Properties

Label 1950.2.a.w
Level $1950$
Weight $2$
Character orbit 1950.a
Self dual yes
Analytic conductor $15.571$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1950.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(15.5708283941\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 78)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q + q^{2} + q^{3} + q^{4} + q^{6} - 4q^{7} + q^{8} + q^{9} + O(q^{10}) \) \( q + q^{2} + q^{3} + q^{4} + q^{6} - 4q^{7} + q^{8} + q^{9} - 4q^{11} + q^{12} - q^{13} - 4q^{14} + q^{16} - 2q^{17} + q^{18} - 8q^{19} - 4q^{21} - 4q^{22} + q^{24} - q^{26} + q^{27} - 4q^{28} + 6q^{29} - 4q^{31} + q^{32} - 4q^{33} - 2q^{34} + q^{36} + 2q^{37} - 8q^{38} - q^{39} - 10q^{41} - 4q^{42} - 4q^{43} - 4q^{44} - 8q^{47} + q^{48} + 9q^{49} - 2q^{51} - q^{52} + 10q^{53} + q^{54} - 4q^{56} - 8q^{57} + 6q^{58} + 4q^{59} - 2q^{61} - 4q^{62} - 4q^{63} + q^{64} - 4q^{66} + 16q^{67} - 2q^{68} - 8q^{71} + q^{72} - 2q^{73} + 2q^{74} - 8q^{76} + 16q^{77} - q^{78} + 8q^{79} + q^{81} - 10q^{82} - 12q^{83} - 4q^{84} - 4q^{86} + 6q^{87} - 4q^{88} + 14q^{89} + 4q^{91} - 4q^{93} - 8q^{94} + q^{96} - 10q^{97} + 9q^{98} - 4q^{99} + O(q^{100}) \)

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 1.00000 1.00000 0 1.00000 −4.00000 1.00000 1.00000 0
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(2\) \(-1\)
\(3\) \(-1\)
\(5\) \(1\)
\(13\) \(1\)

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 1950.2.a.w 1
3.b odd 2 1 5850.2.a.d 1
5.b even 2 1 78.2.a.a 1
5.c odd 4 2 1950.2.e.i 2
15.d odd 2 1 234.2.a.c 1
15.e even 4 2 5850.2.e.bb 2
20.d odd 2 1 624.2.a.h 1
35.c odd 2 1 3822.2.a.j 1
40.e odd 2 1 2496.2.a.b 1
40.f even 2 1 2496.2.a.t 1
45.h odd 6 2 2106.2.e.j 2
45.j even 6 2 2106.2.e.q 2
55.d odd 2 1 9438.2.a.t 1
60.h even 2 1 1872.2.a.c 1
65.d even 2 1 1014.2.a.d 1
65.g odd 4 2 1014.2.b.b 2
65.l even 6 2 1014.2.e.c 2
65.n even 6 2 1014.2.e.f 2
65.s odd 12 4 1014.2.i.d 4
120.i odd 2 1 7488.2.a.bz 1
120.m even 2 1 7488.2.a.bk 1
195.e odd 2 1 3042.2.a.f 1
195.n even 4 2 3042.2.b.g 2
260.g odd 2 1 8112.2.a.v 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
78.2.a.a 1 5.b even 2 1
234.2.a.c 1 15.d odd 2 1
624.2.a.h 1 20.d odd 2 1
1014.2.a.d 1 65.d even 2 1
1014.2.b.b 2 65.g odd 4 2
1014.2.e.c 2 65.l even 6 2
1014.2.e.f 2 65.n even 6 2
1014.2.i.d 4 65.s odd 12 4
1872.2.a.c 1 60.h even 2 1
1950.2.a.w 1 1.a even 1 1 trivial
1950.2.e.i 2 5.c odd 4 2
2106.2.e.j 2 45.h odd 6 2
2106.2.e.q 2 45.j even 6 2
2496.2.a.b 1 40.e odd 2 1
2496.2.a.t 1 40.f even 2 1
3042.2.a.f 1 195.e odd 2 1
3042.2.b.g 2 195.n even 4 2
3822.2.a.j 1 35.c odd 2 1
5850.2.a.d 1 3.b odd 2 1
5850.2.e.bb 2 15.e even 4 2
7488.2.a.bk 1 120.m even 2 1
7488.2.a.bz 1 120.i odd 2 1
8112.2.a.v 1 260.g odd 2 1
9438.2.a.t 1 55.d odd 2 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(1950))\):

\( T_{7} + 4 \)
\( T_{11} + 4 \)
\( T_{17} + 2 \)
\( T_{23} \)
\( T_{31} + 4 \)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( -1 + T \)
$3$ \( -1 + T \)
$5$ \( T \)
$7$ \( 4 + T \)
$11$ \( 4 + T \)
$13$ \( 1 + T \)
$17$ \( 2 + T \)
$19$ \( 8 + T \)
$23$ \( T \)
$29$ \( -6 + T \)
$31$ \( 4 + T \)
$37$ \( -2 + T \)
$41$ \( 10 + T \)
$43$ \( 4 + T \)
$47$ \( 8 + T \)
$53$ \( -10 + T \)
$59$ \( -4 + T \)
$61$ \( 2 + T \)
$67$ \( -16 + T \)
$71$ \( 8 + T \)
$73$ \( 2 + T \)
$79$ \( -8 + T \)
$83$ \( 12 + T \)
$89$ \( -14 + T \)
$97$ \( 10 + T \)
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