Properties

Label 175.6.a.b
Level $175$
Weight $6$
Character orbit 175.a
Self dual yes
Analytic conductor $28.067$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 175 = 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 175.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(28.0671684673\)
Analytic rank: \(0\)
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

\(f(q)\) \(=\) \( q + 10 q^{2} + 14 q^{3} + 68 q^{4} + 140 q^{6} + 49 q^{7} + 360 q^{8} - 47 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( q + 10 q^{2} + 14 q^{3} + 68 q^{4} + 140 q^{6} + 49 q^{7} + 360 q^{8} - 47 q^{9} + 232 q^{11} + 952 q^{12} + 140 q^{13} + 490 q^{14} + 1424 q^{16} + 1722 q^{17} - 470 q^{18} - 98 q^{19} + 686 q^{21} + 2320 q^{22} - 1824 q^{23} + 5040 q^{24} + 1400 q^{26} - 4060 q^{27} + 3332 q^{28} + 3418 q^{29} - 7644 q^{31} + 2720 q^{32} + 3248 q^{33} + 17220 q^{34} - 3196 q^{36} + 10398 q^{37} - 980 q^{38} + 1960 q^{39} - 17962 q^{41} + 6860 q^{42} - 10880 q^{43} + 15776 q^{44} - 18240 q^{46} - 9324 q^{47} + 19936 q^{48} + 2401 q^{49} + 24108 q^{51} + 9520 q^{52} - 2262 q^{53} - 40600 q^{54} + 17640 q^{56} - 1372 q^{57} + 34180 q^{58} - 2730 q^{59} + 25648 q^{61} - 76440 q^{62} - 2303 q^{63} - 18368 q^{64} + 32480 q^{66} + 48404 q^{67} + 117096 q^{68} - 25536 q^{69} - 58560 q^{71} - 16920 q^{72} - 68082 q^{73} + 103980 q^{74} - 6664 q^{76} + 11368 q^{77} + 19600 q^{78} + 31784 q^{79} - 45419 q^{81} - 179620 q^{82} + 20538 q^{83} + 46648 q^{84} - 108800 q^{86} + 47852 q^{87} + 83520 q^{88} - 50582 q^{89} + 6860 q^{91} - 124032 q^{92} - 107016 q^{93} - 93240 q^{94} + 38080 q^{96} + 58506 q^{97} + 24010 q^{98} - 10904 q^{99}+O(q^{100}) \) 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
10.0000 14.0000 68.0000 0 140.000 49.0000 360.000 −47.0000 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 175.6.a.b 1
5.b even 2 1 7.6.a.a 1
5.c odd 4 2 175.6.b.a 2
15.d odd 2 1 63.6.a.e 1
20.d odd 2 1 112.6.a.g 1
35.c odd 2 1 49.6.a.a 1
35.i odd 6 2 49.6.c.b 2
35.j even 6 2 49.6.c.c 2
40.e odd 2 1 448.6.a.c 1
40.f even 2 1 448.6.a.m 1
55.d odd 2 1 847.6.a.b 1
60.h even 2 1 1008.6.a.y 1
105.g even 2 1 441.6.a.k 1
140.c even 2 1 784.6.a.c 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
7.6.a.a 1 5.b even 2 1
49.6.a.a 1 35.c odd 2 1
49.6.c.b 2 35.i odd 6 2
49.6.c.c 2 35.j even 6 2
63.6.a.e 1 15.d odd 2 1
112.6.a.g 1 20.d odd 2 1
175.6.a.b 1 1.a even 1 1 trivial
175.6.b.a 2 5.c odd 4 2
441.6.a.k 1 105.g even 2 1
448.6.a.c 1 40.e odd 2 1
448.6.a.m 1 40.f even 2 1
784.6.a.c 1 140.c even 2 1
847.6.a.b 1 55.d odd 2 1
1008.6.a.y 1 60.h even 2 1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2} - 10 \) acting on \(S_{6}^{\mathrm{new}}(\Gamma_0(175))\). Copy content Toggle raw display

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( T - 10 \) Copy content Toggle raw display
$3$ \( T - 14 \) Copy content Toggle raw display
$5$ \( T \) Copy content Toggle raw display
$7$ \( T - 49 \) Copy content Toggle raw display
$11$ \( T - 232 \) Copy content Toggle raw display
$13$ \( T - 140 \) Copy content Toggle raw display
$17$ \( T - 1722 \) Copy content Toggle raw display
$19$ \( T + 98 \) Copy content Toggle raw display
$23$ \( T + 1824 \) Copy content Toggle raw display
$29$ \( T - 3418 \) Copy content Toggle raw display
$31$ \( T + 7644 \) Copy content Toggle raw display
$37$ \( T - 10398 \) Copy content Toggle raw display
$41$ \( T + 17962 \) Copy content Toggle raw display
$43$ \( T + 10880 \) Copy content Toggle raw display
$47$ \( T + 9324 \) Copy content Toggle raw display
$53$ \( T + 2262 \) Copy content Toggle raw display
$59$ \( T + 2730 \) Copy content Toggle raw display
$61$ \( T - 25648 \) Copy content Toggle raw display
$67$ \( T - 48404 \) Copy content Toggle raw display
$71$ \( T + 58560 \) Copy content Toggle raw display
$73$ \( T + 68082 \) Copy content Toggle raw display
$79$ \( T - 31784 \) Copy content Toggle raw display
$83$ \( T - 20538 \) Copy content Toggle raw display
$89$ \( T + 50582 \) Copy content Toggle raw display
$97$ \( T - 58506 \) Copy content Toggle raw display
show more
show less