Properties

Label 1148.2.n.e
Level $1148$
Weight $2$
Character orbit 1148.n
Analytic conductor $9.167$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1148 = 2^{2} \cdot 7 \cdot 41 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1148.n (of order \(5\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(9.16682615204\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(6\) over \(\Q(\zeta_{5})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 24q + 12q^{3} + 17q^{5} + 6q^{7} + 16q^{9} + O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \( 24q + 12q^{3} + 17q^{5} + 6q^{7} + 16q^{9} - 8q^{11} + 10q^{15} + 8q^{17} - 28q^{19} + 3q^{21} - 23q^{23} + 17q^{25} + 12q^{27} - 31q^{29} + 2q^{31} + 12q^{33} + 13q^{35} + 7q^{37} - 16q^{39} - q^{41} - 2q^{43} + 71q^{45} + 15q^{47} - 6q^{49} + 2q^{51} + 28q^{53} - 16q^{55} - 15q^{57} + 17q^{59} + 35q^{61} - q^{63} + 62q^{65} - 10q^{67} - 9q^{69} - 25q^{71} - 74q^{73} + 17q^{75} + 8q^{77} + 64q^{81} + 96q^{83} - 94q^{85} - q^{87} - 33q^{89} - 15q^{93} - 29q^{95} - 34q^{97} - 3q^{99} + O(q^{100}) \)

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 \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
57.1 0 −2.87361 0 2.43977 + 1.77260i 0 −0.309017 0.951057i 0 5.25763 0
57.2 0 −0.842614 0 2.54946 + 1.85229i 0 −0.309017 0.951057i 0 −2.29000 0
57.3 0 0.325457 0 0.538931 + 0.391556i 0 −0.309017 0.951057i 0 −2.89408 0
57.4 0 1.18943 0 −3.21254 2.33405i 0 −0.309017 0.951057i 0 −1.58525 0
57.5 0 2.26837 0 1.20758 + 0.877362i 0 −0.309017 0.951057i 0 2.14552 0
57.6 0 2.93296 0 3.52188 + 2.55880i 0 −0.309017 0.951057i 0 5.60225 0
141.1 0 −2.87361 0 2.43977 1.77260i 0 −0.309017 + 0.951057i 0 5.25763 0
141.2 0 −0.842614 0 2.54946 1.85229i 0 −0.309017 + 0.951057i 0 −2.29000 0
141.3 0 0.325457 0 0.538931 0.391556i 0 −0.309017 + 0.951057i 0 −2.89408 0
141.4 0 1.18943 0 −3.21254 + 2.33405i 0 −0.309017 + 0.951057i 0 −1.58525 0
141.5 0 2.26837 0 1.20758 0.877362i 0 −0.309017 + 0.951057i 0 2.14552 0
141.6 0 2.93296 0 3.52188 2.55880i 0 −0.309017 + 0.951057i 0 5.60225 0
365.1 0 −2.28641 0 −0.815322 + 2.50930i 0 0.809017 + 0.587785i 0 2.22766 0
365.2 0 −0.660580 0 0.860652 2.64881i 0 0.809017 + 0.587785i 0 −2.56363 0
365.3 0 0.327825 0 0.570293 1.75518i 0 0.809017 + 0.587785i 0 −2.89253 0
365.4 0 0.631465 0 −0.223347 + 0.687390i 0 0.809017 + 0.587785i 0 −2.60125 0
365.5 0 1.73388 0 0.0415270 0.127807i 0 0.809017 + 0.587785i 0 0.00632440 0
365.6 0 3.25382 0 1.02111 3.14266i 0 0.809017 + 0.587785i 0 7.58736 0
953.1 0 −2.28641 0 −0.815322 2.50930i 0 0.809017 0.587785i 0 2.22766 0
953.2 0 −0.660580 0 0.860652 + 2.64881i 0 0.809017 0.587785i 0 −2.56363 0
See all 24 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 953.6
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
41.d even 5 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 1148.2.n.e 24
41.d even 5 1 inner 1148.2.n.e 24
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1148.2.n.e 24 1.a even 1 1 trivial
1148.2.n.e 24 41.d even 5 1 inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \(T_{3}^{12} - \cdots\) acting on \(S_{2}^{\mathrm{new}}(1148, [\chi])\).