Properties

Label 24.4.d
Level 24
Weight 4
Character orbit d
Rep. character \(\chi_{24}(13,\cdot)\)
Character field \(\Q\)
Dimension 6
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.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 8 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(16\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(24, [\chi])\).

Total New Old
Modular forms 14 6 8
Cusp forms 10 6 4
Eisenstein series 4 0 4

Trace form

\( 6q + 2q^{2} + 16q^{4} - 6q^{6} + 28q^{7} - 76q^{8} - 54q^{9} + O(q^{10}) \) \( 6q + 2q^{2} + 16q^{4} - 6q^{6} + 28q^{7} - 76q^{8} - 54q^{9} + 60q^{10} - 12q^{12} - 100q^{14} - 60q^{15} + 56q^{16} + 52q^{17} - 18q^{18} + 56q^{20} + 224q^{22} + 328q^{23} + 204q^{24} - 106q^{25} + 56q^{26} - 352q^{28} + 372q^{30} - 636q^{31} - 248q^{32} - 548q^{34} - 144q^{36} - 776q^{38} + 312q^{39} + 232q^{40} + 236q^{41} - 564q^{42} + 1152q^{44} + 328q^{46} - 408q^{47} + 576q^{48} + 654q^{49} + 1970q^{50} - 368q^{52} + 54q^{54} + 1024q^{55} - 1864q^{56} - 168q^{57} + 140q^{58} - 1152q^{60} - 2108q^{62} - 252q^{63} + 832q^{64} - 1744q^{65} - 1440q^{66} + 2976q^{68} + 1352q^{70} - 1704q^{71} + 684q^{72} + 956q^{73} + 1568q^{74} - 1744q^{76} + 1608q^{78} - 44q^{79} - 2112q^{80} + 486q^{81} - 2236q^{82} - 1992q^{84} - 760q^{86} + 1044q^{87} + 1856q^{88} - 220q^{89} - 540q^{90} + 1728q^{92} + 2088q^{94} + 5104q^{95} + 2184q^{96} - 2444q^{97} + 3354q^{98} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(24, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
24.4.d.a \(6\) \(1.416\) 6.0.8248384.1 None \(2\) \(0\) \(0\) \(28\) \(q+\beta _{3}q^{2}+\beta _{1}q^{3}+(3-\beta _{5})q^{4}+(2\beta _{1}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(24, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(24, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(8, [\chi])\)\(^{\oplus 2}\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( 1 - 2 T - 6 T^{2} + 40 T^{3} - 48 T^{4} - 128 T^{5} + 512 T^{6} \)
$3$ \( ( 1 + 9 T^{2} )^{3} \)
$5$ \( 1 - 322 T^{2} + 49351 T^{4} - 6170684 T^{6} + 771109375 T^{8} - 78613281250 T^{10} + 3814697265625 T^{12} \)
$7$ \( ( 1 - 14 T + 449 T^{2} - 3788 T^{3} + 154007 T^{4} - 1647086 T^{5} + 40353607 T^{6} )^{2} \)
$11$ \( 1 - 2354 T^{2} + 4518503 T^{4} - 5987722076 T^{6} + 8004803693183 T^{8} - 7387860398801234 T^{10} + 5559917313492231481 T^{12} \)
$13$ \( 1 - 8270 T^{2} + 36264983 T^{4} - 97600232804 T^{6} + 175044146329247 T^{8} - 192675163962917870 T^{10} + \)\(11\!\cdots\!29\)\( T^{12} \)
$17$ \( ( 1 - 26 T + 3615 T^{2} + 222100 T^{3} + 17760495 T^{4} - 627576794 T^{5} + 118587876497 T^{6} )^{2} \)
