Properties

Label 175.4.a.b
Level $175$
Weight $4$
Character orbit 175.a
Self dual yes
Analytic conductor $10.325$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 175 = 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 175.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(10.3253342510\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 7)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q + q^{2} + 2q^{3} - 7q^{4} + 2q^{6} + 7q^{7} - 15q^{8} - 23q^{9} + O(q^{10}) \) \( q + q^{2} + 2q^{3} - 7q^{4} + 2q^{6} + 7q^{7} - 15q^{8} - 23q^{9} - 8q^{11} - 14q^{12} - 28q^{13} + 7q^{14} + 41q^{16} - 54q^{17} - 23q^{18} - 110q^{19} + 14q^{21} - 8q^{22} - 48q^{23} - 30q^{24} - 28q^{26} - 100q^{27} - 49q^{28} - 110q^{29} + 12q^{31} + 161q^{32} - 16q^{33} - 54q^{34} + 161q^{36} + 246q^{37} - 110q^{38} - 56q^{39} + 182q^{41} + 14q^{42} - 128q^{43} + 56q^{44} - 48q^{46} - 324q^{47} + 82q^{48} + 49q^{49} - 108q^{51} + 196q^{52} + 162q^{53} - 100q^{54} - 105q^{56} - 220q^{57} - 110q^{58} + 810q^{59} - 488q^{61} + 12q^{62} - 161q^{63} - 167q^{64} - 16q^{66} - 244q^{67} + 378q^{68} - 96q^{69} - 768q^{71} + 345q^{72} + 702q^{73} + 246q^{74} + 770q^{76} - 56q^{77} - 56q^{78} + 440q^{79} + 421q^{81} + 182q^{82} + 1302q^{83} - 98q^{84} - 128q^{86} - 220q^{87} + 120q^{88} + 730q^{89} - 196q^{91} + 336q^{92} + 24q^{93} - 324q^{94} + 322q^{96} - 294q^{97} + 49q^{98} + 184q^{99} + O(q^{100}) \)

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 2.00000 −7.00000 0 2.00000 7.00000 −15.0000 −23.0000 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 175.4.a.b 1
3.b odd 2 1 1575.4.a.e 1
5.b even 2 1 7.4.a.a 1
5.c odd 4 2 175.4.b.b 2
7.b odd 2 1 1225.4.a.j 1
15.d odd 2 1 63.4.a.b 1
20.d odd 2 1 112.4.a.f 1
35.c odd 2 1 49.4.a.b 1
35.i odd 6 2 49.4.c.b 2
35.j even 6 2 49.4.c.c 2
40.e odd 2 1 448.4.a.e 1
40.f even 2 1 448.4.a.i 1
55.d odd 2 1 847.4.a.b 1
60.h even 2 1 1008.4.a.c 1
65.d even 2 1 1183.4.a.b 1
85.c even 2 1 2023.4.a.a 1
105.g even 2 1 441.4.a.i 1
105.o odd 6 2 441.4.e.h 2
105.p even 6 2 441.4.e.e 2
140.c even 2 1 784.4.a.g 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
7.4.a.a 1 5.b even 2 1
49.4.a.b 1 35.c odd 2 1
49.4.c.b 2 35.i odd 6 2
49.4.c.c 2 35.j even 6 2
63.4.a.b 1 15.d odd 2 1
112.4.a.f 1 20.d odd 2 1
175.4.a.b 1 1.a even 1 1 trivial
175.4.b.b 2 5.c odd 4 2
441.4.a.i 1 105.g even 2 1
441.4.e.e 2 105.p even 6 2
441.4.e.h 2 105.o odd 6 2
448.4.a.e 1 40.e odd 2 1
448.4.a.i 1 40.f even 2 1
784.4.a.g 1 140.c even 2 1
847.4.a.b 1 55.d odd 2 1
1008.4.a.c 1 60.h even 2 1
1183.4.a.b 1 65.d even 2 1
1225.4.a.j 1 7.b odd 2 1
1575.4.a.e 1 3.b odd 2 1
2023.4.a.a 1 85.c even 2 1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2} - 1 \) acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(175))\).

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( -1 + T \)
$3$ \( -2 + T \)
$5$ \( T \)
$7$ \( -7 + T \)
$11$ \( 8 + T \)
$13$ \( 28 + T \)
$17$ \( 54 + T \)
$19$ \( 110 + T \)
$23$ \( 48 + T \)
$29$ \( 110 + T \)
$31$ \( -12 + T \)
$37$ \( -246 + T \)
$41$ \( -182 + T \)
$43$ \( 128 + T \)
$47$ \( 324 + T \)
$53$ \( -162 + T \)
$59$ \( -810 + T \)
$61$ \( 488 + T \)
$67$ \( 244 + T \)
$71$ \( 768 + T \)
$73$ \( -702 + T \)
$79$ \( -440 + T \)
$83$ \( -1302 + T \)
$89$ \( -730 + T \)
$97$ \( 294 + T \)
show more
show less