Properties

Label 1452.2.a.f
Level 1452
Weight 2
Character orbit 1452.a
Self dual yes
Analytic conductor 11.594
Analytic rank 0
Dimension 1
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 1452 = 2^{2} \cdot 3 \cdot 11^{2} \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 1452.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(11.5942783735\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 132)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q + q^{3} + 2q^{5} + 2q^{7} + q^{9} + O(q^{10}) \) \( q + q^{3} + 2q^{5} + 2q^{7} + q^{9} + 2q^{13} + 2q^{15} - 4q^{17} + 6q^{19} + 2q^{21} - q^{25} + q^{27} + 8q^{29} - 8q^{31} + 4q^{35} + 10q^{37} + 2q^{39} - 8q^{41} + 2q^{43} + 2q^{45} - 8q^{47} - 3q^{49} - 4q^{51} - 2q^{53} + 6q^{57} + 12q^{59} - 10q^{61} + 2q^{63} + 4q^{65} + 12q^{67} + 8q^{71} - 6q^{73} - q^{75} + 2q^{79} + q^{81} - 16q^{83} - 8q^{85} + 8q^{87} - 14q^{89} + 4q^{91} - 8q^{93} + 12q^{95} - 2q^{97} + O(q^{100}) \)

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
0 1.00000 0 2.00000 0 2.00000 0 1.00000 0
\(n\): 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 1452.2.a.f 1
3.b odd 2 1 4356.2.a.d 1
4.b odd 2 1 5808.2.a.m 1
11.b odd 2 1 132.2.a.b 1
11.c even 5 4 1452.2.i.d 4
11.d odd 10 4 1452.2.i.e 4
33.d even 2 1 396.2.a.a 1
44.c even 2 1 528.2.a.e 1
55.d odd 2 1 3300.2.a.f 1
55.e even 4 2 3300.2.c.j 2
77.b even 2 1 6468.2.a.b 1
88.b odd 2 1 2112.2.a.c 1
88.g even 2 1 2112.2.a.u 1
99.g even 6 2 3564.2.i.i 2
99.h odd 6 2 3564.2.i.d 2
132.d odd 2 1 1584.2.a.e 1
165.d even 2 1 9900.2.a.w 1
165.l odd 4 2 9900.2.c.f 2
264.m even 2 1 6336.2.a.ca 1
264.p odd 2 1 6336.2.a.cg 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
132.2.a.b 1 11.b odd 2 1
396.2.a.a 1 33.d even 2 1
528.2.a.e 1 44.c even 2 1
1452.2.a.f 1 1.a even 1 1 trivial
1452.2.i.d 4 11.c even 5 4
1452.2.i.e 4 11.d odd 10 4
1584.2.a.e 1 132.d odd 2 1
2112.2.a.c 1 88.b odd 2 1
2112.2.a.u 1 88.g even 2 1
3300.2.a.f 1 55.d odd 2 1
3300.2.c.j 2 55.e even 4 2
3564.2.i.d 2 99.h odd 6 2
3564.2.i.i 2 99.g even 6 2
4356.2.a.d 1 3.b odd 2 1
5808.2.a.m 1 4.b odd 2 1
6336.2.a.ca 1 264.m even 2 1
6336.2.a.cg 1 264.p odd 2 1
6468.2.a.b 1 77.b even 2 1
9900.2.a.w 1 165.d even 2 1
9900.2.c.f 2 165.l odd 4 2

Atkin-Lehner signs

\( p \) Sign
\(2\) \(-1\)
\(3\) \(-1\)
\(11\) \(-1\)

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(1452))\):

\( T_{5} - 2 \)
\( T_{7} - 2 \)

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ \( \)
$3$ \( 1 - T \)
$5$ \( 1 - 2 T + 5 T^{2} \)
$7$ \( 1 - 2 T + 7 T^{2} \)
$11$ \( \)
$13$ \( 1 - 2 T + 13 T^{2} \)
$17$ \( 1 + 4 T + 17 T^{2} \)
$19$ \( 1 - 6 T + 19 T^{2} \)
$23$ \( 1 + 23 T^{2} \)
$29$ \( 1 - 8 T + 29 T^{2} \)
$31$ \( 1 + 8 T + 31 T^{2} \)
$37$ \( 1 - 10 T + 37 T^{2} \)
$41$ \( 1 + 8 T + 41 T^{2} \)
$43$ \( 1 - 2 T + 43 T^{2} \)
$47$ \( 1 + 8 T + 47 T^{2} \)
$53$ \( 1 + 2 T + 53 T^{2} \)
$59$ \( 1 - 12 T + 59 T^{2} \)
$61$ \( 1 + 10 T + 61 T^{2} \)
$67$ \( 1 - 12 T + 67 T^{2} \)
$71$ \( 1 - 8 T + 71 T^{2} \)
$73$ \( 1 + 6 T + 73 T^{2} \)
$79$ \( 1 - 2 T + 79 T^{2} \)
$83$ \( 1 + 16 T + 83 T^{2} \)
$89$ \( 1 + 14 T + 89 T^{2} \)
$97$ \( 1 + 2 T + 97 T^{2} \)
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