Properties

Label 25.12.a.b
Level 25
Weight 12
Character orbit 25.a
Self dual yes
Analytic conductor 19.209
Analytic rank 0
Dimension 1
CM no
Inner twists 1

Related objects

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Newspace parameters

Level: \( N \) = \( 25 = 5^{2} \)
Weight: \( k \) = \( 12 \)
Character orbit: \([\chi]\) = 25.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(19.2085795140\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 1)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q + 24q^{2} - 252q^{3} - 1472q^{4} - 6048q^{6} + 16744q^{7} - 84480q^{8} - 113643q^{9} + O(q^{10}) \) \( q + 24q^{2} - 252q^{3} - 1472q^{4} - 6048q^{6} + 16744q^{7} - 84480q^{8} - 113643q^{9} + 534612q^{11} + 370944q^{12} + 577738q^{13} + 401856q^{14} + 987136q^{16} + 6905934q^{17} - 2727432q^{18} + 10661420q^{19} - 4219488q^{21} + 12830688q^{22} - 18643272q^{23} + 21288960q^{24} + 13865712q^{26} + 73279080q^{27} - 24647168q^{28} + 128406630q^{29} - 52843168q^{31} + 196706304q^{32} - 134722224q^{33} + 165742416q^{34} + 167282496q^{36} + 182213314q^{37} + 255874080q^{38} - 145589976q^{39} + 308120442q^{41} - 101267712q^{42} + 17125708q^{43} - 786948864q^{44} - 447438528q^{46} - 2687348496q^{47} - 248758272q^{48} - 1696965207q^{49} - 1740295368q^{51} - 850430336q^{52} + 1596055698q^{53} + 1758697920q^{54} - 1414533120q^{56} - 2686677840q^{57} + 3081759120q^{58} - 5189203740q^{59} + 6956478662q^{61} - 1268236032q^{62} - 1902838392q^{63} + 2699296768q^{64} - 3233333376q^{66} + 15481826884q^{67} - 10165534848q^{68} + 4698104544q^{69} + 9791485272q^{71} + 9600560640q^{72} - 1463791322q^{73} + 4373119536q^{74} - 15693610240q^{76} + 8951543328q^{77} - 3494159424q^{78} + 38116845680q^{79} + 1665188361q^{81} + 7394890608q^{82} + 29335099668q^{83} + 6211086336q^{84} + 411016992q^{86} - 32358470760q^{87} - 45164021760q^{88} - 24992917110q^{89} + 9673645072q^{91} + 27442896384q^{92} + 13316478336q^{93} - 64496363904q^{94} - 49569988608q^{96} - 75013568546q^{97} - 40727164968q^{98} - 60754911516q^{99} + O(q^{100}) \)

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
24.0000 −252.000 −1472.00 0 −6048.00 16744.0 −84480.0 −113643. 0
\(n\): 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 25.12.a.b 1
3.b odd 2 1 225.12.a.b 1
5.b even 2 1 1.12.a.a 1
5.c odd 4 2 25.12.b.b 2
15.d odd 2 1 9.12.a.b 1
15.e even 4 2 225.12.b.d 2
20.d odd 2 1 16.12.a.a 1
35.c odd 2 1 49.12.a.a 1
35.i odd 6 2 49.12.c.c 2
35.j even 6 2 49.12.c.b 2
40.e odd 2 1 64.12.a.f 1
40.f even 2 1 64.12.a.b 1
45.h odd 6 2 81.12.c.b 2
45.j even 6 2 81.12.c.d 2
55.d odd 2 1 121.12.a.b 1
60.h even 2 1 144.12.a.d 1
65.d even 2 1 169.12.a.a 1
80.k odd 4 2 256.12.b.c 2
80.q even 4 2 256.12.b.e 2
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1.12.a.a 1 5.b even 2 1
9.12.a.b 1 15.d odd 2 1
16.12.a.a 1 20.d odd 2 1
25.12.a.b 1 1.a even 1 1 trivial
25.12.b.b 2 5.c odd 4 2
49.12.a.a 1 35.c odd 2 1
49.12.c.b 2 35.j even 6 2
49.12.c.c 2 35.i odd 6 2
64.12.a.b 1 40.f even 2 1
64.12.a.f 1 40.e odd 2 1
81.12.c.b 2 45.h odd 6 2
81.12.c.d 2 45.j even 6 2
121.12.a.b 1 55.d odd 2 1
144.12.a.d 1 60.h even 2 1
169.12.a.a 1 65.d even 2 1
225.12.a.b 1 3.b odd 2 1
225.12.b.d 2 15.e even 4 2
256.12.b.c 2 80.k odd 4 2
256.12.b.e 2 80.q even 4 2

Atkin-Lehner signs

\( p \) Sign
\(5\) \(1\)

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2} - 24 \) acting on \(S_{12}^{\mathrm{new}}(\Gamma_0(25))\).