Newform orbit 207.7.d.a

• Label: 207.7.d.a
• Level: $207$
• Weight: $7$
• Character orbit: 207.d
• Self dual: yes
• Analytic conductor: $47.621$
• Analytic rank: $0$
• Dimension: $1$
• CM discriminant: -23
• Inner twists: $2$

Newspace parameters

Level:	$N$	$=$	$207 = 3^{2} \cdot 23$
Weight:	$k$	$=$	$7$
Character orbit:	$[\chi]$	$=$	207.d (of order $2$, degree $1$, minimal)

Newform invariants

Self dual:	yes
Analytic conductor:	$47.6211953093$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$1$
Twist minimal:	no (minimal twist has level 23)
Sato-Tate group:	$\mathrm{U}(1)[D_{2}]$

$q$-expansion

$f(q)$

$=$

q + 7 * q^2 - 15 * q^4 - 553 * q^8 + 1082 * q^13 - 2911 * q^16 + 12167 * q^23 + 15625 * q^25 + 7574 * q^26 - 30746 * q^29 + 58754 * q^31 + 15015 * q^32 - 43634 * q^41 + 85169 * q^46 + 205342 * q^47 + 117649 * q^49 + 109375 * q^50 - 16230 * q^52 - 215222 * q^58 + 253942 * q^59 + 411278 * q^62 + 291409 * q^64 - 667154 * q^71 + 725042 * q^73 - 305438 * q^82 - 182505 * q^92 + 1437394 * q^94 + 823543 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/207\mathbb{Z}\right)^\times$.

$n$	$28$	$47$
$\chi(n)$	$-1$	$1$

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  

$\iota_m(\nu)$

$a_{2}$

$a_{3}$

$a_{4}$

$a_{5}$

$a_{6}$

$a_{7}$

$a_{8}$

$a_{9}$

$a_{10}$

91.1

0

7.00000

0

−15.0000

0

0

0

−553.000

0

0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
23.b	odd	2	1	CM by $\Q(\sqrt{-23})$

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	207.7.d.a		1
3.b	odd	2	1		23.7.b.a	✓	1
12.b	even	2	1		368.7.f.a		1
23.b	odd	2	1	CM	207.7.d.a		1
69.c	even	2	1		23.7.b.a	✓	1
276.h	odd	2	1		368.7.f.a		1

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
23.7.b.a	✓	1	3.b	odd	2	1
23.7.b.a	✓	1	69.c	even	2	1
207.7.d.a		1	1.a	even	1	1	trivial
207.7.d.a		1	23.b	odd	2	1	CM
368.7.f.a		1	12.b	even	2	1
368.7.f.a		1	276.h	odd	2	1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator $T_{2} - 7$ acting on $S_{7}^{\mathrm{new}}(207, [\chi])$.

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$T - 7$
$3$	$T$
$5$	$T$
$7$	$T$
$11$	$T$