Newform orbit 40.11.e.b

• Label: 40.11.e.b
• Level: $40$
• Weight: $11$
• Character orbit: 40.e
• Self dual: yes
• Analytic conductor: $25.414$
• Analytic rank: $0$
• Dimension: $1$
• CM discriminant: -40
• Inner twists: $2$

Newspace parameters

Level:	$N$	$=$	$40 = 2^{3} \cdot 5$
Weight:	$k$	$=$	$11$
Character orbit:	$[\chi]$	$=$	40.e (of order $2$, degree $1$, minimal)

Newform invariants

Self dual:	yes
Analytic conductor:	$25.4142901069$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$1$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{U}(1)[D_{2}]$

$q$-expansion

$f(q)$

$=$

q + 32 * q^2 + 1024 * q^4 - 3125 * q^5 - 26886 * q^7 + 32768 * q^8 + 59049 * q^9 - 100000 * q^10 + 321102 * q^11 + 682086 * q^13 - 860352 * q^14 + 1048576 * q^16 + 1889568 * q^18 - 1288802 * q^19 - 3200000 * q^20 + 10275264 * q^22 + 1772186 * q^23 + 9765625 * q^25 + 21826752 * q^26 - 27531264 * q^28 + 33554432 * q^32 + 84018750 * q^35 + 60466176 * q^36 - 112652586 * q^37 - 41241664 * q^38 - 102400000 * q^40 - 611598 * q^41 + 328808448 * q^44 - 184528125 * q^45 + 56709952 * q^46 + 222705514 * q^47 + 440381747 * q^49 + 312500000 * q^50 + 698456064 * q^52 + 552886486 * q^53 - 1003443750 * q^55 - 881000448 * q^56 - 646632402 * q^59 - 1587591414 * q^63 + 1073741824 * q^64 - 2131518750 * q^65 + 2688600000 * q^70 + 1934917632 * q^72 - 3604882752 * q^74 - 1319733248 * q^76 - 8633148372 * q^77 - 3276800000 * q^80 + 3486784401 * q^81 - 19571136 * q^82 + 10521870336 * q^88 + 5417714898 * q^89 - 5904900000 * q^90 - 18338564196 * q^91 + 1814718464 * q^92 + 7126576448 * q^94 + 4027506250 * q^95 + 14092215904 * q^98 + 18960751998 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/40\mathbb{Z}\right)^\times$.

$n$	$17$	$21$	$31$
$\chi(n)$	$-1$	$-1$	$-1$

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  

$\iota_m(\nu)$

$a_{2}$

$a_{3}$

$a_{4}$

$a_{5}$

$a_{6}$

$a_{7}$

$a_{8}$

$a_{9}$

$a_{10}$

19.1

0

32.0000

0

1024.00

−3125.00

0

−26886.0

32768.0

59049.0

−100000.

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
40.e	odd	2	1	CM by $\Q(\sqrt{-10})$

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	40.11.e.b	yes	1
4.b	odd	2	1		160.11.e.a		1
5.b	even	2	1		40.11.e.a	✓	1
8.b	even	2	1		160.11.e.b		1
8.d	odd	2	1		40.11.e.a	✓	1
20.d	odd	2	1		160.11.e.b		1
40.e	odd	2	1	CM	40.11.e.b	yes	1
40.f	even	2	1		160.11.e.a		1

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
40.11.e.a	✓	1	5.b	even	2	1
40.11.e.a	✓	1	8.d	odd	2	1
40.11.e.b	yes	1	1.a	even	1	1	trivial
40.11.e.b	yes	1	40.e	odd	2	1	CM
160.11.e.a		1	4.b	odd	2	1
160.11.e.a		1	40.f	even	2	1
160.11.e.b		1	8.b	even	2	1
160.11.e.b		1	20.d	odd	2	1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $S_{11}^{\mathrm{new}}(40, [\chi])$:

$T_{3}$

$T_{7} + 26886$

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$T - 32$
$3$	$T$
$5$	$T + 3125$
$7$	$T + 26886$
$11$	$T - 321102$