Properties

 Label 252.2.o Level 252 Weight 2 Character orbit o Rep. character $$\chi_{252}(95,\cdot)$$ Character field $$\Q(\zeta_{6})$$ Dimension 88 Newform subspaces 1 Sturm bound 96 Trace bound 0

Related objects

Defining parameters

 Level: $$N$$ = $$252 = 2^{2} \cdot 3^{2} \cdot 7$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 252.o (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$252$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$1$$ Sturm bound: $$96$$ Trace bound: $$0$$

Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(252, [\chi])$$.

Total New Old
Modular forms 104 104 0
Cusp forms 88 88 0
Eisenstein series 16 16 0

Trace form

 $$88q - 3q^{2} + q^{4} - 6q^{6} - 2q^{9} + O(q^{10})$$ $$88q - 3q^{2} + q^{4} - 6q^{6} - 2q^{9} + 2q^{10} + 3q^{12} - 4q^{13} - 3q^{14} + q^{16} + 5q^{18} - 6q^{20} - 6q^{22} - 14q^{24} - 60q^{25} - 6q^{26} - 24q^{29} + 22q^{30} + 27q^{32} - 26q^{33} - 4q^{34} + 2q^{36} - 4q^{37} + 8q^{40} - 12q^{41} - 13q^{42} - 57q^{44} + 42q^{45} - 6q^{46} - 43q^{48} - 2q^{49} + 9q^{50} + 14q^{52} - 22q^{54} - 66q^{56} - 28q^{57} - 10q^{58} + 32q^{60} + 2q^{61} - 8q^{64} + 18q^{65} - 93q^{66} - 6q^{69} + 30q^{70} + 53q^{72} - 4q^{73} - 6q^{76} - 30q^{77} + 55q^{78} + 87q^{80} + 26q^{81} - 4q^{82} - 7q^{84} - 14q^{85} - 18q^{88} + 60q^{89} + 41q^{90} + 24q^{92} - 30q^{93} + 9q^{94} - 20q^{96} - 4q^{97} - 57q^{98} + O(q^{100})$$

Decomposition of $$S_{2}^{\mathrm{new}}(252, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
252.2.o.a $$88$$ $$2.012$$ None $$-3$$ $$0$$ $$0$$ $$0$$

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database