Properties

Label 24.2.d
Level $24$
Weight $2$
Character orbit 24.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

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

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

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
24.2.d.a 24.d 8.b $2$ $0.192$ \(\Q(\sqrt{-1}) \) None 24.2.d.a \(-2\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-1+i)q^{2}+iq^{3}-2iq^{4}-2iq^{5}+\cdots\)