Properties

Label 24.10.a
Level 24
Weight 10
Character orbit a
Rep. character \(\chi_{24}(1,\cdot)\)
Character field \(\Q\)
Dimension 5
Newform subspaces 4
Sturm bound 40
Trace bound 5

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Defining parameters

Level: \( N \) \(=\) \( 24 = 2^{3} \cdot 3 \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 24.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(40\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_0(24))\).

Total New Old
Modular forms 40 5 35
Cusp forms 32 5 27
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.
\(+\)\(+\)\(+\)\(1\)
\(+\)\(-\)\(-\)\(1\)
\(-\)\(+\)\(-\)\(2\)
\(-\)\(-\)\(+\)\(1\)
Plus space\(+\)\(2\)
Minus space\(-\)\(3\)

Trace form

\( 5q - 81q^{3} - 122q^{5} - 5904q^{7} + 32805q^{9} + O(q^{10}) \) \( 5q - 81q^{3} - 122q^{5} - 5904q^{7} + 32805q^{9} - 56924q^{11} + 253814q^{13} - 19278q^{15} + 371690q^{17} + 166300q^{19} - 120528q^{21} + 2393560q^{23} + 265051q^{25} - 531441q^{27} - 736818q^{29} + 56248q^{31} + 446796q^{33} - 32502624q^{35} + 21407934q^{37} - 11710494q^{39} + 3652674q^{41} - 38861212q^{43} - 800442q^{45} + 77893536q^{47} + 43083805q^{49} - 62200386q^{51} - 122788058q^{53} + 191168888q^{55} + 12974580q^{57} + 35469124q^{59} + 203888918q^{61} - 38736144q^{63} - 197295884q^{65} - 183464900q^{67} + 163576584q^{69} + 334361960q^{71} + 307233266q^{73} - 491077647q^{75} - 1124684736q^{77} - 598882456q^{79} + 215233605q^{81} + 1832558108q^{83} - 291062708q^{85} - 837938358q^{87} - 1995331614q^{89} + 192513312q^{91} + 1493236296q^{93} + 2022308360q^{95} + 1970064970q^{97} - 373478364q^{99} + O(q^{100}) \)

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_0(24))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 3
24.10.a.a \(1\) \(12.361\) \(\Q\) None \(0\) \(-81\) \(830\) \(672\) \(+\) \(+\) \(q-3^{4}q^{3}+830q^{5}+672q^{7}+3^{8}q^{9}+\cdots\)
24.10.a.b \(1\) \(12.361\) \(\Q\) None \(0\) \(81\) \(-794\) \(-5880\) \(-\) \(-\) \(q+3^{4}q^{3}-794q^{5}-5880q^{7}+3^{8}q^{9}+\cdots\)
24.10.a.c \(1\) \(12.361\) \(\Q\) None \(0\) \(81\) \(614\) \(2184\) \(+\) \(-\) \(q+3^{4}q^{3}+614q^{5}+2184q^{7}+3^{8}q^{9}+\cdots\)
24.10.a.d \(2\) \(12.361\) \(\Q(\sqrt{109}) \) None \(0\) \(-162\) \(-772\) \(-2880\) \(-\) \(+\) \(q-3^{4}q^{3}+(-386-\beta )q^{5}+(-1440+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{10}^{\mathrm{old}}(\Gamma_0(24))\) into lower level spaces

