Properties

Label 24.8.a
Level 24
Weight 8
Character orbit a
Rep. character \(\chi_{24}(1,\cdot)\)
Character field \(\Q\)
Dimension 3
Newform subspaces 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: \(\Q\)
Newform subspaces: \( 3 \)
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

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

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_0(24))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 3
24.8.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

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

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ 1
$3$ (\( 1 + 27 T \))(\( 1 - 27 T \))(\( 1 - 27 T \))
$5$ (\( 1 + 26 T + 78125 T^{2} \))(\( 1 + 530 T + 78125 T^{2} \))(\( 1 - 110 T + 78125 T^{2} \))
$7$ (\( 1 - 1056 T + 823543 T^{2} \))(\( 1 - 120 T + 823543 T^{2} \))(\( 1 - 504 T + 823543 T^{2} \))
$11$ (\( 1 - 6412 T + 19487171 T^{2} \))(\( 1 + 7196 T + 19487171 T^{2} \))(\( 1 - 3812 T + 19487171 T^{2} \))
$13$ (\( 1 - 5206 T + 62748517 T^{2} \))(\( 1 + 9626 T + 62748517 T^{2} \))(\( 1 - 9574 T + 62748517 T^{2} \))
$17$ (\( 1 + 6238 T + 410338673 T^{2} \))(\( 1 - 18674 T + 410338673 T^{2} \))(\( 1 - 26098 T + 410338673 T^{2} \))
$19$ (\( 1 - 41492 T + 893871739 T^{2} \))(\( 1 - 7004 T + 893871739 T^{2} \))(\( 1 + 38308 T + 893871739 T^{2} \))
$23$ (\( 1 + 29432 T + 3404825447 T^{2} \))(\( 1 + 63704 T + 3404825447 T^{2} \))(\( 1 + 71128 T + 3404825447 T^{2} \))
$29$ (\( 1 + 210498 T + 17249876309 T^{2} \))(\( 1 - 29334 T + 17249876309 T^{2} \))(\( 1 - 74262 T + 17249876309 T^{2} \))
$31$ (\( 1 - 185240 T + 27512614111 T^{2} \))(\( 1 - 87968 T + 27512614111 T^{2} \))(\( 1 + 275680 T + 27512614111 T^{2} \))
$37$ (\( 1 - 507630 T + 94931877133 T^{2} \))(\( 1 - 227982 T + 94931877133 T^{2} \))(\( 1 + 266610 T + 94931877133 T^{2} \))
$41$ (\( 1 - 360042 T + 194754273881 T^{2} \))(\( 1 + 160806 T + 194754273881 T^{2} \))(\( 1 - 684762 T + 194754273881 T^{2} \))
$43$ (\( 1 - 620044 T + 271818611107 T^{2} \))(\( 1 - 136132 T + 271818611107 T^{2} \))(\( 1 - 245956 T + 271818611107 T^{2} \))
$47$ (\( 1 + 847680 T + 506623120463 T^{2} \))(\( 1 + 1206960 T + 506623120463 T^{2} \))(\( 1 - 478800 T + 506623120463 T^{2} \))
$53$ (\( 1 - 1423750 T + 1174711139837 T^{2} \))(\( 1 + 398786 T + 1174711139837 T^{2} \))(\( 1 + 569410 T + 1174711139837 T^{2} \))
$59$ (\( 1 + 2548724 T + 2488651484819 T^{2} \))(\( 1 - 1152436 T + 2488651484819 T^{2} \))(\( 1 + 1525324 T + 2488651484819 T^{2} \))
$61$ (\( 1 + 706058 T + 3142742836021 T^{2} \))(\( 1 + 2070602 T + 3142742836021 T^{2} \))(\( 1 + 2640458 T + 3142742836021 T^{2} \))
$67$ (\( 1 + 2418796 T + 6060711605323 T^{2} \))(\( 1 + 4073428 T + 6060711605323 T^{2} \))(\( 1 - 1416236 T + 6060711605323 T^{2} \))
$71$ (\( 1 - 265976 T + 9095120158391 T^{2} \))(\( 1 + 383752 T + 9095120158391 T^{2} \))(\( 1 + 3511304 T + 9095120158391 T^{2} \))
$73$ (\( 1 + 5791238 T + 11047398519097 T^{2} \))(\( 1 - 3006010 T + 11047398519097 T^{2} \))(\( 1 - 4738618 T + 11047398519097 T^{2} \))
$79$ (\( 1 - 2955688 T + 19203908986159 T^{2} \))(\( 1 + 4948112 T + 19203908986159 T^{2} \))(\( 1 - 4661488 T + 19203908986159 T^{2} \))
$83$ (\( 1 - 3462932 T + 27136050989627 T^{2} \))(\( 1 + 9163492 T + 27136050989627 T^{2} \))(\( 1 + 5729252 T + 27136050989627 T^{2} \))
$89$ (\( 1 + 2211126 T + 44231334895529 T^{2} \))(\( 1 - 7304106 T + 44231334895529 T^{2} \))(\( 1 - 11993514 T + 44231334895529 T^{2} \))
$97$ (\( 1 + 15594814 T + 80798284478113 T^{2} \))(\( 1 + 690526 T + 80798284478113 T^{2} \))(\( 1 - 7150754 T + 80798284478113 T^{2} \))
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