Properties

Label 983.2.a.a
Level $983$
Weight $2$
Character orbit 983.a
Self dual yes
Analytic conductor $7.849$
Analytic rank $1$
Dimension $28$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 983 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 983.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(7.84929451869\)
Analytic rank: \(1\)
Dimension: \(28\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 28 q - 7 q^{2} - 6 q^{3} + 17 q^{4} - 7 q^{5} - 7 q^{6} - 25 q^{7} - 15 q^{8} + 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 28 q - 7 q^{2} - 6 q^{3} + 17 q^{4} - 7 q^{5} - 7 q^{6} - 25 q^{7} - 15 q^{8} + 6 q^{9} - 17 q^{10} - 10 q^{11} - 10 q^{12} - 28 q^{13} + 5 q^{14} - 9 q^{15} + 3 q^{16} - 24 q^{17} - 23 q^{18} - 13 q^{19} - 4 q^{20} - 21 q^{21} - 21 q^{22} - 9 q^{23} - 19 q^{24} - 33 q^{25} + 2 q^{26} - 12 q^{27} - 58 q^{28} - 14 q^{29} - 8 q^{30} - 16 q^{31} - 27 q^{32} - 34 q^{33} - 6 q^{34} - 2 q^{35} - 6 q^{36} - 58 q^{37} + 6 q^{38} - 12 q^{39} - 24 q^{40} - 24 q^{41} + 22 q^{42} - 43 q^{43} - 19 q^{45} - 28 q^{46} + 2 q^{47} + 19 q^{48} - 21 q^{49} + 17 q^{50} - 6 q^{51} - 47 q^{52} - 16 q^{53} + 16 q^{54} - 16 q^{55} + 30 q^{56} - 70 q^{57} - 31 q^{58} + 12 q^{59} - q^{60} - 22 q^{61} - 15 q^{63} - 3 q^{64} - 24 q^{65} + 41 q^{66} - 38 q^{67} + 11 q^{68} + 2 q^{69} + 19 q^{70} + 2 q^{71} - 15 q^{72} - 124 q^{73} + 14 q^{74} + 8 q^{75} + 3 q^{76} - 20 q^{77} + 21 q^{78} - 16 q^{79} + 10 q^{80} - 36 q^{81} + 2 q^{82} + 12 q^{83} + 6 q^{84} - 73 q^{85} + 41 q^{86} - 15 q^{87} - 61 q^{88} - 3 q^{89} + 39 q^{90} + 5 q^{91} + 44 q^{92} - 21 q^{93} + 9 q^{94} + 17 q^{95} - 3 q^{96} - 105 q^{97} + 16 q^{98} - 15 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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 \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
1.1 −2.75257 2.22028 5.57661 0.543842 −6.11147 −3.48299 −9.84486 1.92965 −1.49696
1.2 −2.57328 −2.39055 4.62176 1.19059 6.15156 −1.20078 −6.74651 2.71475 −3.06371
1.3 −2.42034 −0.187530 3.85806 −0.842553 0.453886 −4.42798 −4.49714 −2.96483 2.03927
1.4 −2.21759 0.931642 2.91773 0.396530 −2.06600 2.27074 −2.03515 −2.13204 −0.879344
1.5 −2.05764 −2.81984 2.23388 0.650217 5.80222 0.324376 −0.481237 4.95151 −1.33791
1.6 −1.91443 1.82487 1.66503 2.84047 −3.49358 −3.81993 0.641279 0.330154 −5.43787
1.7 −1.85163 −0.818723 1.42855 −3.13539 1.51597 0.698052 1.05812 −2.32969 5.80559
1.8 −1.64859 2.69101 0.717863 −2.78854 −4.43639 −0.853736 2.11372 4.24155 4.59718
1.9 −1.64741 −0.803598 0.713964 2.48769 1.32386 2.09423 2.11863 −2.35423 −4.09824
1.10 −0.971766 −2.84689 −1.05567 −2.58229 2.76651 −3.41775 2.96940 5.10478 2.50939
1.11 −0.930689 −1.12871 −1.13382 3.65614 1.05048 −1.39504 2.91661 −1.72601 −3.40273
1.12 −0.875382 0.413140 −1.23371 0.141089 −0.361655 −0.646767 2.83073 −2.82932 −0.123507
1.13 −0.468024 −2.30825 −1.78095 −2.20940 1.08031 0.238349 1.76958 2.32800 1.03405
1.14 −0.434502 1.46359 −1.81121 −1.89683 −0.635931 1.45633 1.65598 −0.857914 0.824176
1.15 −0.400086 2.91622 −1.83993 0.291591 −1.16674 −3.58224 1.53630 5.50433 −0.116661
1.16 −0.120414 −1.94834 −1.98550 0.840169 0.234608 −0.0546560 0.479911 0.796025 −0.101168
1.17 0.0562061 0.611738 −1.99684 0.503583 0.0343834 3.25094 −0.224647 −2.62578 0.0283044
1.18 0.413754 0.397482 −1.82881 1.10128 0.164460 −2.64498 −1.58419 −2.84201 0.455658
1.19 0.768290 1.84565 −1.40973 −1.02856 1.41799 −1.07434 −2.61966 0.406425 −0.790236
1.20 0.912923 −2.89686 −1.16657 −1.17872 −2.64461 3.45815 −2.89084 5.39181 −1.07608
See all 28 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.28
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(983\) \(1\)

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 983.2.a.a 28
3.b odd 2 1 8847.2.a.b 28
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
983.2.a.a 28 1.a even 1 1 trivial
8847.2.a.b 28 3.b odd 2 1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{28} + 7 T_{2}^{27} - 12 T_{2}^{26} - 184 T_{2}^{25} - 110 T_{2}^{24} + 2026 T_{2}^{23} + 3083 T_{2}^{22} - 12045 T_{2}^{21} - 26802 T_{2}^{20} + 40855 T_{2}^{19} + 128063 T_{2}^{18} - 71590 T_{2}^{17} - 378054 T_{2}^{16} + \cdots + 7 \) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(983))\). Copy content Toggle raw display