Properties

Label 3146.2.a.n
Level $3146$
Weight $2$
Character orbit 3146.a
Self dual yes
Analytic conductor $25.121$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 3146 = 2 \cdot 11^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3146.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(25.1209364759\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 26)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q + q^{2} + q^{3} + q^{4} - 3 q^{5} + q^{6} + q^{7} + q^{8} - 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( q + q^{2} + q^{3} + q^{4} - 3 q^{5} + q^{6} + q^{7} + q^{8} - 2 q^{9} - 3 q^{10} + q^{12} - q^{13} + q^{14} - 3 q^{15} + q^{16} + 3 q^{17} - 2 q^{18} - 2 q^{19} - 3 q^{20} + q^{21} + q^{24} + 4 q^{25} - q^{26} - 5 q^{27} + q^{28} - 6 q^{29} - 3 q^{30} - 4 q^{31} + q^{32} + 3 q^{34} - 3 q^{35} - 2 q^{36} - 7 q^{37} - 2 q^{38} - q^{39} - 3 q^{40} + q^{42} + q^{43} + 6 q^{45} + 3 q^{47} + q^{48} - 6 q^{49} + 4 q^{50} + 3 q^{51} - q^{52} - 5 q^{54} + q^{56} - 2 q^{57} - 6 q^{58} - 6 q^{59} - 3 q^{60} - 8 q^{61} - 4 q^{62} - 2 q^{63} + q^{64} + 3 q^{65} + 14 q^{67} + 3 q^{68} - 3 q^{70} - 3 q^{71} - 2 q^{72} - 2 q^{73} - 7 q^{74} + 4 q^{75} - 2 q^{76} - q^{78} - 8 q^{79} - 3 q^{80} + q^{81} - 12 q^{83} + q^{84} - 9 q^{85} + q^{86} - 6 q^{87} - 6 q^{89} + 6 q^{90} - q^{91} - 4 q^{93} + 3 q^{94} + 6 q^{95} + q^{96} - 10 q^{97} - 6 q^{98}+O(q^{100}) \) 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
1.00000 1.00000 1.00000 −3.00000 1.00000 1.00000 1.00000 −2.00000 −3.00000
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(2\) \(-1\)
\(11\) \(-1\)
\(13\) \(1\)

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 3146.2.a.n 1
11.b odd 2 1 26.2.a.a 1
33.d even 2 1 234.2.a.e 1
44.c even 2 1 208.2.a.a 1
55.d odd 2 1 650.2.a.j 1
55.e even 4 2 650.2.b.d 2
77.b even 2 1 1274.2.a.d 1
77.h odd 6 2 1274.2.f.p 2
77.i even 6 2 1274.2.f.r 2
88.b odd 2 1 832.2.a.d 1
88.g even 2 1 832.2.a.i 1
99.g even 6 2 2106.2.e.b 2
99.h odd 6 2 2106.2.e.ba 2
132.d odd 2 1 1872.2.a.q 1
143.d odd 2 1 338.2.a.f 1
143.g even 4 2 338.2.b.c 2
143.i odd 6 2 338.2.c.a 2
143.k odd 6 2 338.2.c.d 2
143.o even 12 4 338.2.e.a 4
165.d even 2 1 5850.2.a.p 1
165.l odd 4 2 5850.2.e.a 2
176.i even 4 2 3328.2.b.j 2
176.l odd 4 2 3328.2.b.m 2
187.b odd 2 1 7514.2.a.c 1
209.d even 2 1 9386.2.a.j 1
220.g even 2 1 5200.2.a.x 1
264.m even 2 1 7488.2.a.g 1
264.p odd 2 1 7488.2.a.h 1
429.e even 2 1 3042.2.a.a 1
429.l odd 4 2 3042.2.b.a 2
572.b even 2 1 2704.2.a.f 1
572.k odd 4 2 2704.2.f.d 2
715.c odd 2 1 8450.2.a.c 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
26.2.a.a 1 11.b odd 2 1
208.2.a.a 1 44.c even 2 1
234.2.a.e 1 33.d even 2 1
338.2.a.f 1 143.d odd 2 1
338.2.b.c 2 143.g even 4 2
338.2.c.a 2 143.i odd 6 2
338.2.c.d 2 143.k odd 6 2
338.2.e.a 4 143.o even 12 4
650.2.a.j 1 55.d odd 2 1
650.2.b.d 2 55.e even 4 2
832.2.a.d 1 88.b odd 2 1
832.2.a.i 1 88.g even 2 1
1274.2.a.d 1 77.b even 2 1
1274.2.f.p 2 77.h odd 6 2
1274.2.f.r 2 77.i even 6 2
1872.2.a.q 1 132.d odd 2 1
2106.2.e.b 2 99.g even 6 2
2106.2.e.ba 2 99.h odd 6 2
2704.2.a.f 1 572.b even 2 1
2704.2.f.d 2 572.k odd 4 2
3042.2.a.a 1 429.e even 2 1
3042.2.b.a 2 429.l odd 4 2
3146.2.a.n 1 1.a even 1 1 trivial
3328.2.b.j 2 176.i even 4 2
3328.2.b.m 2 176.l odd 4 2
5200.2.a.x 1 220.g even 2 1
5850.2.a.p 1 165.d even 2 1
5850.2.e.a 2 165.l odd 4 2
7488.2.a.g 1 264.m even 2 1
7488.2.a.h 1 264.p odd 2 1
7514.2.a.c 1 187.b odd 2 1
8450.2.a.c 1 715.c odd 2 1
9386.2.a.j 1 209.d even 2 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(3146))\):

\( T_{3} - 1 \) Copy content Toggle raw display
\( T_{5} + 3 \) Copy content Toggle raw display
\( T_{7} - 1 \) Copy content Toggle raw display
\( T_{19} + 2 \) Copy content Toggle raw display

Hecke characteristic polynomials

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