Properties

Label 24.5.h
Level $24$
Weight $5$
Character orbit 24.h
Rep. character $\chi_{24}(5,\cdot)$
Character field $\Q$
Dimension $14$
Newform subspaces $3$
Sturm bound $20$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 24 = 2^{3} \cdot 3 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 24.h (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 24 \)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(20\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(24, [\chi])\).

Total New Old
Modular forms 18 18 0
Cusp forms 14 14 0
Eisenstein series 4 4 0

Trace form

\( 14 q + 12 q^{4} + 16 q^{6} - 4 q^{7} - 2 q^{9} + O(q^{10}) \) \( 14 q + 12 q^{4} + 16 q^{6} - 4 q^{7} - 2 q^{9} - 8 q^{10} - 20 q^{12} - 164 q^{15} - 152 q^{16} - 232 q^{18} - 912 q^{22} + 1064 q^{24} + 746 q^{25} + 1248 q^{28} + 2000 q^{30} + 124 q^{31} - 660 q^{33} + 2320 q^{34} - 2988 q^{36} - 1184 q^{39} - 5824 q^{40} - 5672 q^{42} - 7712 q^{46} + 9432 q^{48} - 822 q^{49} + 11632 q^{52} + 14240 q^{54} + 3384 q^{55} - 400 q^{57} + 18360 q^{58} - 20208 q^{60} + 5116 q^{63} - 21936 q^{64} - 24120 q^{66} - 29072 q^{70} + 29840 q^{72} - 3684 q^{73} + 36392 q^{76} + 36560 q^{78} - 11524 q^{79} + 4430 q^{81} + 45920 q^{82} - 47984 q^{84} - 9060 q^{87} - 52944 q^{88} - 62824 q^{90} - 57984 q^{94} + 65840 q^{96} + 3260 q^{97} + O(q^{100}) \)

Decomposition of \(S_{5}^{\mathrm{new}}(24, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
24.5.h.a 24.h 24.h $1$ $2.481$ \(\Q\) \(\Q(\sqrt{-6}) \) \(-4\) \(-9\) \(46\) \(2\) $\mathrm{U}(1)[D_{2}]$ \(q-4q^{2}-9q^{3}+2^{4}q^{4}+46q^{5}+6^{2}q^{6}+\cdots\)
24.5.h.b 24.h 24.h $1$ $2.481$ \(\Q\) \(\Q(\sqrt{-6}) \) \(4\) \(9\) \(-46\) \(2\) $\mathrm{U}(1)[D_{2}]$ \(q+4q^{2}+9q^{3}+2^{4}q^{4}-46q^{5}+6^{2}q^{6}+\cdots\)
24.5.h.c 24.h 24.h $12$ $2.481$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{3}q^{2}+\beta _{2}q^{3}+(-2+\beta _{5})q^{4}+(\beta _{1}+\cdots)q^{5}+\cdots\)