Properties

Label 27.4.a.b
Level 27
Weight 4
Character orbit 27.a
Self dual yes
Analytic conductor 1.593
Analytic rank 0
Dimension 1
CM no
Inner twists 1

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 27 = 3^{3} \)
Weight: \( k \) = \( 4 \)
Character orbit: \([\chi]\) = 27.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(1.59305157016\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q + 3q^{2} + q^{4} + 15q^{5} - 25q^{7} - 21q^{8} + O(q^{10}) \) \( q + 3q^{2} + q^{4} + 15q^{5} - 25q^{7} - 21q^{8} + 45q^{10} - 15q^{11} + 20q^{13} - 75q^{14} - 71q^{16} + 72q^{17} + 2q^{19} + 15q^{20} - 45q^{22} + 114q^{23} + 100q^{25} + 60q^{26} - 25q^{28} + 30q^{29} + 101q^{31} - 45q^{32} + 216q^{34} - 375q^{35} - 430q^{37} + 6q^{38} - 315q^{40} - 30q^{41} + 110q^{43} - 15q^{44} + 342q^{46} - 330q^{47} + 282q^{49} + 300q^{50} + 20q^{52} + 621q^{53} - 225q^{55} + 525q^{56} + 90q^{58} - 660q^{59} - 376q^{61} + 303q^{62} + 433q^{64} + 300q^{65} - 250q^{67} + 72q^{68} - 1125q^{70} - 360q^{71} + 785q^{73} - 1290q^{74} + 2q^{76} + 375q^{77} + 488q^{79} - 1065q^{80} - 90q^{82} + 489q^{83} + 1080q^{85} + 330q^{86} + 315q^{88} - 450q^{89} - 500q^{91} + 114q^{92} - 990q^{94} + 30q^{95} - 1105q^{97} + 846q^{98} + O(q^{100}) \)

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 \(\iota_m(\nu)\) \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
1.1
0
3.00000 0 1.00000 15.0000 0 −25.0000 −21.0000 0 45.0000
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Inner twists

This newform does not admit any (nontrivial) inner twists.

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 27.4.a.b yes 1
3.b odd 2 1 27.4.a.a 1
4.b odd 2 1 432.4.a.n 1
5.b even 2 1 675.4.a.a 1
5.c odd 4 2 675.4.b.a 2
7.b odd 2 1 1323.4.a.k 1
8.b even 2 1 1728.4.a.c 1
8.d odd 2 1 1728.4.a.d 1
9.c even 3 2 81.4.c.a 2
9.d odd 6 2 81.4.c.c 2
12.b even 2 1 432.4.a.a 1
15.d odd 2 1 675.4.a.j 1
15.e even 4 2 675.4.b.b 2
21.c even 2 1 1323.4.a.d 1
24.f even 2 1 1728.4.a.bd 1
24.h odd 2 1 1728.4.a.bc 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
27.4.a.a 1 3.b odd 2 1
27.4.a.b yes 1 1.a even 1 1 trivial
81.4.c.a 2 9.c even 3 2
81.4.c.c 2 9.d odd 6 2
432.4.a.a 1 12.b even 2 1
432.4.a.n 1 4.b odd 2 1
675.4.a.a 1 5.b even 2 1
675.4.a.j 1 15.d odd 2 1
675.4.b.a 2 5.c odd 4 2
675.4.b.b 2 15.e even 4 2
1323.4.a.d 1 21.c even 2 1
1323.4.a.k 1 7.b odd 2 1
1728.4.a.c 1 8.b even 2 1
1728.4.a.d 1 8.d odd 2 1
1728.4.a.bc 1 24.h odd 2 1
1728.4.a.bd 1 24.f even 2 1

Atkin-Lehner signs

\( p \) Sign
\(3\) \(1\)

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2} - 3 \) acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(27))\).

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ \( 1 - 3 T + 8 T^{2} \)
$3$ \( \)
$5$ \( 1 - 15 T + 125 T^{2} \)
$7$ \( 1 + 25 T + 343 T^{2} \)
$11$ \( 1 + 15 T + 1331 T^{2} \)
$13$ \( 1 - 20 T + 2197 T^{2} \)
$17$ \( 1 - 72 T + 4913 T^{2} \)
$19$ \( 1 - 2 T + 6859 T^{2} \)
$23$ \( 1 - 114 T + 12167 T^{2} \)
$29$ \( 1 - 30 T + 24389 T^{2} \)
$31$ \( 1 - 101 T + 29791 T^{2} \)
$37$ \( 1 + 430 T + 50653 T^{2} \)
$41$ \( 1 + 30 T + 68921 T^{2} \)
$43$ \( 1 - 110 T + 79507 T^{2} \)
$47$ \( 1 + 330 T + 103823 T^{2} \)
$53$ \( 1 - 621 T + 148877 T^{2} \)
$59$ \( 1 + 660 T + 205379 T^{2} \)
$61$ \( 1 + 376 T + 226981 T^{2} \)
$67$ \( 1 + 250 T + 300763 T^{2} \)
$71$ \( 1 + 360 T + 357911 T^{2} \)
$73$ \( 1 - 785 T + 389017 T^{2} \)
$79$ \( 1 - 488 T + 493039 T^{2} \)
$83$ \( 1 - 489 T + 571787 T^{2} \)
$89$ \( 1 + 450 T + 704969 T^{2} \)
$97$ \( 1 + 1105 T + 912673 T^{2} \)
show more
show less