Properties

Label 8.3.d
Level 8
Weight 3
Character orbit d
Rep. character \(\chi_{8}(3,\cdot)\)
Character field \(\Q\)
Dimension 1
Newform subspaces 1
Sturm bound 3
Trace bound 0

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Defining parameters

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

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(8, [\chi])\).

Total New Old
Modular forms 3 3 0
Cusp forms 1 1 0
Eisenstein series 2 2 0

Trace form

\( q - 2q^{2} - 2q^{3} + 4q^{4} + 4q^{6} - 8q^{8} - 5q^{9} + O(q^{10}) \) \( q - 2q^{2} - 2q^{3} + 4q^{4} + 4q^{6} - 8q^{8} - 5q^{9} + 14q^{11} - 8q^{12} + 16q^{16} + 2q^{17} + 10q^{18} - 34q^{19} - 28q^{22} + 16q^{24} + 25q^{25} + 28q^{27} - 32q^{32} - 28q^{33} - 4q^{34} - 20q^{36} + 68q^{38} - 46q^{41} + 14q^{43} + 56q^{44} - 32q^{48} + 49q^{49} - 50q^{50} - 4q^{51} - 56q^{54} + 68q^{57} - 82q^{59} + 64q^{64} + 56q^{66} + 62q^{67} + 8q^{68} + 40q^{72} - 142q^{73} - 50q^{75} - 136q^{76} - 11q^{81} + 92q^{82} + 158q^{83} - 28q^{86} - 112q^{88} + 146q^{89} + 64q^{96} - 94q^{97} - 98q^{98} - 70q^{99} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(8, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
8.3.d.a \(1\) \(0.218\) \(\Q\) \(\Q(\sqrt{-2}) \) \(-2\) \(-2\) \(0\) \(0\) \(q-2q^{2}-2q^{3}+4q^{4}+4q^{6}-8q^{8}+\cdots\)

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ \( 1 + 2 T \)
$3$ \( 1 + 2 T + 9 T^{2} \)
$5$ \( ( 1 - 5 T )( 1 + 5 T ) \)
$7$ \( ( 1 - 7 T )( 1 + 7 T ) \)
$11$ \( 1 - 14 T + 121 T^{2} \)
$13$ \( ( 1 - 13 T )( 1 + 13 T ) \)
$17$ \( 1 - 2 T + 289 T^{2} \)
$19$ \( 1 + 34 T + 361 T^{2} \)
$23$ \( ( 1 - 23 T )( 1 + 23 T ) \)
$29$ \( ( 1 - 29 T )( 1 + 29 T ) \)
$31$ \( ( 1 - 31 T )( 1 + 31 T ) \)
$37$ \( ( 1 - 37 T )( 1 + 37 T ) \)
$41$ \( 1 + 46 T + 1681 T^{2} \)
$43$ \( 1 - 14 T + 1849 T^{2} \)
$47$ \( ( 1 - 47 T )( 1 + 47 T ) \)
$53$ \( ( 1 - 53 T )( 1 + 53 T ) \)
$59$ \( 1 + 82 T + 3481 T^{2} \)
$61$ \( ( 1 - 61 T )( 1 + 61 T ) \)
$67$ \( 1 - 62 T + 4489 T^{2} \)
$71$ \( ( 1 - 71 T )( 1 + 71 T ) \)
$73$ \( 1 + 142 T + 5329 T^{2} \)
$79$ \( ( 1 - 79 T )( 1 + 79 T ) \)
$83$ \( 1 - 158 T + 6889 T^{2} \)
$89$ \( 1 - 146 T + 7921 T^{2} \)
$97$ \( 1 + 94 T + 9409 T^{2} \)
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