Properties

Label 1232.4.a.i
Level $1232$
Weight $4$
Character orbit 1232.a
Self dual yes
Analytic conductor $72.690$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1232 = 2^{4} \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1232.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(72.6903531271\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 154)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q + 10 q^{3} - 14 q^{5} - 7 q^{7} + 73 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( q + 10 q^{3} - 14 q^{5} - 7 q^{7} + 73 q^{9} + 11 q^{11} - 16 q^{13} - 140 q^{15} + 108 q^{17} - 116 q^{19} - 70 q^{21} - 68 q^{23} + 71 q^{25} + 460 q^{27} + 122 q^{29} + 262 q^{31} + 110 q^{33} + 98 q^{35} + 130 q^{37} - 160 q^{39} + 204 q^{41} + 396 q^{43} - 1022 q^{45} - 166 q^{47} + 49 q^{49} + 1080 q^{51} + 442 q^{53} - 154 q^{55} - 1160 q^{57} - 702 q^{59} + 196 q^{61} - 511 q^{63} + 224 q^{65} + 416 q^{67} - 680 q^{69} - 492 q^{71} + 408 q^{73} + 710 q^{75} - 77 q^{77} - 600 q^{79} + 2629 q^{81} + 1212 q^{83} - 1512 q^{85} + 1220 q^{87} + 1146 q^{89} + 112 q^{91} + 2620 q^{93} + 1624 q^{95} - 482 q^{97} + 803 q^{99}+O(q^{100}) \) 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 10.0000 0 −14.0000 0 −7.00000 0 73.0000 0
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(2\) \(-1\)
\(7\) \(1\)
\(11\) \(-1\)

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 1232.4.a.i 1
4.b odd 2 1 154.4.a.c 1
12.b even 2 1 1386.4.a.g 1
28.d even 2 1 1078.4.a.h 1
44.c even 2 1 1694.4.a.a 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
154.4.a.c 1 4.b odd 2 1
1078.4.a.h 1 28.d even 2 1
1232.4.a.i 1 1.a even 1 1 trivial
1386.4.a.g 1 12.b even 2 1
1694.4.a.a 1 44.c even 2 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(1232))\):

\( T_{3} - 10 \) Copy content Toggle raw display
\( T_{5} + 14 \) Copy content Toggle raw display

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( T \) Copy content Toggle raw display
$3$ \( T - 10 \) Copy content Toggle raw display
$5$ \( T + 14 \) Copy content Toggle raw display
$7$ \( T + 7 \) Copy content Toggle raw display
$11$ \( T - 11 \) Copy content Toggle raw display
$13$ \( T + 16 \) Copy content Toggle raw display
$17$ \( T - 108 \) Copy content Toggle raw display
$19$ \( T + 116 \) Copy content Toggle raw display
$23$ \( T + 68 \) Copy content Toggle raw display
$29$ \( T - 122 \) Copy content Toggle raw display
$31$ \( T - 262 \) Copy content Toggle raw display
$37$ \( T - 130 \) Copy content Toggle raw display
$41$ \( T - 204 \) Copy content Toggle raw display
$43$ \( T - 396 \) Copy content Toggle raw display
$47$ \( T + 166 \) Copy content Toggle raw display
$53$ \( T - 442 \) Copy content Toggle raw display
$59$ \( T + 702 \) Copy content Toggle raw display
$61$ \( T - 196 \) Copy content Toggle raw display
$67$ \( T - 416 \) Copy content Toggle raw display
$71$ \( T + 492 \) Copy content Toggle raw display
$73$ \( T - 408 \) Copy content Toggle raw display
$79$ \( T + 600 \) Copy content Toggle raw display
$83$ \( T - 1212 \) Copy content Toggle raw display
$89$ \( T - 1146 \) Copy content Toggle raw display
$97$ \( T + 482 \) Copy content Toggle raw display
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