# Properties

 Label 54.4.c Level $54$ Weight $4$ Character orbit 54.c Rep. character $\chi_{54}(19,\cdot)$ Character field $\Q(\zeta_{3})$ Dimension $6$ Newform subspaces $2$ Sturm bound $36$ Trace bound $1$

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## Defining parameters

 Level: $$N$$ $$=$$ $$54 = 2 \cdot 3^{3}$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 54.c (of order $$3$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$9$$ Character field: $$\Q(\zeta_{3})$$ Newform subspaces: $$2$$ Sturm bound: $$36$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$5$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(54, [\chi])$$.

Total New Old
Modular forms 66 6 60
Cusp forms 42 6 36
Eisenstein series 24 0 24

## Trace form

 $$6 q - 2 q^{2} - 12 q^{4} - 18 q^{5} + 12 q^{7} + 16 q^{8} + O(q^{10})$$ $$6 q - 2 q^{2} - 12 q^{4} - 18 q^{5} + 12 q^{7} + 16 q^{8} - 39 q^{11} - 24 q^{13} - 100 q^{14} - 48 q^{16} + 78 q^{17} + 210 q^{19} - 72 q^{20} - 18 q^{22} + 264 q^{23} - 219 q^{25} + 392 q^{26} - 96 q^{28} + 348 q^{29} - 6 q^{31} - 32 q^{32} + 90 q^{34} - 1332 q^{35} + 192 q^{37} - 322 q^{38} + 207 q^{41} + 129 q^{43} + 312 q^{44} + 504 q^{46} + 660 q^{47} - 585 q^{49} - 614 q^{50} - 96 q^{52} - 528 q^{53} - 1404 q^{55} - 400 q^{56} + 252 q^{58} + 327 q^{59} + 858 q^{61} + 1664 q^{62} + 384 q^{64} - 414 q^{65} + 1587 q^{67} - 156 q^{68} + 216 q^{70} + 312 q^{71} - 258 q^{73} - 856 q^{74} - 420 q^{76} - 708 q^{77} - 1482 q^{79} + 576 q^{80} - 2916 q^{82} + 138 q^{83} + 108 q^{85} + 86 q^{86} - 72 q^{88} + 3084 q^{89} + 2508 q^{91} + 1056 q^{92} + 612 q^{94} + 2016 q^{95} + 1029 q^{97} - 2604 q^{98} + O(q^{100})$$

## Decomposition of $$S_{4}^{\mathrm{new}}(54, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
54.4.c.a $2$ $3.186$ $$\Q(\sqrt{-3})$$ None $$2$$ $$0$$ $$-9$$ $$31$$ $$q+(2-2\zeta_{6})q^{2}-4\zeta_{6}q^{4}-9\zeta_{6}q^{5}+\cdots$$
54.4.c.b $4$ $3.186$ $$\Q(\sqrt{-3}, \sqrt{-35})$$ None $$-4$$ $$0$$ $$-9$$ $$-19$$ $$q+2\beta _{1}q^{2}+(-4-4\beta _{1})q^{4}+(-4-4\beta _{1}+\cdots)q^{5}+\cdots$$

## Decomposition of $$S_{4}^{\mathrm{old}}(54, [\chi])$$ into lower level spaces

$$S_{4}^{\mathrm{old}}(54, [\chi]) \cong$$ $$S_{4}^{\mathrm{new}}(9, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(18, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(27, [\chi])$$$$^{\oplus 2}$$