# Properties

 Label 57.3.c Level $57$ Weight $3$ Character orbit 57.c Rep. character $\chi_{57}(37,\cdot)$ Character field $\Q$ Dimension $6$ Newform subspaces $2$ Sturm bound $20$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$57 = 3 \cdot 19$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 57.c (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$19$$ Character field: $$\Q$$ Newform subspaces: $$2$$ Sturm bound: $$20$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(57, [\chi])$$.

Total New Old
Modular forms 16 6 10
Cusp forms 12 6 6
Eisenstein series 4 0 4

## Trace form

 $$6 q - 4 q^{4} - 2 q^{5} - 12 q^{6} + 14 q^{7} - 18 q^{9} + O(q^{10})$$ $$6 q - 4 q^{4} - 2 q^{5} - 12 q^{6} + 14 q^{7} - 18 q^{9} + 6 q^{11} - 44 q^{16} + 14 q^{17} + 38 q^{19} + 80 q^{20} + 12 q^{23} + 12 q^{24} - 36 q^{25} + 16 q^{26} - 128 q^{28} + 48 q^{30} - 222 q^{35} + 12 q^{36} + 152 q^{38} + 24 q^{39} - 48 q^{42} + 14 q^{43} - 16 q^{44} + 6 q^{45} - 74 q^{47} + 252 q^{49} + 36 q^{54} + 58 q^{55} + 256 q^{58} - 90 q^{61} - 256 q^{62} - 42 q^{63} - 44 q^{64} - 96 q^{66} - 256 q^{68} + 70 q^{73} + 336 q^{74} - 76 q^{76} - 262 q^{77} + 24 q^{80} + 54 q^{81} - 16 q^{82} + 204 q^{83} - 190 q^{85} + 240 q^{87} - 232 q^{92} - 72 q^{93} + 38 q^{95} + 204 q^{96} - 18 q^{99} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(57, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
57.3.c.a $2$ $1.553$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$8$$ $$-20$$ $$q-\zeta_{6}q^{2}-\zeta_{6}q^{3}+q^{4}+4q^{5}-3q^{6}+\cdots$$
57.3.c.b $4$ $1.553$ $$\Q(\sqrt{-3}, \sqrt{-19})$$ None $$0$$ $$0$$ $$-10$$ $$34$$ $$q+(-\beta _{1}-\beta _{3})q^{2}-\beta _{1}q^{3}+(-2+\beta _{2}+\cdots)q^{4}+\cdots$$

## Decomposition of $$S_{3}^{\mathrm{old}}(57, [\chi])$$ into lower level spaces

$$S_{3}^{\mathrm{old}}(57, [\chi]) \cong$$ $$S_{3}^{\mathrm{new}}(19, [\chi])$$$$^{\oplus 2}$$