Properties

Label 1815.4.a.a
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

\(f(q)\) \(=\) \( q - 3 q^{2} - 3 q^{3} + q^{4} - 5 q^{5} + 9 q^{6} - 20 q^{7} + 21 q^{8} + 9 q^{9} + O(q^{10}) \) \( q - 3 q^{2} - 3 q^{3} + q^{4} - 5 q^{5} + 9 q^{6} - 20 q^{7} + 21 q^{8} + 9 q^{9} + 15 q^{10} - 3 q^{12} - 74 q^{13} + 60 q^{14} + 15 q^{15} - 71 q^{16} - 54 q^{17} - 27 q^{18} + 124 q^{19} - 5 q^{20} + 60 q^{21} - 120 q^{23} - 63 q^{24} + 25 q^{25} + 222 q^{26} - 27 q^{27} - 20 q^{28} + 78 q^{29} - 45 q^{30} + 200 q^{31} + 45 q^{32} + 162 q^{34} + 100 q^{35} + 9 q^{36} - 70 q^{37} - 372 q^{38} + 222 q^{39} - 105 q^{40} - 330 q^{41} - 180 q^{42} - 92 q^{43} - 45 q^{45} + 360 q^{46} - 24 q^{47} + 213 q^{48} + 57 q^{49} - 75 q^{50} + 162 q^{51} - 74 q^{52} + 450 q^{53} + 81 q^{54} - 420 q^{56} - 372 q^{57} - 234 q^{58} + 24 q^{59} + 15 q^{60} + 322 q^{61} - 600 q^{62} - 180 q^{63} + 433 q^{64} + 370 q^{65} - 196 q^{67} - 54 q^{68} + 360 q^{69} - 300 q^{70} - 288 q^{71} + 189 q^{72} + 430 q^{73} + 210 q^{74} - 75 q^{75} + 124 q^{76} - 666 q^{78} + 520 q^{79} + 355 q^{80} + 81 q^{81} + 990 q^{82} - 156 q^{83} + 60 q^{84} + 270 q^{85} + 276 q^{86} - 234 q^{87} + 1026 q^{89} + 135 q^{90} + 1480 q^{91} - 120 q^{92} - 600 q^{93} + 72 q^{94} - 620 q^{95} - 135 q^{96} - 286 q^{97} - 171 q^{98} + O(q^{100}) \)

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
−3.00000 −3.00000 1.00000 −5.00000 9.00000 −20.0000 21.0000 9.00000 15.0000
\(n\): 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.a 1
11.b odd 2 1 15.4.a.b 1
33.d even 2 1 45.4.a.b 1
44.c even 2 1 240.4.a.f 1
55.d odd 2 1 75.4.a.a 1
55.e even 4 2 75.4.b.a 2
77.b even 2 1 735.4.a.i 1
88.b odd 2 1 960.4.a.bi 1
88.g even 2 1 960.4.a.l 1
99.g even 6 2 405.4.e.k 2
99.h odd 6 2 405.4.e.d 2
132.d odd 2 1 720.4.a.r 1
165.d even 2 1 225.4.a.g 1
165.l odd 4 2 225.4.b.d 2
220.g even 2 1 1200.4.a.o 1
220.i odd 4 2 1200.4.f.m 2
231.h odd 2 1 2205.4.a.c 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
15.4.a.b 1 11.b odd 2 1
45.4.a.b 1 33.d even 2 1
75.4.a.a 1 55.d odd 2 1
75.4.b.a 2 55.e even 4 2
225.4.a.g 1 165.d even 2 1
225.4.b.d 2 165.l odd 4 2
240.4.a.f 1 44.c even 2 1
405.4.e.d 2 99.h odd 6 2
405.4.e.k 2 99.g even 6 2
720.4.a.r 1 132.d odd 2 1
735.4.a.i 1 77.b even 2 1
960.4.a.l 1 88.g even 2 1
960.4.a.bi 1 88.b odd 2 1
1200.4.a.o 1 220.g even 2 1
1200.4.f.m 2 220.i odd 4 2
1815.4.a.a 1 1.a even 1 1 trivial
2205.4.a.c 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 \(S_{4}^{\mathrm{new}}(\Gamma_0(1815))\):

\( T_{2} + 3 \)
\( T_{7} + 20 \)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( 3 + T \)
$3$ \( 3 + T \)
$5$ \( 5 + T \)
$7$ \( 20 + T \)
$11$ \( T \)
$13$ \( 74 + T \)
$17$ \( 54 + T \)
$19$ \( -124 + T \)
$23$ \( 120 + T \)
$29$ \( -78 + T \)
$31$ \( -200 + T \)
$37$ \( 70 + T \)
$41$ \( 330 + T \)
$43$ \( 92 + T \)
$47$ \( 24 + T \)
$53$ \( -450 + T \)
$59$ \( -24 + T \)
$61$ \( -322 + T \)
$67$ \( 196 + T \)
$71$ \( 288 + T \)
$73$ \( -430 + T \)
$79$ \( -520 + T \)
$83$ \( 156 + T \)
$89$ \( -1026 + T \)
$97$ \( 286 + T \)
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