Properties

Label 24.8.a
Level 24
Weight 8
Character orbit a
Rep. character \(\chi_{24}(1,\cdot)\)
Character field \(\Q\)
Dimension 3
Newforms 3
Sturm bound 32
Trace bound 5

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Defining parameters

Level: \( N \) = \( 24 = 2^{3} \cdot 3 \)
Weight: \( k \) = \( 8 \)
Character orbit: \([\chi]\) = 24.a (trivial)
Character field: \(\Q\)
Newforms: \( 3 \)
Sturm bound: \(32\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_0(24))\).

Total New Old
Modular forms 32 3 29
Cusp forms 24 3 21
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\(+\)\(2\)
Minus space\(-\)\(1\)

Trace form

\(3q \) \(\mathstrut +\mathstrut 27q^{3} \) \(\mathstrut -\mathstrut 446q^{5} \) \(\mathstrut +\mathstrut 1680q^{7} \) \(\mathstrut +\mathstrut 2187q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(3q \) \(\mathstrut +\mathstrut 27q^{3} \) \(\mathstrut -\mathstrut 446q^{5} \) \(\mathstrut +\mathstrut 1680q^{7} \) \(\mathstrut +\mathstrut 2187q^{9} \) \(\mathstrut +\mathstrut 3028q^{11} \) \(\mathstrut +\mathstrut 5154q^{13} \) \(\mathstrut -\mathstrut 10638q^{15} \) \(\mathstrut +\mathstrut 38534q^{17} \) \(\mathstrut +\mathstrut 10188q^{19} \) \(\mathstrut -\mathstrut 11664q^{21} \) \(\mathstrut -\mathstrut 164264q^{23} \) \(\mathstrut +\mathstrut 59301q^{25} \) \(\mathstrut +\mathstrut 19683q^{27} \) \(\mathstrut -\mathstrut 106902q^{29} \) \(\mathstrut -\mathstrut 2472q^{31} \) \(\mathstrut -\mathstrut 264492q^{33} \) \(\mathstrut -\mathstrut 35616q^{35} \) \(\mathstrut +\mathstrut 469002q^{37} \) \(\mathstrut -\mathstrut 141966q^{39} \) \(\mathstrut +\mathstrut 883998q^{41} \) \(\mathstrut +\mathstrut 1002132q^{43} \) \(\mathstrut -\mathstrut 325134q^{45} \) \(\mathstrut -\mathstrut 1575840q^{47} \) \(\mathstrut -\mathstrut 1087077q^{49} \) \(\mathstrut +\mathstrut 1377270q^{51} \) \(\mathstrut +\mathstrut 455554q^{53} \) \(\mathstrut +\mathstrut 4066488q^{55} \) \(\mathstrut -\mathstrut 1965492q^{57} \) \(\mathstrut -\mathstrut 2921612q^{59} \) \(\mathstrut -\mathstrut 5417118q^{61} \) \(\mathstrut +\mathstrut 1224720q^{63} \) \(\mathstrut +\mathstrut 6019564q^{65} \) \(\mathstrut -\mathstrut 5075988q^{67} \) \(\mathstrut -\mathstrut 2845800q^{69} \) \(\mathstrut -\mathstrut 3629080q^{71} \) \(\mathstrut +\mathstrut 1953390q^{73} \) \(\mathstrut +\mathstrut 5783373q^{75} \) \(\mathstrut +\mathstrut 7828800q^{77} \) \(\mathstrut +\mathstrut 2669064q^{79} \) \(\mathstrut +\mathstrut 1594323q^{81} \) \(\mathstrut -\mathstrut 11429812q^{83} \) \(\mathstrut -\mathstrut 6864252q^{85} \) \(\mathstrut +\mathstrut 8480538q^{87} \) \(\mathstrut +\mathstrut 17086494q^{89} \) \(\mathstrut +\mathstrut 9167712q^{91} \) \(\mathstrut -\mathstrut 10069704q^{93} \) \(\mathstrut -\mathstrut 9004792q^{95} \) \(\mathstrut -\mathstrut 9134586q^{97} \) \(\mathstrut +\mathstrut 2207412q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_0(24))\) 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
24.8.a.a \(1\) \(7.497\) \(\Q\) None \(0\) \(-27\) \(-26\) \(1056\) \(+\) \(+\) \(q-3^{3}q^{3}-26q^{5}+1056q^{7}+3^{6}q^{9}+\cdots\)
24.8.a.b \(1\) \(7.497\) \(\Q\) None \(0\) \(27\) \(-530\) \(120\) \(+\) \(-\) \(q+3^{3}q^{3}-530q^{5}+120q^{7}+3^{6}q^{9}+\cdots\)
24.8.a.c \(1\) \(7.497\) \(\Q\) None \(0\) \(27\) \(110\) \(504\) \(-\) \(-\) \(q+3^{3}q^{3}+110q^{5}+504q^{7}+3^{6}q^{9}+\cdots\)

Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_0(24))\) into lower level spaces

\( S_{8}^{\mathrm{old}}(\Gamma_0(24)) \cong \) \(S_{8}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_0(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_0(6))\)\(^{\oplus 3}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_0(8))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_0(12))\)\(^{\oplus 2}\)