Properties

Label 24.3.b
Level 24
Weight 3
Character orbit b
Rep. character \(\chi_{24}(19,\cdot)\)
Character field \(\Q\)
Dimension 4
Newform subspaces 1
Sturm bound 12
Trace bound 0

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) \(=\) \( 24 = 2^{3} \cdot 3 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 24.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 8 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(12\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(24, [\chi])\).

Total New Old
Modular forms 10 4 6
Cusp forms 6 4 2
Eisenstein series 4 0 4

Trace form

\( 4q + 2q^{2} - 8q^{4} - 6q^{6} - 4q^{8} + 12q^{9} + O(q^{10}) \) \( 4q + 2q^{2} - 8q^{4} - 6q^{6} - 4q^{8} + 12q^{9} + 12q^{10} - 32q^{11} - 12q^{12} + 36q^{14} - 8q^{16} - 8q^{17} + 6q^{18} + 32q^{19} + 72q^{20} - 16q^{22} + 36q^{24} - 44q^{25} - 96q^{26} - 48q^{28} - 60q^{30} - 88q^{32} + 44q^{34} + 96q^{35} - 24q^{36} + 40q^{38} + 120q^{40} + 40q^{41} + 84q^{42} + 32q^{43} + 64q^{44} - 72q^{46} + 96q^{48} - 44q^{49} - 118q^{50} - 96q^{51} - 48q^{52} - 18q^{54} - 168q^{56} - 48q^{57} + 156q^{58} - 128q^{59} - 96q^{60} + 204q^{62} - 32q^{64} + 96q^{65} + 48q^{66} - 256q^{67} + 112q^{68} + 24q^{70} - 12q^{72} + 200q^{73} - 120q^{74} + 192q^{75} - 16q^{76} - 48q^{78} - 96q^{80} + 36q^{81} - 124q^{82} + 160q^{83} - 24q^{84} + 88q^{86} + 32q^{88} - 200q^{89} + 36q^{90} + 288q^{91} + 96q^{92} - 168q^{94} - 24q^{96} + 56q^{97} + 170q^{98} - 96q^{99} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(24, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
24.3.b.a \(4\) \(0.654\) 4.0.4752.1 None \(2\) \(0\) \(0\) \(0\) \(q+(\beta _{1}-\beta _{2})q^{2}+\beta _{2}q^{3}+(-2-\beta _{2}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(24, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(24, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(8, [\chi])\)\(^{\oplus 2}\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( 1 - 2 T + 6 T^{2} - 8 T^{3} + 16 T^{4} \)
$3$ \( ( 1 - 3 T^{2} )^{2} \)
$5$ \( 1 - 28 T^{2} + 678 T^{4} - 17500 T^{6} + 390625 T^{8} \)
$7$ \( 1 - 76 T^{2} + 3174 T^{4} - 182476 T^{6} + 5764801 T^{8} \)
$11$ \( ( 1 + 8 T + 121 T^{2} )^{4} \)
$13$ \( 1 - 292 T^{2} + 75366 T^{4} - 8339812 T^{6} + 815730721 T^{8} \)
$17$ \( ( 1 + 4 T + 390 T^{2} + 1156 T^{3} + 83521 T^{4} )^{2} \)
$19$ \( ( 1 - 16 T + 738 T^{2} - 5776 T^{3} + 130321 T^{4} )^{2} \)
$23$ \( 1 - 1636 T^{2} + 1179654 T^{4} - 457819876 T^{6} + 78310985281 T^{8} \)
$29$ \( 1 - 1756 T^{2} + 1539558 T^{4} - 1241985436 T^{6} + 500246412961 T^{8} \)
$31$ \( 1 - 460 T^{2} - 683610 T^{4} - 424819660 T^{6} + 852891037441 T^{8} \)
$37$ \( 1 - 4612 T^{2} + 8955366 T^{4} - 8643630532 T^{6} + 3512479453921 T^{8} \)
$41$ \( ( 1 - 20 T + 1734 T^{2} - 33620 T^{3} + 2825761 T^{4} )^{2} \)
$43$ \( ( 1 - 16 T + 3330 T^{2} - 29584 T^{3} + 3418801 T^{4} )^{2} \)
$47$ \( 1 - 5284 T^{2} + 13593798 T^{4} - 25784234404 T^{6} + 23811286661761 T^{8} \)
$53$ \( 1 - 9436 T^{2} + 38033574 T^{4} - 74454578716 T^{6} + 62259690411361 T^{8} \)
$59$ \( ( 1 + 64 T + 7554 T^{2} + 222784 T^{3} + 12117361 T^{4} )^{2} \)
$61$ \( 1 - 11332 T^{2} + 56649510 T^{4} - 156901070212 T^{6} + 191707312997281 T^{8} \)
$67$ \( ( 1 + 128 T + 12642 T^{2} + 574592 T^{3} + 20151121 T^{4} )^{2} \)
$71$ \( 1 - 11236 T^{2} + 75307398 T^{4} - 285525647716 T^{6} + 645753531245761 T^{8} \)
$73$ \( ( 1 - 100 T + 10086 T^{2} - 532900 T^{3} + 28398241 T^{4} )^{2} \)
$79$ \( 1 - 17548 T^{2} + 151931046 T^{4} - 683496021388 T^{6} + 1517108809906561 T^{8} \)
$83$ \( ( 1 - 80 T + 14610 T^{2} - 551120 T^{3} + 47458321 T^{4} )^{2} \)
$89$ \( ( 1 + 100 T + 11430 T^{2} + 792100 T^{3} + 62742241 T^{4} )^{2} \)
$97$ \( ( 1 - 28 T + 12102 T^{2} - 263452 T^{3} + 88529281 T^{4} )^{2} \)
show more
show less