Properties

Label 175.2.a.c
Level $175$
Weight $2$
Character orbit 175.a
Self dual yes
Analytic conductor $1.397$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 175 = 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 175.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(1.39738203537\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 35)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q + 2 q^{2} + q^{3} + 2 q^{4} + 2 q^{6} - q^{7} - 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( q + 2 q^{2} + q^{3} + 2 q^{4} + 2 q^{6} - q^{7} - 2 q^{9} - 3 q^{11} + 2 q^{12} + q^{13} - 2 q^{14} - 4 q^{16} + 7 q^{17} - 4 q^{18} - q^{21} - 6 q^{22} + 6 q^{23} + 2 q^{26} - 5 q^{27} - 2 q^{28} - 5 q^{29} + 2 q^{31} - 8 q^{32} - 3 q^{33} + 14 q^{34} - 4 q^{36} + 2 q^{37} + q^{39} + 2 q^{41} - 2 q^{42} - 4 q^{43} - 6 q^{44} + 12 q^{46} - 3 q^{47} - 4 q^{48} + q^{49} + 7 q^{51} + 2 q^{52} + 6 q^{53} - 10 q^{54} - 10 q^{58} + 10 q^{59} - 8 q^{61} + 4 q^{62} + 2 q^{63} - 8 q^{64} - 6 q^{66} + 2 q^{67} + 14 q^{68} + 6 q^{69} - 8 q^{71} + 6 q^{73} + 4 q^{74} + 3 q^{77} + 2 q^{78} - 5 q^{79} + q^{81} + 4 q^{82} - 4 q^{83} - 2 q^{84} - 8 q^{86} - 5 q^{87} - q^{91} + 12 q^{92} + 2 q^{93} - 6 q^{94} - 8 q^{96} + 7 q^{97} + 2 q^{98} + 6 q^{99}+O(q^{100}) \) 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
2.00000 1.00000 2.00000 0 2.00000 −1.00000 0 −2.00000 0
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(5\) \(-1\)
\(7\) \(1\)

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 175.2.a.c 1
3.b odd 2 1 1575.2.a.a 1
4.b odd 2 1 2800.2.a.l 1
5.b even 2 1 175.2.a.a 1
5.c odd 4 2 35.2.b.a 2
7.b odd 2 1 1225.2.a.i 1
15.d odd 2 1 1575.2.a.k 1
15.e even 4 2 315.2.d.a 2
20.d odd 2 1 2800.2.a.w 1
20.e even 4 2 560.2.g.b 2
35.c odd 2 1 1225.2.a.a 1
35.f even 4 2 245.2.b.a 2
35.k even 12 4 245.2.j.d 4
35.l odd 12 4 245.2.j.e 4
40.i odd 4 2 2240.2.g.h 2
40.k even 4 2 2240.2.g.g 2
60.l odd 4 2 5040.2.t.p 2
105.k odd 4 2 2205.2.d.b 2
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
35.2.b.a 2 5.c odd 4 2
175.2.a.a 1 5.b even 2 1
175.2.a.c 1 1.a even 1 1 trivial
245.2.b.a 2 35.f even 4 2
245.2.j.d 4 35.k even 12 4
245.2.j.e 4 35.l odd 12 4
315.2.d.a 2 15.e even 4 2
560.2.g.b 2 20.e even 4 2
1225.2.a.a 1 35.c odd 2 1
1225.2.a.i 1 7.b odd 2 1
1575.2.a.a 1 3.b odd 2 1
1575.2.a.k 1 15.d odd 2 1
2205.2.d.b 2 105.k odd 4 2
2240.2.g.g 2 40.k even 4 2
2240.2.g.h 2 40.i odd 4 2
2800.2.a.l 1 4.b odd 2 1
2800.2.a.w 1 20.d odd 2 1
5040.2.t.p 2 60.l odd 4 2

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2} - 2 \) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(175))\). Copy content Toggle raw display

Hecke characteristic polynomials

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