 + q^7 + (-z^3 + z^2 - 1) * q^9 + (z^4 + z^3 - z^2 - z) * q^15 + q^17 + (z^4 + z) * q^21 + (z^4 - z - 1) * q^25 + (-z^4 + z^3 + z^2 - z) * q^27 + (z^3 - z^2) * q^31 + (z^3 + z^2) * q^35 + (-z^4 + z) * q^41 + (z^4 + z) * q^43 + (z^4 - z^3 - z^2 + z) * q^45 + q^49 + (z^4 + z) * q^51 + (-z^3 - z^2) * q^53 + (-z^4 - z) * q^61 + (-z^3 + z^2 - 1) * q^63 + (-z^3 - z^2) * q^67 + (z^4 - z) * q^73 + (-z^4 - z^3 - z^2 - z) * q^75 + (z^4 + z^3 - z^2 - z + 1) * q^81 + (z^3 + z^2) * q^85 + (z^4 - z^3 - z^2 + z) * q^93 + (z^3 - z^2) * q^97
$\operatorname{Tr}(f)(q)$	$=$	$4 q + 4 q^{7} - 6 q^{9} + 4 q^{17} - 6 q^{25} + 2 q^{31} + 2 q^{41} + 4 q^{49} - 6 q^{63} - 2 q^{73} + 4 q^{81} + 2 q^{97}+O(q^{100})$

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3808\mathbb{Z}\right)^\times$.

$n$	$2143$	$2689$	$3265$	$3333$
$\chi(n)$	$1$	$-1$	$-1$	$-1$

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  

$\iota_m(\nu)$

$a_{2}$

$a_{3}$

$a_{4}$

$a_{5}$

$a_{6}$

$a_{7}$

$a_{8}$

$a_{9}$

$a_{10}$

3569.1

−0.309017	−	0.951057i
0.809017	−	0.587785i
0.809017	+	0.587785i
−0.309017	+	0.951057i

0

−

1.90211i

0

1.17557i

0

1.00000

0

−2.61803

0

3569.2

0

−

1.17557i

0

−

1.90211i

0

1.00000

0

−0.381966

0

3569.3

0

1.17557i

0

1.90211i

0

1.00000

0

−0.381966

0

3569.4

0

1.90211i

0

−

1.17557i

0

1.00000

0

−2.61803

0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
119.d	odd	2	1	CM by $\Q(\sqrt{-119})$
8.b	even	2	1	inner
952.e	odd	2	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	3808.1.e.d		4
4.b	odd	2	1		952.1.e.d	yes	4
7.b	odd	2	1		3808.1.e.c		4
8.b	even	2	1	inner	3808.1.e.d		4
8.d	odd	2	1		952.1.e.d	yes	4
17.b	even	2	1		3808.1.e.c		4
28.d	even	2	1		952.1.e.c	✓	4
56.e	even	2	1		952.1.e.c	✓	4
56.h	odd	2	1		3808.1.e.c		4
68.d	odd	2	1		952.1.e.c	✓	4
119.d	odd	2	1	CM	3808.1.e.d		4
136.e	odd	2	1		952.1.e.c	✓	4
136.h	even	2	1		3808.1.e.c		4
476.e	even	2	1		952.1.e.d	yes	4
952.e	odd	2	1	inner	3808.1.e.d		4
952.k	even	2	1		952.1.e.d	yes	4

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
952.1.e.c	✓	4	28.d	even	2	1
952.1.e.c	✓	4	56.e	even	2	1
952.1.e.c	✓	4	68.d	odd	2	1
952.1.e.c	✓	4	136.e	odd	2	1
952.1.e.d	yes	4	4.b	odd	2	1
952.1.e.d	yes	4	8.d	odd	2	1
952.1.e.d	yes	4	476.e	even	2	1
952.1.e.d	yes	4	952.k	even	2	1
3808.1.e.c		4	7.b	odd	2	1
3808.1.e.c		4	17.b	even	2	1
3808.1.e.c		4	56.h	odd	2	1
3808.1.e.c		4	136.h	even	2	1
3808.1.e.d		4	1.a	even	1	1	trivial
3808.1.e.d		4	8.b	even	2	1	inner
3808.1.e.d		4	119.d	odd	2	1	CM
3808.1.e.d		4	952.e	odd	2	1	inner

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $S_{1}^{\mathrm{new}}(3808, [\chi])$:

$T_{3}^{4} + 5T_{3}^{2} + 5$

$T_{31}^{2} - T_{31} - 1$

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$T^{4}$
$3$	$T^{4} + 5T^{2} + 5$
$5$	$T^{4} + 5T^{2} + 5$
$7$	$(T - 1)^{4}$
$11$	$T^{4}$