Properties

Label 24.5.e
Level $24$
Weight $5$
Character orbit 24.e
Rep. character $\chi_{24}(17,\cdot)$
Character field $\Q$
Dimension $4$
Newform subspaces $1$
Sturm bound $20$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 24 = 2^{3} \cdot 3 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 24.e (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(20\)
Trace bound: \(0\)

Dimensions

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

Total New Old
Modular forms 20 4 16
Cusp forms 12 4 8
Eisenstein series 8 0 8

Trace form

\( 4 q - 4 q^{3} + 24 q^{7} + 100 q^{9} + O(q^{10}) \) \( 4 q - 4 q^{3} + 24 q^{7} + 100 q^{9} - 248 q^{13} - 544 q^{15} + 824 q^{19} + 1224 q^{21} - 2044 q^{25} - 1540 q^{27} + 3800 q^{31} + 2528 q^{33} - 2808 q^{37} - 4744 q^{39} - 968 q^{43} + 2752 q^{45} - 1972 q^{49} + 3712 q^{51} + 4672 q^{55} - 2072 q^{57} + 8584 q^{61} - 4392 q^{63} - 15112 q^{67} - 7360 q^{69} + 5512 q^{73} + 27004 q^{75} - 1064 q^{79} - 14588 q^{81} + 2816 q^{85} - 7008 q^{87} - 31440 q^{91} - 17528 q^{93} + 32456 q^{97} + 36544 q^{99} + O(q^{100}) \)

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.e.a 24.e 3.b $4$ $2.481$ \(\Q(\sqrt{-2}, \sqrt{13})\) None \(0\) \(-4\) \(0\) \(24\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-1-\beta _{1})q^{3}+(-2\beta _{1}+\beta _{2}+\beta _{3})q^{5}+\cdots\)

Decomposition of \(S_{5}^{\mathrm{old}}(24, [\chi])\) into lower level spaces

\( S_{5}^{\mathrm{old}}(24, [\chi]) \cong \) \(S_{5}^{\mathrm{new}}(6, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 2}\)