# 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

## 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

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