Properties

Label 2075.2.a.d
Level $2075$
Weight $2$
Character orbit 2075.a
Self dual yes
Analytic conductor $16.569$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 2075 = 5^{2} \cdot 83 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2075.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(16.5689584194\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 83)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q + q^{2} + q^{3} - q^{4} + q^{6} + 3 q^{7} - 3 q^{8} - 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( q + q^{2} + q^{3} - q^{4} + q^{6} + 3 q^{7} - 3 q^{8} - 2 q^{9} + 3 q^{11} - q^{12} + 6 q^{13} + 3 q^{14} - q^{16} - 5 q^{17} - 2 q^{18} + 2 q^{19} + 3 q^{21} + 3 q^{22} + 4 q^{23} - 3 q^{24} + 6 q^{26} - 5 q^{27} - 3 q^{28} - 7 q^{29} + 5 q^{31} + 5 q^{32} + 3 q^{33} - 5 q^{34} + 2 q^{36} + 11 q^{37} + 2 q^{38} + 6 q^{39} - 2 q^{41} + 3 q^{42} + 8 q^{43} - 3 q^{44} + 4 q^{46} - q^{48} + 2 q^{49} - 5 q^{51} - 6 q^{52} - 6 q^{53} - 5 q^{54} - 9 q^{56} + 2 q^{57} - 7 q^{58} + 5 q^{59} + 5 q^{61} + 5 q^{62} - 6 q^{63} + 7 q^{64} + 3 q^{66} + 2 q^{67} + 5 q^{68} + 4 q^{69} + 2 q^{71} + 6 q^{72} + 11 q^{74} - 2 q^{76} + 9 q^{77} + 6 q^{78} + 14 q^{79} + q^{81} - 2 q^{82} + q^{83} - 3 q^{84} + 8 q^{86} - 7 q^{87} - 9 q^{88} + 18 q^{91} - 4 q^{92} + 5 q^{93} + 5 q^{96} + 8 q^{97} + 2 q^{98} - 6 q^{99}+O(q^{100}) \) 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
1.00000 1.00000 −1.00000 0 1.00000 3.00000 −3.00000 −2.00000 0
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(5\) \(1\)
\(83\) \(-1\)

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 2075.2.a.d 1
5.b even 2 1 83.2.a.a 1
15.d odd 2 1 747.2.a.d 1
20.d odd 2 1 1328.2.a.c 1
35.c odd 2 1 4067.2.a.a 1
40.e odd 2 1 5312.2.a.h 1
40.f even 2 1 5312.2.a.l 1
415.d odd 2 1 6889.2.a.a 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
83.2.a.a 1 5.b even 2 1
747.2.a.d 1 15.d odd 2 1
1328.2.a.c 1 20.d odd 2 1
2075.2.a.d 1 1.a even 1 1 trivial
4067.2.a.a 1 35.c odd 2 1
5312.2.a.h 1 40.e odd 2 1
5312.2.a.l 1 40.f even 2 1
6889.2.a.a 1 415.d odd 2 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(2075))\):

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