# Properties

 Label 57.3.g Level $57$ Weight $3$ Character orbit 57.g Rep. character $\chi_{57}(31,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $12$ Newform subspaces $2$ Sturm bound $20$ Trace bound $2$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$57 = 3 \cdot 19$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 57.g (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$19$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$2$$ Sturm bound: $$20$$ Trace bound: $$2$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

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

Total New Old
Modular forms 32 12 20
Cusp forms 24 12 12
Eisenstein series 8 0 8

## Trace form

 $$12 q + 10 q^{4} + 2 q^{5} - 6 q^{6} + 4 q^{7} + 18 q^{9} + O(q^{10})$$ $$12 q + 10 q^{4} + 2 q^{5} - 6 q^{6} + 4 q^{7} + 18 q^{9} + 84 q^{10} - 36 q^{11} - 18 q^{13} - 138 q^{14} - 18 q^{15} - 22 q^{16} + 28 q^{17} - 56 q^{19} - 92 q^{20} + 72 q^{21} - 48 q^{22} + 30 q^{23} + 60 q^{24} - 6 q^{25} + 176 q^{26} - 82 q^{28} - 36 q^{29} - 48 q^{30} - 12 q^{32} + 54 q^{33} - 60 q^{34} - 30 q^{35} - 30 q^{36} + 202 q^{38} - 24 q^{39} + 192 q^{40} + 120 q^{41} - 24 q^{42} + 118 q^{43} + 82 q^{44} + 12 q^{45} - 76 q^{47} + 72 q^{48} + 48 q^{49} - 144 q^{51} + 78 q^{52} + 90 q^{53} + 18 q^{54} - 28 q^{55} - 144 q^{57} - 304 q^{58} + 162 q^{59} - 234 q^{60} - 114 q^{61} - 230 q^{62} + 6 q^{63} + 212 q^{64} - 120 q^{66} - 102 q^{67} - 176 q^{68} - 96 q^{70} - 288 q^{71} - 54 q^{72} + 26 q^{73} - 96 q^{74} - 2 q^{76} + 244 q^{77} - 90 q^{78} - 114 q^{79} + 318 q^{80} - 54 q^{81} + 76 q^{82} - 600 q^{83} + 184 q^{85} + 210 q^{86} + 336 q^{87} + 570 q^{89} + 252 q^{90} - 306 q^{91} - 14 q^{92} + 108 q^{93} - 110 q^{95} + 228 q^{96} - 240 q^{97} + 276 q^{98} - 54 q^{99} + O(q^{100})$$

## 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.g.a $6$ $1.553$ 6.0.6967728.1 None $$-3$$ $$9$$ $$-2$$ $$26$$ $$q+\beta _{3}q^{2}+(2-\beta _{1})q^{3}+(-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$$
57.3.g.b $6$ $1.553$ 6.0.92607408.1 None $$3$$ $$-9$$ $$4$$ $$-22$$ $$q-\beta _{4}q^{2}+(-2-\beta _{3})q^{3}+(1+\beta _{1}+2\beta _{3}+\cdots)q^{4}+\cdots$$

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

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