Properties

Label 24.6.d
Level $24$
Weight $6$
Character orbit 24.d
Rep. character $\chi_{24}(13,\cdot)$
Character field $\Q$
Dimension $10$
Newform subspaces $1$
Sturm bound $24$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 24 = 2^{3} \cdot 3 \)
Weight: \( k \) \(=\) \( 6 \)
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: \(24\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(24, [\chi])\).

Total New Old
Modular forms 22 10 12
Cusp forms 18 10 8
Eisenstein series 4 0 4

Trace form

\( 10 q + 2 q^{2} - 32 q^{4} + 90 q^{6} - 196 q^{7} + 68 q^{8} - 810 q^{9} - 868 q^{10} - 396 q^{12} + 3692 q^{14} + 900 q^{15} + 3064 q^{16} - 404 q^{17} - 162 q^{18} - 6376 q^{20} + 5888 q^{22} + 1672 q^{23}+ \cdots - 459846 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{6}^{\mathrm{new}}(24, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
24.6.d.a 24.d 8.b $10$ $3.849$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None 24.6.d.a \(2\) \(0\) \(0\) \(-196\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{2}-\beta _{1}q^{3}+(-3-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(24, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(24, [\chi]) \simeq \) \(S_{6}^{\mathrm{new}}(8, [\chi])\)\(^{\oplus 2}\)