Properties

Label 18.6.a.c
Level $18$
Weight $6$
Character orbit 18.a
Self dual yes
Analytic conductor $2.887$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 18 = 2 \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 18.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(2.88690875663\)
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

\(f(q)\) \(=\) \( q + 4 q^{2} + 16 q^{4} + 96 q^{5} - 148 q^{7} + 64 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( q + 4 q^{2} + 16 q^{4} + 96 q^{5} - 148 q^{7} + 64 q^{8} + 384 q^{10} - 384 q^{11} - 334 q^{13} - 592 q^{14} + 256 q^{16} - 576 q^{17} - 664 q^{19} + 1536 q^{20} - 1536 q^{22} + 3840 q^{23} + 6091 q^{25} - 1336 q^{26} - 2368 q^{28} - 96 q^{29} - 4564 q^{31} + 1024 q^{32} - 2304 q^{34} - 14208 q^{35} + 5798 q^{37} - 2656 q^{38} + 6144 q^{40} + 6720 q^{41} - 14872 q^{43} - 6144 q^{44} + 15360 q^{46} + 19200 q^{47} + 5097 q^{49} + 24364 q^{50} - 5344 q^{52} - 7776 q^{53} - 36864 q^{55} - 9472 q^{56} - 384 q^{58} + 13056 q^{59} + 42782 q^{61} - 18256 q^{62} + 4096 q^{64} - 32064 q^{65} + 36656 q^{67} - 9216 q^{68} - 56832 q^{70} - 64512 q^{71} - 16810 q^{73} + 23192 q^{74} - 10624 q^{76} + 56832 q^{77} + 28076 q^{79} + 24576 q^{80} + 26880 q^{82} + 66432 q^{83} - 55296 q^{85} - 59488 q^{86} - 24576 q^{88} + 81792 q^{89} + 49432 q^{91} + 61440 q^{92} + 76800 q^{94} - 63744 q^{95} - 29938 q^{97} + 20388 q^{98}+O(q^{100}) \) Copy content Toggle raw display

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
4.00000 0 16.0000 96.0000 0 −148.000 64.0000 0 384.000
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(2\) \(-1\)
\(3\) \(1\)

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 18.6.a.c yes 1
3.b odd 2 1 18.6.a.a 1
4.b odd 2 1 144.6.a.l 1
5.b even 2 1 450.6.a.k 1
5.c odd 4 2 450.6.c.c 2
7.b odd 2 1 882.6.a.l 1
8.b even 2 1 576.6.a.a 1
8.d odd 2 1 576.6.a.b 1
9.c even 3 2 162.6.c.a 2
9.d odd 6 2 162.6.c.l 2
12.b even 2 1 144.6.a.a 1
15.d odd 2 1 450.6.a.v 1
15.e even 4 2 450.6.c.m 2
21.c even 2 1 882.6.a.k 1
24.f even 2 1 576.6.a.bi 1
24.h odd 2 1 576.6.a.bh 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
18.6.a.a 1 3.b odd 2 1
18.6.a.c yes 1 1.a even 1 1 trivial
144.6.a.a 1 12.b even 2 1
144.6.a.l 1 4.b odd 2 1
162.6.c.a 2 9.c even 3 2
162.6.c.l 2 9.d odd 6 2
450.6.a.k 1 5.b even 2 1
450.6.a.v 1 15.d odd 2 1
450.6.c.c 2 5.c odd 4 2
450.6.c.m 2 15.e even 4 2
576.6.a.a 1 8.b even 2 1
576.6.a.b 1 8.d odd 2 1
576.6.a.bh 1 24.h odd 2 1
576.6.a.bi 1 24.f even 2 1
882.6.a.k 1 21.c even 2 1
882.6.a.l 1 7.b odd 2 1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{5} - 96 \) acting on \(S_{6}^{\mathrm{new}}(\Gamma_0(18))\). Copy content Toggle raw display

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( T - 4 \) Copy content Toggle raw display
$3$ \( T \) Copy content Toggle raw display
$5$ \( T - 96 \) Copy content Toggle raw display
$7$ \( T + 148 \) Copy content Toggle raw display
$11$ \( T + 384 \) Copy content Toggle raw display
$13$ \( T + 334 \) Copy content Toggle raw display
$17$ \( T + 576 \) Copy content Toggle raw display
$19$ \( T + 664 \) Copy content Toggle raw display
$23$ \( T - 3840 \) Copy content Toggle raw display
$29$ \( T + 96 \) Copy content Toggle raw display
$31$ \( T + 4564 \) Copy content Toggle raw display
$37$ \( T - 5798 \) Copy content Toggle raw display
$41$ \( T - 6720 \) Copy content Toggle raw display
$43$ \( T + 14872 \) Copy content Toggle raw display
$47$ \( T - 19200 \) Copy content Toggle raw display
$53$ \( T + 7776 \) Copy content Toggle raw display
$59$ \( T - 13056 \) Copy content Toggle raw display
$61$ \( T - 42782 \) Copy content Toggle raw display
$67$ \( T - 36656 \) Copy content Toggle raw display
$71$ \( T + 64512 \) Copy content Toggle raw display
$73$ \( T + 16810 \) Copy content Toggle raw display
$79$ \( T - 28076 \) Copy content Toggle raw display
$83$ \( T - 66432 \) Copy content Toggle raw display
$89$ \( T - 81792 \) Copy content Toggle raw display
$97$ \( T + 29938 \) Copy content Toggle raw display
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