Properties

Label 966.2.h.a
Level $966$
Weight $2$
Character orbit 966.h
Analytic conductor $7.714$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 966.h (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.71354883526\)
Analytic rank: \(0\)
Dimension: \(24\)
Twist minimal: yes
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.

\(\operatorname{Tr}(f)(q) = \) \( 24q + 4q^{3} - 24q^{4} - 4q^{5} - 4q^{9} + O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \( 24q + 4q^{3} - 24q^{4} - 4q^{5} - 4q^{9} - 4q^{12} + 8q^{13} + 24q^{14} - 4q^{15} + 24q^{16} + 32q^{17} + 4q^{18} + 4q^{20} - 8q^{23} - 12q^{25} + 16q^{27} - 4q^{30} - 16q^{31} + 20q^{33} + 4q^{36} - 8q^{39} + 4q^{42} + 24q^{45} - 4q^{46} + 4q^{48} - 24q^{49} + 24q^{51} - 8q^{52} + 24q^{53} - 12q^{54} + 16q^{55} - 24q^{56} + 4q^{57} + 4q^{58} + 4q^{60} - 4q^{63} - 24q^{64} - 12q^{66} - 32q^{68} - 24q^{69} - 4q^{70} - 4q^{72} - 32q^{73} - 16q^{74} + 48q^{75} + 12q^{78} - 4q^{80} - 8q^{81} - 8q^{82} + 16q^{83} - 16q^{85} + 16q^{86} + 20q^{87} + 24q^{89} - 28q^{90} + 8q^{92} + 16q^{93} + 8q^{94} - 48q^{99} + O(q^{100}) \)

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 \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
827.1 1.00000i −1.69648 0.349201i −1.00000 1.62492 −0.349201 + 1.69648i 1.00000i 1.00000i 2.75612 + 1.18483i 1.62492i
827.2 1.00000i −1.33692 1.10121i −1.00000 −0.136871 −1.10121 + 1.33692i 1.00000i 1.00000i 0.574695 + 2.94444i 0.136871i
827.3 1.00000i −1.01359 + 1.40450i −1.00000 −1.51059 1.40450 + 1.01359i 1.00000i 1.00000i −0.945264 2.84719i 1.51059i
827.4 1.00000i −0.798999 + 1.53675i −1.00000 2.11859 1.53675 + 0.798999i 1.00000i 1.00000i −1.72320 2.45572i 2.11859i
827.5 1.00000i −0.529264 1.64921i −1.00000 −2.93995 −1.64921 + 0.529264i 1.00000i 1.00000i −2.43976 + 1.74573i 2.93995i
827.6 1.00000i −0.0866531 1.72988i −1.00000 0.713996 −1.72988 + 0.0866531i 1.00000i 1.00000i −2.98498 + 0.299799i 0.713996i
827.7 1.00000i 0.656415 + 1.60285i −1.00000 −0.252332 1.60285 0.656415i 1.00000i 1.00000i −2.13824 + 2.10426i 0.252332i
827.8 1.00000i 0.696580 + 1.58580i −1.00000 −3.16093 1.58580 0.696580i 1.00000i 1.00000i −2.02955 + 2.20928i 3.16093i
827.9 1.00000i 1.23024 1.21923i −1.00000 0.666555 −1.21923 1.23024i 1.00000i 1.00000i 0.0269708 2.99988i 0.666555i
827.10 1.00000i 1.55095 0.771068i −1.00000 2.18892 −0.771068 1.55095i 1.00000i 1.00000i 1.81091 2.39178i 2.18892i
827.11 1.00000i 1.59575 + 0.673481i −1.00000 2.44752 0.673481 1.59575i 1.00000i 1.00000i 2.09285 + 2.14942i 2.44752i
827.12 1.00000i 1.73197 + 0.0164012i −1.00000 −3.75984 0.0164012 1.73197i 1.00000i 1.00000i 2.99946 + 0.0568128i 3.75984i
827.13 1.00000i −1.69648 + 0.349201i −1.00000 1.62492 −0.349201 1.69648i 1.00000i 1.00000i 2.75612 1.18483i 1.62492i
827.14 1.00000i −1.33692 + 1.10121i −1.00000 −0.136871 −1.10121 1.33692i 1.00000i 1.00000i 0.574695 2.94444i 0.136871i
827.15 1.00000i −1.01359 1.40450i −1.00000 −1.51059 1.40450 1.01359i 1.00000i 1.00000i −0.945264 + 2.84719i 1.51059i
827.16 1.00000i −0.798999 1.53675i −1.00000 2.11859 1.53675 0.798999i 1.00000i 1.00000i −1.72320 + 2.45572i 2.11859i
827.17 1.00000i −0.529264 + 1.64921i −1.00000 −2.93995 −1.64921 0.529264i 1.00000i 1.00000i −2.43976 1.74573i 2.93995i
827.18 1.00000i −0.0866531 + 1.72988i −1.00000 0.713996 −1.72988 0.0866531i 1.00000i 1.00000i −2.98498 0.299799i 0.713996i
827.19 1.00000i 0.656415 1.60285i −1.00000 −0.252332 1.60285 + 0.656415i 1.00000i 1.00000i −2.13824 2.10426i 0.252332i
827.20 1.00000i 0.696580 1.58580i −1.00000 −3.16093 1.58580 + 0.696580i 1.00000i 1.00000i −2.02955 2.20928i 3.16093i
See all 24 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 827.24
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
69.c even 2 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 966.2.h.a 24
3.b odd 2 1 966.2.h.b yes 24
23.b odd 2 1 966.2.h.b yes 24
69.c even 2 1 inner 966.2.h.a 24
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
966.2.h.a 24 1.a even 1 1 trivial
966.2.h.a 24 69.c even 2 1 inner
966.2.h.b yes 24 3.b odd 2 1
966.2.h.b yes 24 23.b odd 2 1