Properties

Label 8.4.b
Level 8
Weight 4
Character orbit b
Rep. character \(\chi_{8}(5,\cdot)\)
Character field \(\Q\)
Dimension 2
Newform subspaces 1
Sturm bound 4
Trace bound 0

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Defining parameters

Level: \( N \) \(=\) \( 8 = 2^{3} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 8.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 8 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(4\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(8, [\chi])\).

Total New Old
Modular forms 4 4 0
Cusp forms 2 2 0
Eisenstein series 2 2 0

Trace form

\( 2q - 2q^{2} - 12q^{4} + 28q^{6} - 16q^{7} + 40q^{8} - 2q^{9} + O(q^{10}) \) \( 2q - 2q^{2} - 12q^{4} + 28q^{6} - 16q^{7} + 40q^{8} - 2q^{9} - 56q^{10} - 56q^{12} + 16q^{14} + 112q^{15} + 16q^{16} - 28q^{17} + 2q^{18} + 112q^{20} - 84q^{22} - 304q^{23} - 112q^{24} + 26q^{25} + 280q^{26} + 96q^{28} - 112q^{30} + 448q^{31} - 352q^{32} + 168q^{33} + 28q^{34} + 12q^{36} - 196q^{38} - 560q^{39} + 224q^{40} - 140q^{41} - 224q^{42} + 168q^{44} + 304q^{46} + 672q^{47} + 672q^{48} - 558q^{49} - 26q^{50} - 560q^{52} + 728q^{54} - 336q^{55} - 320q^{56} + 392q^{57} - 840q^{58} - 672q^{60} - 448q^{62} + 16q^{63} + 576q^{64} + 1120q^{65} - 168q^{66} + 168q^{68} + 448q^{70} - 144q^{71} - 40q^{72} - 588q^{73} + 1288q^{74} + 392q^{76} + 560q^{78} - 928q^{79} - 1344q^{80} - 1510q^{81} + 140q^{82} + 448q^{84} - 2324q^{86} + 1680q^{87} + 336q^{88} + 532q^{89} + 56q^{90} + 1824q^{92} - 672q^{94} - 784q^{95} - 448q^{96} + 1988q^{97} + 558q^{98} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(8, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
8.4.b.a \(2\) \(0.472\) \(\Q(\sqrt{-7}) \) None \(-2\) \(0\) \(0\) \(-16\) \(q+(-1-\beta )q^{2}+2\beta q^{3}+(-6+2\beta )q^{4}+\cdots\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( 1 + 2 T + 8 T^{2} \)
$3$ \( 1 - 26 T^{2} + 729 T^{4} \)
$5$ \( 1 - 138 T^{2} + 15625 T^{4} \)
$7$ \( ( 1 + 8 T + 343 T^{2} )^{2} \)
$11$ \( 1 - 2410 T^{2} + 1771561 T^{4} \)
$13$ \( 1 - 1594 T^{2} + 4826809 T^{4} \)
$17$ \( ( 1 + 14 T + 4913 T^{2} )^{2} \)
$19$ \( 1 - 12346 T^{2} + 47045881 T^{4} \)
$23$ \( ( 1 + 152 T + 12167 T^{2} )^{2} \)
$29$ \( 1 - 23578 T^{2} + 594823321 T^{4} \)
$31$ \( ( 1 - 224 T + 29791 T^{2} )^{2} \)
$37$ \( 1 - 42058 T^{2} + 2565726409 T^{4} \)
$41$ \( ( 1 + 70 T + 68921 T^{2} )^{2} \)
$43$ \( 1 + 33878 T^{2} + 6321363049 T^{4} \)
$47$ \( ( 1 - 336 T + 103823 T^{2} )^{2} \)
$53$ \( 1 - 296746 T^{2} + 22164361129 T^{4} \)
$59$ \( 1 - 125130 T^{2} + 42180533641 T^{4} \)
$61$ \( 1 - 444890 T^{2} + 51520374361 T^{4} \)
$67$ \( 1 - 571034 T^{2} + 90458382169 T^{4} \)
$71$ \( ( 1 + 72 T + 357911 T^{2} )^{2} \)
$73$ \( ( 1 + 294 T + 389017 T^{2} )^{2} \)
$79$ \( ( 1 + 464 T + 493039 T^{2} )^{2} \)
$83$ \( 1 - 846522 T^{2} + 326940373369 T^{4} \)
$89$ \( ( 1 - 266 T + 704969 T^{2} )^{2} \)
$97$ \( ( 1 - 994 T + 912673 T^{2} )^{2} \)
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