\( S_{10}^{\mathrm{old}}(\Gamma_0(24)) \cong \) \(S_{10}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_0(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_0(4))\)\(^{\oplus 4}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_0(6))\)\(^{\oplus 3}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_0(8))\)\(^{\oplus 2}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_0(12))\)\(^{\oplus 2}\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ 1
$3$ (\( 1 + 81 T \))(\( 1 - 81 T \))(\( 1 - 81 T \))(\( ( 1 + 81 T )^{2} \))
$5$ (\( 1 - 830 T + 1953125 T^{2} \))(\( 1 + 794 T + 1953125 T^{2} \))(\( 1 - 614 T + 1953125 T^{2} \))(\( 1 + 772 T + 37070 T^{2} + 1507812500 T^{3} + 3814697265625 T^{4} \))
$7$ (\( 1 - 672 T + 40353607 T^{2} \))(\( 1 + 5880 T + 40353607 T^{2} \))(\( 1 - 2184 T + 40353607 T^{2} \))(\( 1 + 2880 T - 17673586 T^{2} + 116218388160 T^{3} + 1628413597910449 T^{4} \))
$11$ (\( 1 + 73468 T + 2357947691 T^{2} \))(\( 1 + 30644 T + 2357947691 T^{2} \))(\( 1 - 4940 T + 2357947691 T^{2} \))(\( 1 - 42248 T + 1545760358 T^{2} - 99618574049368 T^{3} + 5559917313492231481 T^{4} \))
$13$ (\( 1 + 78242 T + 10604499373 T^{2} \))(\( 1 + 15314 T + 10604499373 T^{2} \))(\( 1 - 69934 T + 10604499373 T^{2} \))(\( 1 - 277436 T + 40049864670 T^{2} - 2942069888047628 T^{3} + \)\(11\!\cdots\!29\)\( T^{4} \))
$17$ (\( 1 + 161726 T + 118587876497 T^{2} \))(\( 1 + 575086 T + 118587876497 T^{2} \))(\( 1 - 376978 T + 118587876497 T^{2} \))(\( 1 - 731524 T + 351268531238 T^{2} - 86749877766591428 T^{3} + \)\(14\!\cdots\!09\)\( T^{4} \))
$19$ (\( 1 + 653572 T + 322687697779 T^{2} \))(\( 1 + 617644 T + 322687697779 T^{2} \))(\( 1 - 780884 T + 322687697779 T^{2} \))(\( 1 - 656632 T + 540605281014 T^{2} - 211887068368020328 T^{3} + \)\(10\!\cdots\!41\)\( T^{4} \))
$23$ (\( 1 + 1066696 T + 1801152661463 T^{2} \))(\( 1 - 441880 T + 1801152661463 T^{2} \))(\( 1 - 1764632 T + 1801152661463 T^{2} \))(\( 1 - 1253744 T + 3030509769710 T^{2} - 2258184342393267472 T^{3} + \)\(32\!\cdots\!69\)\( T^{4} \))
$29$ (\( 1 - 3824838 T + 14507145975869 T^{2} \))(\( 1 + 2328642 T + 14507145975869 T^{2} \))(\( 1 + 3212226 T + 14507145975869 T^{2} \))(\( 1 - 979212 T + 21876534396574 T^{2} - 14205571425322635228 T^{3} + \)\(21\!\cdots\!61\)\( T^{4} \))
$31$ (\( 1 + 1579480 T + 26439622160671 T^{2} \))(\( 1 - 9588512 T + 26439622160671 T^{2} \))(\( 1 + 342880 T + 26439622160671 T^{2} \))(\( 1 + 7609904 T + 63217278674046 T^{2} + \)\(20\!\cdots\!84\)\( T^{3} + \)\(69\!\cdots\!41\)\( T^{4} \))
$37$ (\( 1 - 16015590 T + 129961739795077 T^{2} \))(\( 1 - 9276678 T + 129961739795077 T^{2} \))(\( 1 + 19744506 T + 129961739795077 T^{2} \))(\( 1 - 15860172 T + 316226363999150 T^{2} - \)\(20\!\cdots\!44\)\( T^{3} + \)\(16\!\cdots\!29\)\( T^{4} \))
$41$ (\( 1 - 26268282 T + 327381934393961 T^{2} \))(\( 1 + 5903766 T + 327381934393961 T^{2} \))(\( 1 + 15882390 T + 327381934393961 T^{2} \))(\( 1 + 829452 T + 642909867492598 T^{2} + \)\(27\!\cdots\!72\)\( T^{3} + \)\(10\!\cdots\!21\)\( T^{4} \))
