Properties

Label 24.6.a
Level $24$
Weight $6$
Character orbit 24.a
Rep. character $\chi_{24}(1,\cdot)$
Character field $\Q$
Dimension $3$
Newform subspaces $3$
Sturm bound $24$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 24 = 2^{3} \cdot 3 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 24.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(24\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_0(24))\).

Total New Old
Modular forms 24 3 21
Cusp forms 16 3 13
Eisenstein series 8 0 8

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)\(3\)FrickeDim
\(+\)\(+\)$+$\(1\)
\(+\)\(-\)$-$\(1\)
\(-\)\(+\)$-$\(1\)
Plus space\(+\)\(1\)
Minus space\(-\)\(2\)

Trace form

\( 3 q - 9 q^{3} + 98 q^{5} + 24 q^{7} + 243 q^{9} + O(q^{10}) \) \( 3 q - 9 q^{3} + 98 q^{5} + 24 q^{7} + 243 q^{9} + 20 q^{11} - 102 q^{13} - 198 q^{15} - 266 q^{17} - 5364 q^{19} + 1944 q^{21} + 4904 q^{23} + 2061 q^{25} - 729 q^{27} - 10422 q^{29} + 1920 q^{31} + 9252 q^{33} + 26256 q^{35} - 1662 q^{37} - 16398 q^{39} - 23202 q^{41} - 13068 q^{43} + 7938 q^{45} + 3216 q^{47} + 42315 q^{49} - 22050 q^{51} - 64846 q^{53} - 11592 q^{55} + 7164 q^{57} + 51236 q^{59} + 37098 q^{61} + 1944 q^{63} + 38396 q^{65} - 11364 q^{67} + 1800 q^{69} - 32264 q^{71} + 24510 q^{73} - 48807 q^{75} + 37920 q^{77} + 39120 q^{79} + 19683 q^{81} - 57524 q^{83} - 199068 q^{85} + 165186 q^{87} + 32046 q^{89} - 9264 q^{91} - 71136 q^{93} - 130040 q^{95} - 180954 q^{97} + 1620 q^{99} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_0(24))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 3
24.6.a.a 24.a 1.a $1$ $3.849$ \(\Q\) None \(0\) \(-9\) \(-34\) \(-240\) $+$ $+$ $\mathrm{SU}(2)$ \(q-9q^{3}-34q^{5}-240q^{7}+3^{4}q^{9}+\cdots\)
24.6.a.b 24.a 1.a $1$ $3.849$ \(\Q\) None \(0\) \(-9\) \(94\) \(144\) $-$ $+$ $\mathrm{SU}(2)$ \(q-9q^{3}+94q^{5}+12^{2}q^{7}+3^{4}q^{9}+\cdots\)
24.6.a.c 24.a 1.a $1$ $3.849$ \(\Q\) None \(0\) \(9\) \(38\) \(120\) $+$ $-$ $\mathrm{SU}(2)$ \(q+9q^{3}+38q^{5}+120q^{7}+3^{4}q^{9}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_0(24))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_0(24)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_0(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(4))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(6))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(8))\)\(^{\oplus 2}\)