Properties

Label 24.4.a
Level 24
Weight 4
Character orbit a
Rep. character \(\chi_{24}(1,\cdot)\)
Character field \(\Q\)
Dimension 1
Newform subspaces 1
Sturm bound 16
Trace bound 0

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Defining parameters

Level: \( N \) \(=\) \( 24 = 2^{3} \cdot 3 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 24.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(16\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(24))\).

Total New Old
Modular forms 16 1 15
Cusp forms 8 1 7
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.
\(-\)\(-\)\(+\)\(1\)
Plus space\(+\)\(1\)
Minus space\(-\)\(0\)

Trace form

\( q + 3q^{3} + 14q^{5} - 24q^{7} + 9q^{9} + O(q^{10}) \) \( q + 3q^{3} + 14q^{5} - 24q^{7} + 9q^{9} - 28q^{11} - 74q^{13} + 42q^{15} + 82q^{17} + 92q^{19} - 72q^{21} + 8q^{23} + 71q^{25} + 27q^{27} - 138q^{29} + 80q^{31} - 84q^{33} - 336q^{35} + 30q^{37} - 222q^{39} + 282q^{41} + 4q^{43} + 126q^{45} + 240q^{47} + 233q^{49} + 246q^{51} - 130q^{53} - 392q^{55} + 276q^{57} + 596q^{59} - 218q^{61} - 216q^{63} - 1036q^{65} - 436q^{67} + 24q^{69} + 856q^{71} - 998q^{73} + 213q^{75} + 672q^{77} - 32q^{79} + 81q^{81} - 1508q^{83} + 1148q^{85} - 414q^{87} - 246q^{89} + 1776q^{91} + 240q^{93} + 1288q^{95} + 866q^{97} - 252q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(24))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 3
24.4.a.a \(1\) \(1.416\) \(\Q\) None \(0\) \(3\) \(14\) \(-24\) \(-\) \(-\) \(q+3q^{3}+14q^{5}-24q^{7}+9q^{9}-28q^{11}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(24))\) into lower level spaces

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

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ 1
$3$ \( 1 - 3 T \)
$5$ \( 1 - 14 T + 125 T^{2} \)
$7$ \( 1 + 24 T + 343 T^{2} \)
$11$ \( 1 + 28 T + 1331 T^{2} \)
$13$ \( 1 + 74 T + 2197 T^{2} \)
$17$ \( 1 - 82 T + 4913 T^{2} \)
$19$ \( 1 - 92 T + 6859 T^{2} \)
$23$ \( 1 - 8 T + 12167 T^{2} \)
$29$ \( 1 + 138 T + 24389 T^{2} \)
$31$ \( 1 - 80 T + 29791 T^{2} \)
$37$ \( 1 - 30 T + 50653 T^{2} \)
$41$ \( 1 - 282 T + 68921 T^{2} \)
$43$ \( 1 - 4 T + 79507 T^{2} \)
$47$ \( 1 - 240 T + 103823 T^{2} \)
$53$ \( 1 + 130 T + 148877 T^{2} \)
$59$ \( 1 - 596 T + 205379 T^{2} \)
$61$ \( 1 + 218 T + 226981 T^{2} \)
$67$ \( 1 + 436 T + 300763 T^{2} \)
$71$ \( 1 - 856 T + 357911 T^{2} \)
$73$ \( 1 + 998 T + 389017 T^{2} \)
$79$ \( 1 + 32 T + 493039 T^{2} \)
$83$ \( 1 + 1508 T + 571787 T^{2} \)
$89$ \( 1 + 246 T + 704969 T^{2} \)
$97$ \( 1 - 866 T + 912673 T^{2} \)
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