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Properties

Label 175.2.a.a
Level $175$
Weight $2$
Character orbit 175.a
Self dual yes
Analytic conductor $1.397$
Analytic rank $1$
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: \(1\)
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

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

Display 100 coefficients 10 coefficients

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.a 1
3.b odd 2 1 1575.2.a.k 1
4.b odd 2 1 2800.2.a.w 1
5.b even 2 1 175.2.a.c 1
5.c odd 4 2 35.2.b.a ✓ 2
7.b odd 2 1 1225.2.a.a 1
15.d odd 2 1 1575.2.a.a 1
15.e even 4 2 315.2.d.a 2
20.d odd 2 1 2800.2.a.l 1
20.e even 4 2 560.2.g.b 2
35.c odd 2 1 1225.2.a.i 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 1.a even 1 1 trivial
175.2.a.c 1 5.b even 2 1
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 7.b odd 2 1
1225.2.a.i 1 35.c odd 2 1
1575.2.a.a 1 15.d odd 2 1
1575.2.a.k 1 3.b 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 20.d odd 2 1
2800.2.a.w 1 4.b 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 \(S_{2}^{\mathrm{new}}(\Gamma_0(175))\).

Hecke characteristic polynomials

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