Properties

Label 153.2.a.c
Level $153$
Weight $2$
Character orbit 153.a
Self dual yes
Analytic conductor $1.222$
Analytic rank $0$
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: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 17)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q + q^{2} - q^{4} + 2 q^{5} + 4 q^{7} - 3 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( q + q^{2} - q^{4} + 2 q^{5} + 4 q^{7} - 3 q^{8} + 2 q^{10} - 2 q^{13} + 4 q^{14} - q^{16} - q^{17} - 4 q^{19} - 2 q^{20} - 4 q^{23} - q^{25} - 2 q^{26} - 4 q^{28} - 6 q^{29} + 4 q^{31} + 5 q^{32} - q^{34} + 8 q^{35} - 2 q^{37} - 4 q^{38} - 6 q^{40} + 6 q^{41} + 4 q^{43} - 4 q^{46} + 9 q^{49} - q^{50} + 2 q^{52} - 6 q^{53} - 12 q^{56} - 6 q^{58} + 12 q^{59} - 10 q^{61} + 4 q^{62} + 7 q^{64} - 4 q^{65} + 4 q^{67} + q^{68} + 8 q^{70} + 4 q^{71} - 6 q^{73} - 2 q^{74} + 4 q^{76} + 12 q^{79} - 2 q^{80} + 6 q^{82} + 4 q^{83} - 2 q^{85} + 4 q^{86} - 10 q^{89} - 8 q^{91} + 4 q^{92} - 8 q^{95} + 2 q^{97} + 9 q^{98}+O(q^{100}) \) 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 0 −1.00000 2.00000 0 4.00000 −3.00000 0 2.00000
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

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

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 153.2.a.c 1
3.b odd 2 1 17.2.a.a 1
4.b odd 2 1 2448.2.a.o 1
5.b even 2 1 3825.2.a.d 1
7.b odd 2 1 7497.2.a.l 1
8.b even 2 1 9792.2.a.n 1
8.d odd 2 1 9792.2.a.i 1
12.b even 2 1 272.2.a.b 1
15.d odd 2 1 425.2.a.d 1
15.e even 4 2 425.2.b.b 2
17.b even 2 1 2601.2.a.g 1
21.c even 2 1 833.2.a.a 1
21.g even 6 2 833.2.e.a 2
21.h odd 6 2 833.2.e.b 2
24.f even 2 1 1088.2.a.h 1
24.h odd 2 1 1088.2.a.i 1
33.d even 2 1 2057.2.a.e 1
39.d odd 2 1 2873.2.a.c 1
51.c odd 2 1 289.2.a.a 1
51.f odd 4 2 289.2.b.a 2
51.g odd 8 4 289.2.c.a 4
51.i even 16 8 289.2.d.d 8
57.d even 2 1 6137.2.a.b 1
60.h even 2 1 6800.2.a.n 1
69.c even 2 1 8993.2.a.a 1
204.h even 2 1 4624.2.a.d 1
255.h odd 2 1 7225.2.a.g 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
17.2.a.a 1 3.b odd 2 1
153.2.a.c 1 1.a even 1 1 trivial
272.2.a.b 1 12.b even 2 1
289.2.a.a 1 51.c odd 2 1
289.2.b.a 2 51.f odd 4 2
289.2.c.a 4 51.g odd 8 4
289.2.d.d 8 51.i even 16 8
425.2.a.d 1 15.d odd 2 1
425.2.b.b 2 15.e even 4 2
833.2.a.a 1 21.c even 2 1
833.2.e.a 2 21.g even 6 2
833.2.e.b 2 21.h odd 6 2
1088.2.a.h 1 24.f even 2 1
1088.2.a.i 1 24.h odd 2 1
2057.2.a.e 1 33.d even 2 1
2448.2.a.o 1 4.b odd 2 1
2601.2.a.g 1 17.b even 2 1
2873.2.a.c 1 39.d odd 2 1
3825.2.a.d 1 5.b even 2 1
4624.2.a.d 1 204.h even 2 1
6137.2.a.b 1 57.d even 2 1
6800.2.a.n 1 60.h even 2 1
7225.2.a.g 1 255.h odd 2 1
7497.2.a.l 1 7.b odd 2 1
8993.2.a.a 1 69.c even 2 1
9792.2.a.i 1 8.d odd 2 1
9792.2.a.n 1 8.b even 2 1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2} - 1 \) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(153))\). Copy content Toggle raw display

Hecke characteristic polynomials

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