Properties

Label 3267.2.a.f
Level $3267$
Weight $2$
Character orbit 3267.a
Self dual yes
Analytic conductor $26.087$
Analytic rank $1$
Dimension $1$
CM discriminant -3
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 3267 = 3^{3} \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3267.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(26.0871263404\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 27)
Fricke sign: \(1\)
Sato-Tate group: $N(\mathrm{U}(1))$

$q$-expansion

\(f(q)\) \(=\) \( q - 2 q^{4} + q^{7}+O(q^{10}) \) Copy content Toggle raw display \( q - 2 q^{4} + q^{7} - 5 q^{13} + 4 q^{16} + 7 q^{19} - 5 q^{25} - 2 q^{28} - 4 q^{31} + 11 q^{37} - 8 q^{43} - 6 q^{49} + 10 q^{52} + q^{61} - 8 q^{64} + 5 q^{67} + 7 q^{73} - 14 q^{76} - 17 q^{79} - 5 q^{91} - 19 q^{97}+O(q^{100}) \) 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
0 0 −2.00000 0 0 1.00000 0 0 0
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(3\) \(-1\)
\(11\) \(-1\)

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
3.b odd 2 1 CM by \(\Q(\sqrt{-3}) \)

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 3267.2.a.f 1
3.b odd 2 1 CM 3267.2.a.f 1
11.b odd 2 1 27.2.a.a 1
33.d even 2 1 27.2.a.a 1
44.c even 2 1 432.2.a.e 1
55.d odd 2 1 675.2.a.e 1
55.e even 4 2 675.2.b.f 2
77.b even 2 1 1323.2.a.i 1
88.b odd 2 1 1728.2.a.n 1
88.g even 2 1 1728.2.a.o 1
99.g even 6 2 81.2.c.a 2
99.h odd 6 2 81.2.c.a 2
132.d odd 2 1 432.2.a.e 1
143.d odd 2 1 4563.2.a.e 1
165.d even 2 1 675.2.a.e 1
165.l odd 4 2 675.2.b.f 2
187.b odd 2 1 7803.2.a.k 1
209.d even 2 1 9747.2.a.f 1
231.h odd 2 1 1323.2.a.i 1
264.m even 2 1 1728.2.a.n 1
264.p odd 2 1 1728.2.a.o 1
297.o even 18 6 729.2.e.f 6
297.q odd 18 6 729.2.e.f 6
396.k even 6 2 1296.2.i.i 2
396.o odd 6 2 1296.2.i.i 2
429.e even 2 1 4563.2.a.e 1
561.h even 2 1 7803.2.a.k 1
627.b odd 2 1 9747.2.a.f 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
27.2.a.a 1 11.b odd 2 1
27.2.a.a 1 33.d even 2 1
81.2.c.a 2 99.g even 6 2
81.2.c.a 2 99.h odd 6 2
432.2.a.e 1 44.c even 2 1
432.2.a.e 1 132.d odd 2 1
675.2.a.e 1 55.d odd 2 1
675.2.a.e 1 165.d even 2 1
675.2.b.f 2 55.e even 4 2
675.2.b.f 2 165.l odd 4 2
729.2.e.f 6 297.o even 18 6
729.2.e.f 6 297.q odd 18 6
1296.2.i.i 2 396.k even 6 2
1296.2.i.i 2 396.o odd 6 2
1323.2.a.i 1 77.b even 2 1
1323.2.a.i 1 231.h odd 2 1
1728.2.a.n 1 88.b odd 2 1
1728.2.a.n 1 264.m even 2 1
1728.2.a.o 1 88.g even 2 1
1728.2.a.o 1 264.p odd 2 1
3267.2.a.f 1 1.a even 1 1 trivial
3267.2.a.f 1 3.b odd 2 1 CM
4563.2.a.e 1 143.d odd 2 1
4563.2.a.e 1 429.e even 2 1
7803.2.a.k 1 187.b odd 2 1
7803.2.a.k 1 561.h even 2 1
9747.2.a.f 1 209.d even 2 1
9747.2.a.f 1 627.b odd 2 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(3267))\):

\( T_{2} \) Copy content Toggle raw display
\( T_{5} \) Copy content Toggle raw display
\( T_{7} - 1 \) Copy content Toggle raw display
\( T_{23} \) Copy content Toggle raw display

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( T \) Copy content Toggle raw display
$3$ \( T \) Copy content Toggle raw display
$5$ \( T \) Copy content Toggle raw display
$7$ \( T - 1 \) Copy content Toggle raw display
$11$ \( T \) Copy content Toggle raw display
$13$ \( T + 5 \) Copy content Toggle raw display
$17$ \( T \) Copy content Toggle raw display
$19$ \( T - 7 \) Copy content Toggle raw display
$23$ \( T \) Copy content Toggle raw display
$29$ \( T \) Copy content Toggle raw display
$31$ \( T + 4 \) Copy content Toggle raw display
$37$ \( T - 11 \) Copy content Toggle raw display
$41$ \( T \) Copy content Toggle raw display
$43$ \( T + 8 \) Copy content Toggle raw display
$47$ \( T \) Copy content Toggle raw display
$53$ \( T \) Copy content Toggle raw display
$59$ \( T \) Copy content Toggle raw display
$61$ \( T - 1 \) Copy content Toggle raw display
$67$ \( T - 5 \) Copy content Toggle raw display
$71$ \( T \) Copy content Toggle raw display
$73$ \( T - 7 \) Copy content Toggle raw display
$79$ \( T + 17 \) Copy content Toggle raw display
$83$ \( T \) Copy content Toggle raw display
$89$ \( T \) Copy content Toggle raw display
$97$ \( T + 19 \) Copy content Toggle raw display
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