Properties

Label 230.4.a.c
Level $230$
Weight $4$
Character orbit 230.a
Self dual yes
Analytic conductor $13.570$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 230 = 2 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 230.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(13.5704393013\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q - 2q^{2} + 7q^{3} + 4q^{4} + 5q^{5} - 14q^{6} + 20q^{7} - 8q^{8} + 22q^{9} + O(q^{10}) \) \( q - 2q^{2} + 7q^{3} + 4q^{4} + 5q^{5} - 14q^{6} + 20q^{7} - 8q^{8} + 22q^{9} - 10q^{10} + 6q^{11} + 28q^{12} + 47q^{13} - 40q^{14} + 35q^{15} + 16q^{16} - 132q^{17} - 44q^{18} + 146q^{19} + 20q^{20} + 140q^{21} - 12q^{22} + 23q^{23} - 56q^{24} + 25q^{25} - 94q^{26} - 35q^{27} + 80q^{28} - 99q^{29} - 70q^{30} - 253q^{31} - 32q^{32} + 42q^{33} + 264q^{34} + 100q^{35} + 88q^{36} - 118q^{37} - 292q^{38} + 329q^{39} - 40q^{40} + 495q^{41} - 280q^{42} + 272q^{43} + 24q^{44} + 110q^{45} - 46q^{46} + 639q^{47} + 112q^{48} + 57q^{49} - 50q^{50} - 924q^{51} + 188q^{52} - 342q^{53} + 70q^{54} + 30q^{55} - 160q^{56} + 1022q^{57} + 198q^{58} + 240q^{59} + 140q^{60} - 370q^{61} + 506q^{62} + 440q^{63} + 64q^{64} + 235q^{65} - 84q^{66} + 698q^{67} - 528q^{68} + 161q^{69} - 200q^{70} - 357q^{71} - 176q^{72} - 259q^{73} + 236q^{74} + 175q^{75} + 584q^{76} + 120q^{77} - 658q^{78} + 542q^{79} + 80q^{80} - 839q^{81} - 990q^{82} - 1248q^{83} + 560q^{84} - 660q^{85} - 544q^{86} - 693q^{87} - 48q^{88} - 828q^{89} - 220q^{90} + 940q^{91} + 92q^{92} - 1771q^{93} - 1278q^{94} + 730q^{95} - 224q^{96} + 992q^{97} - 114q^{98} + 132q^{99} + O(q^{100}) \)

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
−2.00000 7.00000 4.00000 5.00000 −14.0000 20.0000 −8.00000 22.0000 −10.0000
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(2\) \(1\)
\(5\) \(-1\)
\(23\) \(-1\)

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 230.4.a.c 1
3.b odd 2 1 2070.4.a.j 1
4.b odd 2 1 1840.4.a.a 1
5.b even 2 1 1150.4.a.e 1
5.c odd 4 2 1150.4.b.b 2
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
230.4.a.c 1 1.a even 1 1 trivial
1150.4.a.e 1 5.b even 2 1
1150.4.b.b 2 5.c odd 4 2
1840.4.a.a 1 4.b odd 2 1
2070.4.a.j 1 3.b odd 2 1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{3} - 7 \) acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(230))\).

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( 2 + T \)
$3$ \( -7 + T \)
$5$ \( -5 + T \)
$7$ \( -20 + T \)
$11$ \( -6 + T \)
$13$ \( -47 + T \)
$17$ \( 132 + T \)
$19$ \( -146 + T \)
$23$ \( -23 + T \)
$29$ \( 99 + T \)
$31$ \( 253 + T \)
$37$ \( 118 + T \)
$41$ \( -495 + T \)
$43$ \( -272 + T \)
$47$ \( -639 + T \)
$53$ \( 342 + T \)
$59$ \( -240 + T \)
$61$ \( 370 + T \)
$67$ \( -698 + T \)
$71$ \( 357 + T \)
$73$ \( 259 + T \)
$79$ \( -542 + T \)
$83$ \( 1248 + T \)
$89$ \( 828 + T \)
$97$ \( -992 + T \)
show more
show less