Properties

Label 15.4.a.a
Level 15
Weight 4
Character orbit 15.a
Self dual yes
Analytic conductor 0.885
Analytic rank 0
Dimension 1
CM no
Inner twists 1

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 15 = 3 \cdot 5 \)
Weight: \( k \) = \( 4 \)
Character orbit: \([\chi]\) = 15.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(0.885028650086\)
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

\(f(q)\) \(=\) \( q + q^{2} + 3q^{3} - 7q^{4} + 5q^{5} + 3q^{6} - 24q^{7} - 15q^{8} + 9q^{9} + O(q^{10}) \) \( q + q^{2} + 3q^{3} - 7q^{4} + 5q^{5} + 3q^{6} - 24q^{7} - 15q^{8} + 9q^{9} + 5q^{10} + 52q^{11} - 21q^{12} + 22q^{13} - 24q^{14} + 15q^{15} + 41q^{16} - 14q^{17} + 9q^{18} - 20q^{19} - 35q^{20} - 72q^{21} + 52q^{22} - 168q^{23} - 45q^{24} + 25q^{25} + 22q^{26} + 27q^{27} + 168q^{28} + 230q^{29} + 15q^{30} - 288q^{31} + 161q^{32} + 156q^{33} - 14q^{34} - 120q^{35} - 63q^{36} - 34q^{37} - 20q^{38} + 66q^{39} - 75q^{40} + 122q^{41} - 72q^{42} - 188q^{43} - 364q^{44} + 45q^{45} - 168q^{46} + 256q^{47} + 123q^{48} + 233q^{49} + 25q^{50} - 42q^{51} - 154q^{52} - 338q^{53} + 27q^{54} + 260q^{55} + 360q^{56} - 60q^{57} + 230q^{58} + 100q^{59} - 105q^{60} + 742q^{61} - 288q^{62} - 216q^{63} - 167q^{64} + 110q^{65} + 156q^{66} - 84q^{67} + 98q^{68} - 504q^{69} - 120q^{70} - 328q^{71} - 135q^{72} - 38q^{73} - 34q^{74} + 75q^{75} + 140q^{76} - 1248q^{77} + 66q^{78} - 240q^{79} + 205q^{80} + 81q^{81} + 122q^{82} + 1212q^{83} + 504q^{84} - 70q^{85} - 188q^{86} + 690q^{87} - 780q^{88} + 330q^{89} + 45q^{90} - 528q^{91} + 1176q^{92} - 864q^{93} + 256q^{94} - 100q^{95} + 483q^{96} + 866q^{97} + 233q^{98} + 468q^{99} + O(q^{100}) \)

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 3.00000 −7.00000 5.00000 3.00000 −24.0000 −15.0000 9.00000 5.00000
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

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 15.4.a.a 1
3.b odd 2 1 45.4.a.c 1
4.b odd 2 1 240.4.a.e 1
5.b even 2 1 75.4.a.b 1
5.c odd 4 2 75.4.b.b 2
7.b odd 2 1 735.4.a.e 1
8.b even 2 1 960.4.a.b 1
8.d odd 2 1 960.4.a.ba 1
9.c even 3 2 405.4.e.g 2
9.d odd 6 2 405.4.e.i 2
11.b odd 2 1 1815.4.a.e 1
12.b even 2 1 720.4.a.n 1
15.d odd 2 1 225.4.a.f 1
15.e even 4 2 225.4.b.e 2
20.d odd 2 1 1200.4.a.t 1
20.e even 4 2 1200.4.f.b 2
21.c even 2 1 2205.4.a.l 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
15.4.a.a 1 1.a even 1 1 trivial
45.4.a.c 1 3.b odd 2 1
75.4.a.b 1 5.b even 2 1
75.4.b.b 2 5.c odd 4 2
225.4.a.f 1 15.d odd 2 1
225.4.b.e 2 15.e even 4 2
240.4.a.e 1 4.b odd 2 1
405.4.e.g 2 9.c even 3 2
405.4.e.i 2 9.d odd 6 2
720.4.a.n 1 12.b even 2 1
735.4.a.e 1 7.b odd 2 1
960.4.a.b 1 8.b even 2 1
960.4.a.ba 1 8.d odd 2 1
1200.4.a.t 1 20.d odd 2 1
1200.4.f.b 2 20.e even 4 2
1815.4.a.e 1 11.b odd 2 1
2205.4.a.l 1 21.c even 2 1

Atkin-Lehner signs

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

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2} - 1 \) acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(15))\).