# Properties

 Label 18.3.b Level 18 Weight 3 Character orbit b Rep. character $$\chi_{18}(17,\cdot)$$ Character field $$\Q$$ Dimension 2 Newform subspaces 1 Sturm bound 9 Trace bound 0

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$18 = 2 \cdot 3^{2}$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 18.b (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$3$$ Character field: $$\Q$$ Newform subspaces: $$1$$ Sturm bound: $$9$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(18, [\chi])$$.

Total New Old
Modular forms 10 2 8
Cusp forms 2 2 0
Eisenstein series 8 0 8

## Trace form

 $$2q - 4q^{4} - 8q^{7} + O(q^{10})$$ $$2q - 4q^{4} - 8q^{7} + 12q^{10} + 16q^{13} + 8q^{16} - 32q^{19} - 48q^{22} + 14q^{25} + 16q^{28} + 88q^{31} + 36q^{34} - 68q^{37} - 24q^{40} - 80q^{43} + 48q^{46} - 66q^{49} - 32q^{52} + 144q^{55} - 12q^{58} + 100q^{61} - 16q^{64} + 16q^{67} - 48q^{70} - 32q^{73} + 64q^{76} - 152q^{79} - 132q^{82} - 108q^{85} + 96q^{88} - 64q^{91} + 240q^{94} + 352q^{97} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(18, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
18.3.b.a $$2$$ $$0.490$$ $$\Q(\sqrt{-2})$$ None $$0$$ $$0$$ $$0$$ $$-8$$ $$q+\beta q^{2}-2q^{4}-3\beta q^{5}-4q^{7}-2\beta q^{8}+\cdots$$

## Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ $$1 + 2 T^{2}$$
$3$ 1
$5$ $$1 - 32 T^{2} + 625 T^{4}$$
$7$ $$( 1 + 4 T + 49 T^{2} )^{2}$$
$11$ $$( 1 - 14 T + 121 T^{2} )( 1 + 14 T + 121 T^{2} )$$
$13$ $$( 1 - 8 T + 169 T^{2} )^{2}$$
$17$ $$1 - 416 T^{2} + 83521 T^{4}$$
$19$ $$( 1 + 16 T + 361 T^{2} )^{2}$$
$23$ $$1 - 770 T^{2} + 279841 T^{4}$$
$29$ $$1 - 1664 T^{2} + 707281 T^{4}$$
$31$ $$( 1 - 44 T + 961 T^{2} )^{2}$$
$37$ $$( 1 + 34 T + 1369 T^{2} )^{2}$$
$41$ $$1 - 1184 T^{2} + 2825761 T^{4}$$
$43$ $$( 1 + 40 T + 1849 T^{2} )^{2}$$
$47$ $$1 + 2782 T^{2} + 4879681 T^{4}$$
$53$ $$1 - 4160 T^{2} + 7890481 T^{4}$$
$59$ $$1 - 5810 T^{2} + 12117361 T^{4}$$
$61$ $$( 1 - 50 T + 3721 T^{2} )^{2}$$
$67$ $$( 1 - 8 T + 4489 T^{2} )^{2}$$
$71$ $$1 - 7490 T^{2} + 25411681 T^{4}$$
$73$ $$( 1 + 16 T + 5329 T^{2} )^{2}$$
$79$ $$( 1 + 76 T + 6241 T^{2} )^{2}$$
$83$ $$1 + 334 T^{2} + 47458321 T^{4}$$
$89$ $$1 - 15680 T^{2} + 62742241 T^{4}$$
$97$ $$( 1 - 176 T + 9409 T^{2} )^{2}$$