$43$ (\( 1 + 44495228 T + 502592611936843 T^{2} \))(\( 1 - 33593452 T + 502592611936843 T^{2} \))(\( 1 + 22575764 T + 502592611936843 T^{2} \))(\( 1 + 5383672 T + 614621735484582 T^{2} + \)\(27\!\cdots\!96\)\( T^{3} + \)\(25\!\cdots\!49\)\( T^{4} \))
$47$ (\( 1 - 14324160 T + 1119130473102767 T^{2} \))(\( 1 - 21135408 T + 1119130473102767 T^{2} \))(\( 1 - 48948528 T + 1119130473102767 T^{2} \))(\( 1 + 6514560 T + 2160486618090334 T^{2} + \)\(72\!\cdots\!20\)\( T^{3} + \)\(12\!\cdots\!89\)\( T^{4} \))
$53$ (\( 1 + 24386050 T + 3299763591802133 T^{2} \))(\( 1 + 108575594 T + 3299763591802133 T^{2} \))(\( 1 - 52342550 T + 3299763591802133 T^{2} \))(\( 1 + 42168964 T + 2468484998758190 T^{2} + \)\(13\!\cdots\!12\)\( T^{3} + \)\(10\!\cdots\!89\)\( T^{4} \))
$59$ (\( 1 - 11942084 T + 8662995818654939 T^{2} \))(\( 1 + 127636868 T + 8662995818654939 T^{2} \))(\( 1 - 77057660 T + 8662995818654939 T^{2} \))(\( 1 - 74106248 T + 18085070495219654 T^{2} - \)\(64\!\cdots\!72\)\( T^{3} + \)\(75\!\cdots\!21\)\( T^{4} \))
$61$ (\( 1 + 189740258 T + 11694146092834141 T^{2} \))(\( 1 - 147189214 T + 11694146092834141 T^{2} \))(\( 1 - 13045726 T + 11694146092834141 T^{2} \))(\( 1 - 233394236 T + 35613390235999806 T^{2} - \)\(27\!\cdots\!76\)\( T^{3} + \)\(13\!\cdots\!81\)\( T^{4} \))
$67$ (\( 1 + 106709572 T + 27206534396294947 T^{2} \))(\( 1 + 33157756 T + 27206534396294947 T^{2} \))(\( 1 + 280727164 T + 27206534396294947 T^{2} \))(\( 1 - 237129592 T + 68424229528551510 T^{2} - \)\(64\!\cdots\!24\)\( T^{3} + \)\(74\!\cdots\!09\)\( T^{4} \))
$71$ (\( 1 - 302754376 T + 45848500718449031 T^{2} \))(\( 1 + 9293752 T + 45848500718449031 T^{2} \))(\( 1 + 88554680 T + 45848500718449031 T^{2} \))(\( 1 - 129456016 T + 41696884105211726 T^{2} - \)\(59\!\cdots\!96\)\( T^{3} + \)\(21\!\cdots\!61\)\( T^{4} \))
$73$ (\( 1 - 81769546 T + 58871586708267913 T^{2} \))(\( 1 - 351080074 T + 58871586708267913 T^{2} \))(\( 1 + 59105654 T + 58871586708267913 T^{2} \))(\( 1 + 66510700 T + 18336084212292726 T^{2} + \)\(39\!\cdots\!00\)\( T^{3} + \)\(34\!\cdots\!69\)\( T^{4} \))
$79$ (\( 1 - 315315352 T + 119851595982618319 T^{2} \))(\( 1 + 126193328 T + 119851595982618319 T^{2} \))(\( 1 + 415337264 T + 119851595982618319 T^{2} \))(\( 1 + 372667216 T + 91034201472756702 T^{2} + \)\(44\!\cdots\!04\)\( T^{3} + \)\(14\!\cdots\!61\)\( T^{4} \))
$83$ (\( 1 - 752833276 T + 186940255267540403 T^{2} \))(\( 1 - 475037588 T + 186940255267540403 T^{2} \))(\( 1 - 42806932 T + 186940255267540403 T^{2} \))(\( 1 - 561880312 T + 395647990537594742 T^{2} - \)\(10\!\cdots\!36\)\( T^{3} + \)\(34\!\cdots\!09\)\( T^{4} \))
$89$ (\( 1 + 433284294 T + 350356403707485209 T^{2} \))(\( 1 + 566133990 T + 350356403707485209 T^{2} \))(\( 1 + 803465958 T + 350356403707485209 T^{2} \))(\( 1 + 192447372 T + 579174645744950614 T^{2} + \)\(67\!\cdots\!48\)\( T^{3} + \)\(12\!\cdots\!81\)\( T^{4} \))
$97$ (\( 1 - 1282496642 T + 760231058654565217 T^{2} \))(\( 1 + 1474684318 T + 760231058654565217 T^{2} \))(\( 1 - 674417762 T + 760231058654565217 T^{2} \))(\( 1 - 1487834884 T + 2073185718637593798 T^{2} - \)\(11\!\cdots\!28\)\( T^{3} + \)\(57\!\cdots\!89\)\( T^{4} \))
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