# Properties

 Label 27.3.d Level 27 Weight 3 Character orbit d Rep. character $$\chi_{27}(8,\cdot)$$ Character field $$\Q(\zeta_{6})$$ Dimension 2 Newform subspaces 1 Sturm bound 9 Trace bound 0

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$27 = 3^{3}$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 27.d (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$9$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$1$$ Sturm bound: $$9$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(27, [\chi])$$.

Total New Old
Modular forms 18 6 12
Cusp forms 6 2 4
Eisenstein series 12 4 8

## Trace form

 $$2q + 3q^{2} - q^{4} - 6q^{5} - 2q^{7} + O(q^{10})$$ $$2q + 3q^{2} - q^{4} - 6q^{5} - 2q^{7} - 12q^{10} + 3q^{11} + 4q^{13} - 6q^{14} + 11q^{16} + 22q^{19} + 6q^{20} + 3q^{22} + 48q^{23} - 13q^{25} + 4q^{28} - 78q^{29} - 32q^{31} - 27q^{32} - 27q^{34} - 68q^{37} + 33q^{38} + 30q^{40} + 21q^{41} + 61q^{43} + 96q^{46} + 84q^{47} + 45q^{49} - 39q^{50} + 4q^{52} - 12q^{55} + 30q^{56} - 78q^{58} - 87q^{59} - 56q^{61} - 142q^{64} - 24q^{65} + 31q^{67} + 27q^{68} + 12q^{70} + 130q^{73} - 102q^{74} - 11q^{76} - 6q^{77} - 38q^{79} + 42q^{82} + 84q^{83} - 54q^{85} + 183q^{86} + 15q^{88} - 16q^{91} - 48q^{92} + 84q^{94} - 66q^{95} + 115q^{97} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(27, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
27.3.d.a $$2$$ $$0.736$$ $$\Q(\sqrt{-3})$$ None $$3$$ $$0$$ $$-6$$ $$-2$$ $$q+(1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+(-4+2\zeta_{6})q^{5}+\cdots$$

## Decomposition of $$S_{3}^{\mathrm{old}}(27, [\chi])$$ into lower level spaces

$$S_{3}^{\mathrm{old}}(27, [\chi]) \cong$$ $$S_{3}^{\mathrm{new}}(9, [\chi])$$$$^{\oplus 2}$$

## Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ $$1 - 3 T + 7 T^{2} - 12 T^{3} + 16 T^{4}$$
$3$ 1
$5$ $$1 + 6 T + 37 T^{2} + 150 T^{3} + 625 T^{4}$$
$7$ $$( 1 - 11 T + 49 T^{2} )( 1 + 13 T + 49 T^{2} )$$
$11$ $$1 - 3 T + 124 T^{2} - 363 T^{3} + 14641 T^{4}$$
$13$ $$1 - 4 T - 153 T^{2} - 676 T^{3} + 28561 T^{4}$$
$17$ $$1 - 335 T^{2} + 83521 T^{4}$$
$19$ $$( 1 - 11 T + 361 T^{2} )^{2}$$
$23$ $$1 - 48 T + 1297 T^{2} - 25392 T^{3} + 279841 T^{4}$$
$29$ $$1 + 78 T + 2869 T^{2} + 65598 T^{3} + 707281 T^{4}$$
$31$ $$1 + 32 T + 63 T^{2} + 30752 T^{3} + 923521 T^{4}$$
$37$ $$( 1 + 34 T + 1369 T^{2} )^{2}$$
$41$ $$1 - 21 T + 1828 T^{2} - 35301 T^{3} + 2825761 T^{4}$$
$43$ $$( 1 - 83 T + 1849 T^{2} )( 1 + 22 T + 1849 T^{2} )$$
$47$ $$1 - 84 T + 4561 T^{2} - 185556 T^{3} + 4879681 T^{4}$$
$53$ $$( 1 - 53 T )^{2}( 1 + 53 T )^{2}$$
$59$ $$1 + 87 T + 6004 T^{2} + 302847 T^{3} + 12117361 T^{4}$$
$61$ $$1 + 56 T - 585 T^{2} + 208376 T^{3} + 13845841 T^{4}$$
$67$ $$1 - 31 T - 3528 T^{2} - 139159 T^{3} + 20151121 T^{4}$$
$71$ $$1 - 9110 T^{2} + 25411681 T^{4}$$
$73$ $$( 1 - 65 T + 5329 T^{2} )^{2}$$
$79$ $$1 + 38 T - 4797 T^{2} + 237158 T^{3} + 38950081 T^{4}$$
$83$ $$1 - 84 T + 9241 T^{2} - 578676 T^{3} + 47458321 T^{4}$$
$89$ $$1 - 290 T^{2} + 62742241 T^{4}$$
$97$ $$1 - 115 T + 3816 T^{2} - 1082035 T^{3} + 88529281 T^{4}$$