Properties

Label 24.2.d
Level 24
Weight 2
Character orbit d
Rep. character \(\chi_{24}(13,\cdot)\)
Character field \(\Q\)
Dimension 2
Newform subspaces 1
Sturm bound 8
Trace bound 0

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Defining parameters

Level: \( N \) = \( 24 = 2^{3} \cdot 3 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 24.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 8 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(8\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(24, [\chi])\).

Total New Old
Modular forms 6 2 4
Cusp forms 2 2 0
Eisenstein series 4 0 4

Trace form

\( 2q - 2q^{2} - 2q^{6} - 4q^{7} + 4q^{8} - 2q^{9} + O(q^{10}) \) \( 2q - 2q^{2} - 2q^{6} - 4q^{7} + 4q^{8} - 2q^{9} + 4q^{10} + 4q^{12} + 4q^{14} + 4q^{15} - 8q^{16} - 4q^{17} + 2q^{18} - 8q^{20} + 8q^{23} - 4q^{24} + 2q^{25} - 8q^{26} - 4q^{30} + 4q^{31} + 8q^{32} + 4q^{34} + 8q^{38} - 8q^{39} + 8q^{40} + 4q^{41} + 4q^{42} - 8q^{46} - 24q^{47} - 6q^{49} - 2q^{50} + 16q^{52} + 2q^{54} - 8q^{56} + 8q^{57} - 12q^{58} - 4q^{62} + 4q^{63} + 16q^{65} - 8q^{70} + 24q^{71} - 4q^{72} - 12q^{73} + 16q^{74} - 16q^{76} + 8q^{78} + 20q^{79} + 2q^{81} - 4q^{82} - 8q^{84} - 8q^{86} - 12q^{87} - 20q^{89} - 4q^{90} + 24q^{94} - 16q^{95} + 8q^{96} - 4q^{97} + 6q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(24, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
24.2.d.a \(2\) \(0.192\) \(\Q(\sqrt{-1}) \) None \(-2\) \(0\) \(0\) \(-4\) \(q+(-1+i)q^{2}+iq^{3}-2iq^{4}-2iq^{5}+\cdots\)

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ \( 1 + 2 T + 2 T^{2} \)
$3$ \( 1 + T^{2} \)
$5$ \( ( 1 - 4 T + 5 T^{2} )( 1 + 4 T + 5 T^{2} ) \)
$7$ \( ( 1 + 2 T + 7 T^{2} )^{2} \)
$11$ \( ( 1 - 11 T^{2} )^{2} \)
$13$ \( ( 1 - 6 T + 13 T^{2} )( 1 + 6 T + 13 T^{2} ) \)
$17$ \( ( 1 + 2 T + 17 T^{2} )^{2} \)
$19$ \( 1 - 22 T^{2} + 361 T^{4} \)
$23$ \( ( 1 - 4 T + 23 T^{2} )^{2} \)
$29$ \( 1 - 22 T^{2} + 841 T^{4} \)
$31$ \( ( 1 - 2 T + 31 T^{2} )^{2} \)
$37$ \( 1 - 10 T^{2} + 1369 T^{4} \)
$41$ \( ( 1 - 2 T + 41 T^{2} )^{2} \)
$43$ \( 1 - 70 T^{2} + 1849 T^{4} \)
$47$ \( ( 1 + 12 T + 47 T^{2} )^{2} \)
$53$ \( 1 - 70 T^{2} + 2809 T^{4} \)
$59$ \( 1 - 102 T^{2} + 3481 T^{4} \)
$61$ \( ( 1 - 61 T^{2} )^{2} \)
$67$ \( 1 + 10 T^{2} + 4489 T^{4} \)
$71$ \( ( 1 - 12 T + 71 T^{2} )^{2} \)
$73$ \( ( 1 + 6 T + 73 T^{2} )^{2} \)
$79$ \( ( 1 - 10 T + 79 T^{2} )^{2} \)
$83$ \( 1 + 90 T^{2} + 6889 T^{4} \)
$89$ \( ( 1 + 10 T + 89 T^{2} )^{2} \)
$97$ \( ( 1 + 2 T + 97 T^{2} )^{2} \)
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