Properties

Label 24.6.a
Level 24
Weight 6
Character orbit a
Rep. character \(\chi_{24}(1,\cdot)\)
Character field \(\Q\)
Dimension 3
Newforms 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: \(\Q\)
Newforms: \( 3 \)
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

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

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_0(24))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 3
24.6.a.a \(1\) \(3.849\) \(\Q\) None \(0\) \(-9\) \(-34\) \(-240\) \(+\) \(+\) \(q-9q^{3}-34q^{5}-240q^{7}+3^{4}q^{9}+\cdots\)
24.6.a.b \(1\) \(3.849\) \(\Q\) None \(0\) \(-9\) \(94\) \(144\) \(-\) \(+\) \(q-9q^{3}+94q^{5}+12^{2}q^{7}+3^{4}q^{9}+\cdots\)
24.6.a.c \(1\) \(3.849\) \(\Q\) None \(0\) \(9\) \(38\) \(120\) \(+\) \(-\) \(q+9q^{3}+38q^{5}+120q^{7}+3^{4}q^{9}+\cdots\)

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

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