Properties

 Label 43.11.b.a Level 43 Weight 11 Character orbit 43.b Self dual yes Analytic conductor 27.320 Analytic rank 0 Dimension 1 CM discriminant -43 Inner twists 2

Related objects

Newspace parameters

 Level: $$N$$ = $$43$$ Weight: $$k$$ = $$11$$ Character orbit: $$[\chi]$$ = 43.b (of order $$2$$, degree $$1$$, minimal)

Newform invariants

 Self dual: yes Analytic conductor: $$27.3203618650$$ 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

 $$f(q)$$ $$=$$ $$q + 1024q^{4} + 59049q^{9} + O(q^{10})$$ $$q + 1024q^{4} + 59049q^{9} - 18501q^{11} + 303943q^{13} + 1048576q^{16} - 2764089q^{17} + 4126443q^{23} + 9765625q^{25} + 57253099q^{31} + 60466176q^{36} + 142671399q^{41} - 147008443q^{43} - 18945024q^{44} + 451176882q^{47} + 282475249q^{49} + 311237632q^{52} - 33972057q^{53} - 990191574q^{59} + 1073741824q^{64} - 1504819589q^{67} - 2830427136q^{68} - 2641416974q^{79} + 3486784401q^{81} - 6757639557q^{83} + 4225477632q^{92} - 15006753793q^{97} - 1092465549q^{99} + O(q^{100})$$

Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/43\mathbb{Z}\right)^\times$$.

 $$n$$ $$3$$ $$\chi(n)$$ $$-1$$

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 $$\iota_m(\nu)$$ $$a_{2}$$ $$a_{3}$$ $$a_{4}$$ $$a_{5}$$ $$a_{6}$$ $$a_{7}$$ $$a_{8}$$ $$a_{9}$$ $$a_{10}$$
42.1
 0
0 0 1024.00 0 0 0 0 59049.0 0
 $$n$$: e.g. 2-40 or 990-1000 Significant digits: Format: Complex embeddings Normalized embeddings Satake parameters Satake angles

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
43.b odd 2 1 CM by $$\Q(\sqrt{-43})$$

Twists

By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 43.11.b.a 1
43.b odd 2 1 CM 43.11.b.a 1

By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
43.11.b.a 1 1.a even 1 1 trivial
43.11.b.a 1 43.b odd 2 1 CM

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator $$T_{2}$$ acting on $$S_{11}^{\mathrm{new}}(43, [\chi])$$.

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ $$( 1 - 32 T )( 1 + 32 T )$$
$3$ $$( 1 - 243 T )( 1 + 243 T )$$
$5$ $$( 1 - 3125 T )( 1 + 3125 T )$$
$7$ $$( 1 - 16807 T )( 1 + 16807 T )$$
$11$ $$1 + 18501 T + 25937424601 T^{2}$$
$13$ $$1 - 303943 T + 137858491849 T^{2}$$
$17$ $$1 + 2764089 T + 2015993900449 T^{2}$$
$19$ $$( 1 - 2476099 T )( 1 + 2476099 T )$$
$23$ $$1 - 4126443 T + 41426511213649 T^{2}$$
$29$ $$( 1 - 20511149 T )( 1 + 20511149 T )$$
$31$ $$1 - 57253099 T + 819628286980801 T^{2}$$
$37$ $$( 1 - 69343957 T )( 1 + 69343957 T )$$
$41$ $$1 - 142671399 T + 13422659310152401 T^{2}$$
$43$ $$1 + 147008443 T$$
$47$ $$1 - 451176882 T + 52599132235830049 T^{2}$$
$53$ $$1 + 33972057 T + 174887470365513049 T^{2}$$
$59$ $$1 + 990191574 T + 511116753300641401 T^{2}$$
$61$ $$( 1 - 844596301 T )( 1 + 844596301 T )$$
$67$ $$1 + 1504819589 T + 1822837804551761449 T^{2}$$
$71$ $$( 1 - 1804229351 T )( 1 + 1804229351 T )$$
$73$ $$( 1 - 2073071593 T )( 1 + 2073071593 T )$$
$79$ $$1 + 2641416974 T + 9468276082626847201 T^{2}$$
$83$ $$1 + 6757639557 T + 15516041187205853449 T^{2}$$
$89$ $$( 1 - 5584059449 T )( 1 + 5584059449 T )$$
$97$ $$1 + 15006753793 T + 73742412689492826049 T^{2}$$