# Properties

 Label 27.4.c Level $27$ Weight $4$ Character orbit 27.c Rep. character $\chi_{27}(10,\cdot)$ Character field $\Q(\zeta_{3})$ Dimension $4$ Newform subspaces $1$ Sturm bound $12$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$27 = 3^{3}$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 27.c (of order $$3$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$9$$ Character field: $$\Q(\zeta_{3})$$ Newform subspaces: $$1$$ Sturm bound: $$12$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(27, [\chi])$$.

Total New Old
Modular forms 24 8 16
Cusp forms 12 4 8
Eisenstein series 12 4 8

## Trace form

 $$4 q + 3 q^{2} - 5 q^{4} + 15 q^{5} - 7 q^{7} - 66 q^{8} + O(q^{10})$$ $$4 q + 3 q^{2} - 5 q^{4} + 15 q^{5} - 7 q^{7} - 66 q^{8} + 12 q^{10} + 66 q^{11} + 11 q^{13} + 60 q^{14} + 7 q^{16} - 198 q^{17} - 154 q^{19} - 12 q^{20} + 33 q^{22} + 33 q^{23} + 121 q^{25} + 528 q^{26} + 332 q^{28} - 51 q^{29} - 43 q^{31} - 423 q^{32} - 297 q^{34} - 6 q^{35} - 100 q^{37} - 561 q^{38} - 264 q^{40} + 132 q^{41} - 88 q^{43} + 462 q^{44} - 528 q^{46} + 399 q^{47} + 513 q^{49} - 429 q^{50} + 770 q^{52} - 108 q^{53} + 1254 q^{55} + 66 q^{56} + 60 q^{58} + 798 q^{59} - 439 q^{61} - 228 q^{62} - 1454 q^{64} + 165 q^{65} - 988 q^{67} + 693 q^{68} - 318 q^{70} - 2736 q^{71} - 910 q^{73} + 816 q^{74} + 1529 q^{76} - 165 q^{77} + 803 q^{79} - 192 q^{80} + 3630 q^{82} + 813 q^{83} - 594 q^{85} + 33 q^{86} - 1221 q^{88} + 792 q^{89} - 1562 q^{91} - 858 q^{92} - 2100 q^{94} - 132 q^{95} - 736 q^{97} + 846 q^{98} + O(q^{100})$$

## Decomposition of $$S_{4}^{\mathrm{new}}(27, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
27.4.c.a $4$ $1.593$ $$\Q(\sqrt{-3}, \sqrt{-11})$$ None $$3$$ $$0$$ $$15$$ $$-7$$ $$q+(\beta _{1}+\beta _{3})q^{2}+(-4+\beta _{1}-3\beta _{2}+3\beta _{3})q^{4}+\cdots$$

## Decomposition of $$S_{4}^{\mathrm{old}}(27, [\chi])$$ into lower level spaces

$$S_{4}^{\mathrm{old}}(27, [\chi]) \simeq$$ $$S_{4}^{\mathrm{new}}(9, [\chi])$$$$^{\oplus 2}$$