# Properties

 Label 18.2.c Level 18 Weight 2 Character orbit c Rep. character $$\chi_{18}(7,\cdot)$$ Character field $$\Q(\zeta_{3})$$ Dimension 2 Newform subspaces 1 Sturm bound 6 Trace bound 0

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$18 = 2 \cdot 3^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 18.c (of order $$3$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$9$$ Character field: $$\Q(\zeta_{3})$$ Newform subspaces: $$1$$ Sturm bound: $$6$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(18, [\chi])$$.

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

## Trace form

 $$2q - q^{2} - 3q^{3} - q^{4} + 3q^{6} - 2q^{7} + 2q^{8} + 3q^{9} + O(q^{10})$$ $$2q - q^{2} - 3q^{3} - q^{4} + 3q^{6} - 2q^{7} + 2q^{8} + 3q^{9} + 3q^{11} - 2q^{13} - 2q^{14} - q^{16} - 6q^{17} - 6q^{18} - 2q^{19} + 6q^{21} + 3q^{22} + 6q^{23} - 3q^{24} + 5q^{25} + 4q^{26} + 4q^{28} - 6q^{29} + 4q^{31} - q^{32} - 9q^{33} + 3q^{34} + 3q^{36} - 8q^{37} + q^{38} - 9q^{41} + q^{43} - 6q^{44} - 12q^{46} + 6q^{47} + 3q^{48} + 3q^{49} + 5q^{50} + 9q^{51} - 2q^{52} + 24q^{53} + 9q^{54} - 2q^{56} + 3q^{57} - 6q^{58} - 3q^{59} - 8q^{61} - 8q^{62} - 12q^{63} + 2q^{64} - 5q^{67} + 3q^{68} - 24q^{71} + 3q^{72} + 22q^{73} + 4q^{74} - 15q^{75} + q^{76} + 6q^{77} - 6q^{78} + 4q^{79} - 9q^{81} + 18q^{82} - 12q^{83} - 6q^{84} + q^{86} + 18q^{87} + 3q^{88} + 12q^{89} + 8q^{91} + 6q^{92} + 6q^{94} - 5q^{97} - 6q^{98} + 18q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(18, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
18.2.c.a $$2$$ $$0.144$$ $$\Q(\sqrt{-3})$$ None $$-1$$ $$-3$$ $$0$$ $$-2$$ $$q-\zeta_{6}q^{2}+(-2+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots$$

## Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ $$1 + T + T^{2}$$
$3$ $$1 + 3 T + 3 T^{2}$$
$5$ $$1 - 5 T^{2} + 25 T^{4}$$
$7$ $$1 + 2 T - 3 T^{2} + 14 T^{3} + 49 T^{4}$$
$11$ $$1 - 3 T - 2 T^{2} - 33 T^{3} + 121 T^{4}$$
$13$ $$( 1 - 5 T + 13 T^{2} )( 1 + 7 T + 13 T^{2} )$$
$17$ $$( 1 + 3 T + 17 T^{2} )^{2}$$
$19$ $$( 1 + T + 19 T^{2} )^{2}$$
$23$ $$1 - 6 T + 13 T^{2} - 138 T^{3} + 529 T^{4}$$
$29$ $$1 + 6 T + 7 T^{2} + 174 T^{3} + 841 T^{4}$$
$31$ $$( 1 - 11 T + 31 T^{2} )( 1 + 7 T + 31 T^{2} )$$
$37$ $$( 1 + 4 T + 37 T^{2} )^{2}$$
$41$ $$1 + 9 T + 40 T^{2} + 369 T^{3} + 1681 T^{4}$$
$43$ $$1 - T - 42 T^{2} - 43 T^{3} + 1849 T^{4}$$
$47$ $$1 - 6 T - 11 T^{2} - 282 T^{3} + 2209 T^{4}$$
$53$ $$( 1 - 12 T + 53 T^{2} )^{2}$$
$59$ $$1 + 3 T - 50 T^{2} + 177 T^{3} + 3481 T^{4}$$
$61$ $$1 + 8 T + 3 T^{2} + 488 T^{3} + 3721 T^{4}$$
$67$ $$( 1 - 11 T + 67 T^{2} )( 1 + 16 T + 67 T^{2} )$$
$71$ $$( 1 + 12 T + 71 T^{2} )^{2}$$
$73$ $$( 1 - 11 T + 73 T^{2} )^{2}$$
$79$ $$( 1 - 17 T + 79 T^{2} )( 1 + 13 T + 79 T^{2} )$$
$83$ $$1 + 12 T + 61 T^{2} + 996 T^{3} + 6889 T^{4}$$
$89$ $$( 1 - 6 T + 89 T^{2} )^{2}$$
$97$ $$( 1 - 14 T + 97 T^{2} )( 1 + 19 T + 97 T^{2} )$$