$19$ \( 1 - 18194 T^{2} + 183315287 T^{4} - 1372700323292 T^{6} + 8624229177682847 T^{8} - 40269051637489733234 T^{10} + \)\(10\!\cdots\!41\)\( T^{12} \)
$23$ \( ( 1 - 164 T + 42885 T^{2} - 4036280 T^{3} + 521781795 T^{4} - 24277885796 T^{5} + 1801152661463 T^{6} )^{2} \)
$29$ \( 1 - 123986 T^{2} + 6779237687 T^{4} - 212188653261788 T^{6} + 4032448674829698527 T^{8} - \)\(43\!\cdots\!26\)\( T^{10} + \)\(21\!\cdots\!61\)\( T^{12} \)
$31$ \( ( 1 + 318 T + 93849 T^{2} + 15197452 T^{3} + 2795855559 T^{4} + 282226170558 T^{5} + 26439622160671 T^{6} )^{2} \)
$37$ \( 1 - 124142 T^{2} + 4233590471 T^{4} - 51775900405988 T^{6} + 10862234876335448639 T^{8} - \)\(81\!\cdots\!02\)\( T^{10} + \)\(16\!\cdots\!29\)\( T^{12} \)
$41$ \( ( 1 - 118 T + 89463 T^{2} + 3720620 T^{3} + 6165879423 T^{4} - 560512300438 T^{5} + 327381934393961 T^{6} )^{2} \)
$43$ \( 1 - 247490 T^{2} + 32846327015 T^{4} - 3025278566260412 T^{6} + \)\(20\!\cdots\!35\)\( T^{8} - \)\(98\!\cdots\!90\)\( T^{10} + \)\(25\!\cdots\!49\)\( T^{12} \)
$47$ \( ( 1 + 204 T + 283677 T^{2} + 40395048 T^{3} + 29452197171 T^{4} + 2198959927116 T^{5} + 1119130473102767 T^{6} )^{2} \)
$53$ \( 1 - 292802 T^{2} + 13793539751 T^{4} + 2699981198933572 T^{6} + \)\(30\!\cdots\!79\)\( T^{8} - \)\(14\!\cdots\!82\)\( T^{10} + \)\(10\!\cdots\!89\)\( T^{12} \)
$59$ \( 1 - 1093858 T^{2} + 524838290887 T^{4} - 140555838506313212 T^{6} + \)\(22\!\cdots\!67\)\( T^{8} - \)\(19\!\cdots\!98\)\( T^{10} + \)\(75\!\cdots\!21\)\( T^{12} \)
$61$ \( 1 - 459870 T^{2} + 162687674679 T^{4} - 38865284671151684 T^{6} + \)\(83\!\cdots\!19\)\( T^{8} - \)\(12\!\cdots\!70\)\( T^{10} + \)\(13\!\cdots\!81\)\( T^{12} \)
$67$ \( 1 - 750066 T^{2} + 226548162807 T^{4} - 53949461413257884 T^{6} + \)\(20\!\cdots\!83\)\( T^{8} - \)\(61\!\cdots\!26\)\( T^{10} + \)\(74\!\cdots\!09\)\( T^{12} \)
$71$ \( ( 1 + 852 T + 1006773 T^{2} + 524795352 T^{3} + 360335131203 T^{4} + 109141441900692 T^{5} + 45848500718449031 T^{6} )^{2} \)
$73$ \( ( 1 - 478 T + 911095 T^{2} - 251066948 T^{3} + 354431443615 T^{4} - 72337760166142 T^{5} + 58871586708267913 T^{6} )^{2} \)
$79$ \( ( 1 + 22 T + 1407593 T^{2} + 13791100 T^{3} + 693998245127 T^{4} + 5347924021462 T^{5} + 119851595982618319 T^{6} )^{2} \)
$83$ \( 1 - 2910274 T^{2} + 3775777045015 T^{4} - 2787348361783974908 T^{6} + \)\(12\!\cdots\!35\)\( T^{8} - \)\(31\!\cdots\!14\)\( T^{10} + \)\(34\!\cdots\!09\)\( T^{12} \)
$89$ \( ( 1 + 110 T + 2073543 T^{2} + 156516836 T^{3} + 1461783535167 T^{4} + 54667942005710 T^{5} + 350356403707485209 T^{6} )^{2} \)
$97$ \( ( 1 + 1222 T + 2989679 T^{2} + 2155770388 T^{3} + 2728599301967 T^{4} + 1017891790023238 T^{5} + 760231058654565217 T^{6} )^{2} \)
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