Properties

Label 2070.3.c.b
Level $2070$
Weight $3$
Character orbit 2070.c
Analytic conductor $56.403$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 2070 = 2 \cdot 3^{2} \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 2070.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(56.4034147226\)
Analytic rank: \(0\)
Dimension: \(32\)
Twist minimal: no (minimal twist has level 690)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

$q$-expansion

The dimension is sufficiently large that we do not compute an algebraic \(q\)-expansion, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 32q + 64q^{4} + O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \( 32q + 64q^{4} - 48q^{13} + 128q^{16} + 80q^{23} - 160q^{25} - 120q^{29} + 248q^{31} + 120q^{35} - 72q^{41} + 160q^{46} - 400q^{47} - 344q^{49} - 96q^{52} - 256q^{58} - 120q^{59} - 160q^{62} + 256q^{64} - 104q^{71} + 16q^{73} - 240q^{77} + 64q^{82} - 120q^{85} + 160q^{92} + 96q^{94} + 160q^{95} - 64q^{98} + O(q^{100}) \)

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 \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
91.1 −1.41421 0 2.00000 2.23607i 0 11.4203i −2.82843 0 3.16228i
91.2 −1.41421 0 2.00000 2.23607i 0 3.95881i −2.82843 0 3.16228i
91.3 −1.41421 0 2.00000 2.23607i 0 3.80775i −2.82843 0 3.16228i
91.4 −1.41421 0 2.00000 2.23607i 0 1.37049i −2.82843 0 3.16228i
91.5 −1.41421 0 2.00000 2.23607i 0 6.64524i −2.82843 0 3.16228i
91.6 −1.41421 0 2.00000 2.23607i 0 7.54509i −2.82843 0 3.16228i
91.7 −1.41421 0 2.00000 2.23607i 0 7.96402i −2.82843 0 3.16228i
91.8 −1.41421 0 2.00000 2.23607i 0 11.8194i −2.82843 0 3.16228i
91.9 −1.41421 0 2.00000 2.23607i 0 11.8194i −2.82843 0 3.16228i
91.10 −1.41421 0 2.00000 2.23607i 0 7.96402i −2.82843 0 3.16228i
91.11 −1.41421 0 2.00000 2.23607i 0 7.54509i −2.82843 0 3.16228i
91.12 −1.41421 0 2.00000 2.23607i 0 6.64524i −2.82843 0 3.16228i
91.13 −1.41421 0 2.00000 2.23607i 0 1.37049i −2.82843 0 3.16228i
91.14 −1.41421 0 2.00000 2.23607i 0 3.80775i −2.82843 0 3.16228i
91.15 −1.41421 0 2.00000 2.23607i 0 3.95881i −2.82843 0 3.16228i
91.16 −1.41421 0 2.00000 2.23607i 0 11.4203i −2.82843 0 3.16228i
91.17 1.41421 0 2.00000 2.23607i 0 12.3097i 2.82843 0 3.16228i
91.18 1.41421 0 2.00000 2.23607i 0 5.52876i 2.82843 0 3.16228i
91.19 1.41421 0 2.00000 2.23607i 0 1.52229i 2.82843 0 3.16228i
91.20 1.41421 0 2.00000 2.23607i 0 0.411309i 2.82843 0 3.16228i
See all 32 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 91.32
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
23.b odd 2 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 2070.3.c.b 32
3.b odd 2 1 690.3.c.a 32
23.b odd 2 1 inner 2070.3.c.b 32
69.c even 2 1 690.3.c.a 32
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
690.3.c.a 32 3.b odd 2 1
690.3.c.a 32 69.c even 2 1
2070.3.c.b 32 1.a even 1 1 trivial
2070.3.c.b 32 23.b odd 2 1 inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \(17\!\cdots\!64\)\( T_{7}^{22} + \)\(13\!\cdots\!44\)\( T_{7}^{20} + \)\(76\!\cdots\!96\)\( T_{7}^{18} + \)\(30\!\cdots\!23\)\( T_{7}^{16} + \)\(83\!\cdots\!60\)\( T_{7}^{14} + \)\(15\!\cdots\!98\)\( T_{7}^{12} + \)\(20\!\cdots\!08\)\( T_{7}^{10} + \)\(16\!\cdots\!77\)\( T_{7}^{8} + \)\(73\!\cdots\!36\)\( T_{7}^{6} + \)\(15\!\cdots\!24\)\( T_{7}^{4} + \)\(13\!\cdots\!20\)\( T_{7}^{2} + \)\(18\!\cdots\!56\)\( \)">\(T_{7}^{32} + \cdots\) acting on \(S_{3}^{\mathrm{new}}(2070, [\chi])\).