# Properties

 Label 24.3.e Level 24 Weight 3 Character orbit e Rep. character $$\chi_{24}(17,\cdot)$$ Character field $$\Q$$ Dimension 2 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.e (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$3$$ 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 12 2 10
Cusp forms 4 2 2
Eisenstein series 8 0 8

## Trace form

 $$2q + 2q^{3} - 12q^{7} - 14q^{9} + O(q^{10})$$ $$2q + 2q^{3} - 12q^{7} - 14q^{9} + 20q^{13} + 32q^{15} + 4q^{19} - 12q^{21} - 14q^{25} - 46q^{27} - 44q^{31} + 32q^{33} - 12q^{37} + 20q^{39} + 164q^{43} + 64q^{45} - 26q^{49} - 128q^{51} - 64q^{55} + 4q^{57} - 172q^{61} + 84q^{63} + 4q^{67} - 64q^{69} + 164q^{73} - 14q^{75} + 20q^{79} + 34q^{81} + 256q^{85} + 96q^{87} - 120q^{91} - 44q^{93} - 188q^{97} + 64q^{99} + O(q^{100})$$

## 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.e.a $$2$$ $$0.654$$ $$\Q(\sqrt{-2})$$ None $$0$$ $$2$$ $$0$$ $$-12$$ $$q+(1+\beta )q^{3}-2\beta q^{5}-6q^{7}+(-7+2\beta )q^{9}+\cdots$$

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

$$S_{3}^{\mathrm{old}}(24, [\chi]) \cong$$ $$S_{3}^{\mathrm{new}}(12, [\chi])$$$$^{\oplus 2}$$

## Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ 1
$3$ $$1 - 2 T + 9 T^{2}$$
$5$ $$1 - 18 T^{2} + 625 T^{4}$$
$7$ $$( 1 + 6 T + 49 T^{2} )^{2}$$
$11$ $$1 - 210 T^{2} + 14641 T^{4}$$
$13$ $$( 1 - 10 T + 169 T^{2} )^{2}$$
$17$ $$1 - 66 T^{2} + 83521 T^{4}$$
$19$ $$( 1 - 2 T + 361 T^{2} )^{2}$$
$23$ $$1 - 930 T^{2} + 279841 T^{4}$$
$29$ $$1 - 1394 T^{2} + 707281 T^{4}$$
$31$ $$( 1 + 22 T + 961 T^{2} )^{2}$$
$37$ $$( 1 + 6 T + 1369 T^{2} )^{2}$$
$41$ $$1 - 2210 T^{2} + 2825761 T^{4}$$
$43$ $$( 1 - 82 T + 1849 T^{2} )^{2}$$
$47$ $$1 + 190 T^{2} + 4879681 T^{4}$$
$53$ $$1 - 1746 T^{2} + 7890481 T^{4}$$
$59$ $$1 - 1554 T^{2} + 12117361 T^{4}$$
$61$ $$( 1 + 86 T + 3721 T^{2} )^{2}$$
$67$ $$( 1 - 2 T + 4489 T^{2} )^{2}$$
$71$ $$1 + 5406 T^{2} + 25411681 T^{4}$$
$73$ $$( 1 - 82 T + 5329 T^{2} )^{2}$$
$79$ $$( 1 - 10 T + 6241 T^{2} )^{2}$$
$83$ $$1 - 8370 T^{2} + 47458321 T^{4}$$
$89$ $$1 - 14690 T^{2} + 62742241 T^{4}$$
$97$ $$( 1 + 94 T + 9409 T^{2} )^{2}$$