Properties

Label 153.2.a.b
Level 153
Weight 2
Character orbit 153.a
Self dual yes
Analytic conductor 1.222
Analytic rank 1
Dimension 1
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 153 = 3^{2} \cdot 17 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 153.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(1.22171115093\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 51)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q - 2q^{4} - 3q^{5} - 4q^{7} + O(q^{10}) \) \( q - 2q^{4} - 3q^{5} - 4q^{7} + 3q^{11} - q^{13} + 4q^{16} + q^{17} - q^{19} + 6q^{20} - 9q^{23} + 4q^{25} + 8q^{28} - 6q^{29} + 2q^{31} + 12q^{35} - 4q^{37} + 3q^{41} - 7q^{43} - 6q^{44} + 6q^{47} + 9q^{49} + 2q^{52} + 6q^{53} - 9q^{55} - 6q^{59} + 8q^{61} - 8q^{64} + 3q^{65} - 4q^{67} - 2q^{68} - 12q^{71} + 2q^{73} + 2q^{76} - 12q^{77} - 10q^{79} - 12q^{80} + 6q^{83} - 3q^{85} + 4q^{91} + 18q^{92} + 3q^{95} - 16q^{97} + O(q^{100}) \)

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 0 −2.00000 −3.00000 0 −4.00000 0 0 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 153.2.a.b 1
3.b odd 2 1 51.2.a.a 1
4.b odd 2 1 2448.2.a.c 1
5.b even 2 1 3825.2.a.i 1
7.b odd 2 1 7497.2.a.j 1
8.b even 2 1 9792.2.a.by 1
8.d odd 2 1 9792.2.a.cd 1
12.b even 2 1 816.2.a.g 1
15.d odd 2 1 1275.2.a.d 1
15.e even 4 2 1275.2.b.b 2
17.b even 2 1 2601.2.a.f 1
21.c even 2 1 2499.2.a.d 1
24.f even 2 1 3264.2.a.r 1
24.h odd 2 1 3264.2.a.a 1
33.d even 2 1 6171.2.a.e 1
39.d odd 2 1 8619.2.a.g 1
51.c odd 2 1 867.2.a.c 1
51.f odd 4 2 867.2.d.a 2
51.g odd 8 4 867.2.e.e 4
51.i even 16 8 867.2.h.c 8
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
51.2.a.a 1 3.b odd 2 1
153.2.a.b 1 1.a even 1 1 trivial
816.2.a.g 1 12.b even 2 1
867.2.a.c 1 51.c odd 2 1
867.2.d.a 2 51.f odd 4 2
867.2.e.e 4 51.g odd 8 4
867.2.h.c 8 51.i even 16 8
1275.2.a.d 1 15.d odd 2 1
1275.2.b.b 2 15.e even 4 2
2448.2.a.c 1 4.b odd 2 1
2499.2.a.d 1 21.c even 2 1
2601.2.a.f 1 17.b even 2 1
3264.2.a.a 1 24.h odd 2 1
3264.2.a.r 1 24.f even 2 1
3825.2.a.i 1 5.b even 2 1
6171.2.a.e 1 33.d even 2 1
7497.2.a.j 1 7.b odd 2 1
8619.2.a.g 1 39.d odd 2 1
9792.2.a.by 1 8.b even 2 1
9792.2.a.cd 1 8.d odd 2 1

Atkin-Lehner signs

\( p \) Sign
\(3\) \(-1\)
\(17\) \(-1\)

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2} \) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(153))\).