Properties

Label 1815.4.a.e
Level $1815$
Weight $4$
Character orbit 1815.a
Self dual yes
Analytic conductor $107.088$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1815 = 3 \cdot 5 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1815.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(107.088466660\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 15)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

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

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:

Atkin-Lehner signs

\( p \) Sign
\(3\) \(-1\)
\(5\) \(-1\)
\(11\) \(-1\)

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 1815.4.a.e 1
11.b odd 2 1 15.4.a.a 1
33.d even 2 1 45.4.a.c 1
44.c even 2 1 240.4.a.e 1
55.d odd 2 1 75.4.a.b 1
55.e even 4 2 75.4.b.b 2
77.b even 2 1 735.4.a.e 1
88.b odd 2 1 960.4.a.b 1
88.g even 2 1 960.4.a.ba 1
99.g even 6 2 405.4.e.i 2
99.h odd 6 2 405.4.e.g 2
132.d odd 2 1 720.4.a.n 1
165.d even 2 1 225.4.a.f 1
165.l odd 4 2 225.4.b.e 2
220.g even 2 1 1200.4.a.t 1
220.i odd 4 2 1200.4.f.b 2
231.h odd 2 1 2205.4.a.l 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
15.4.a.a 1 11.b odd 2 1
45.4.a.c 1 33.d even 2 1
75.4.a.b 1 55.d odd 2 1
75.4.b.b 2 55.e even 4 2
225.4.a.f 1 165.d even 2 1
225.4.b.e 2 165.l odd 4 2
240.4.a.e 1 44.c even 2 1
405.4.e.g 2 99.h odd 6 2
405.4.e.i 2 99.g even 6 2
720.4.a.n 1 132.d odd 2 1
735.4.a.e 1 77.b even 2 1
960.4.a.b 1 88.b odd 2 1
960.4.a.ba 1 88.g even 2 1
1200.4.a.t 1 220.g even 2 1
1200.4.f.b 2 220.i odd 4 2
1815.4.a.e 1 1.a even 1 1 trivial
2205.4.a.l 1 231.h odd 2 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(1815))\):

\( T_{2} + 1 \)
\( T_{7} - 24 \)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( 1 + T \)
$3$ \( -3 + T \)
$5$ \( -5 + T \)
$7$ \( -24 + T \)
$11$ \( T \)
$13$ \( 22 + T \)
$17$ \( -14 + T \)
$19$ \( -20 + T \)
$23$ \( 168 + T \)
$29$ \( 230 + T \)
$31$ \( 288 + T \)
$37$ \( 34 + T \)
$41$ \( 122 + T \)
$43$ \( -188 + T \)
$47$ \( -256 + T \)
$53$ \( 338 + T \)
$59$ \( -100 + T \)
$61$ \( 742 + T \)
$67$ \( 84 + T \)
$71$ \( 328 + T \)
$73$ \( -38 + T \)
$79$ \( -240 + T \)
$83$ \( 1212 + T \)
$89$ \( -330 + T \)
$97$ \( -866 + T \)
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