Properties

 Label 57.2.j Level $57$ Weight $2$ Character orbit 57.j Rep. character $\chi_{57}(2,\cdot)$ Character field $\Q(\zeta_{18})$ Dimension $30$ Newform subspaces $2$ Sturm bound $13$ Trace bound $1$

Related objects

Defining parameters

 Level: $$N$$ $$=$$ $$57 = 3 \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 57.j (of order $$18$$ and degree $$6$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$57$$ Character field: $$\Q(\zeta_{18})$$ Newform subspaces: $$2$$ Sturm bound: $$13$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$2$$

Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(57, [\chi])$$.

Total New Old
Modular forms 54 54 0
Cusp forms 30 30 0
Eisenstein series 24 24 0

Trace form

 $$30 q - 9 q^{3} - 18 q^{4} - 9 q^{6} - 6 q^{7} + 3 q^{9} + O(q^{10})$$ $$30 q - 9 q^{3} - 18 q^{4} - 9 q^{6} - 6 q^{7} + 3 q^{9} - 6 q^{10} - 9 q^{12} - 9 q^{13} - 9 q^{15} + 30 q^{16} - 9 q^{19} + 3 q^{21} + 24 q^{22} - 21 q^{24} + 12 q^{25} - 18 q^{28} + 42 q^{30} - 18 q^{31} + 21 q^{33} - 42 q^{34} + 63 q^{36} + 30 q^{40} + 105 q^{42} + 15 q^{43} + 6 q^{45} - 54 q^{46} - 33 q^{48} - 15 q^{49} + 3 q^{51} - 60 q^{52} - 87 q^{54} - 90 q^{55} - 6 q^{57} + 24 q^{58} - 66 q^{60} - 48 q^{61} - 45 q^{63} + 42 q^{64} - 57 q^{66} + 33 q^{67} - 36 q^{69} + 18 q^{70} + 24 q^{72} + 141 q^{73} + 12 q^{76} + 9 q^{78} + 42 q^{79} + 3 q^{81} + 126 q^{82} + 99 q^{84} - 6 q^{85} + 15 q^{87} + 54 q^{88} + 24 q^{90} + 114 q^{91} + 87 q^{93} - 18 q^{96} - 78 q^{97} + 12 q^{99} + O(q^{100})$$

Decomposition of $$S_{2}^{\mathrm{new}}(57, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
57.2.j.a $6$ $0.455$ $$\Q(\zeta_{18})$$ $$\Q(\sqrt{-3})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q+(-\zeta_{18}^{2}+2\zeta_{18}^{5})q^{3}+2\zeta_{18}q^{4}+\cdots$$
57.2.j.b $24$ $0.455$ None $$0$$ $$-9$$ $$0$$ $$-6$$