Properties

 Label 7.3.b Level 7 Weight 3 Character orbit b Rep. character $$\chi_{7}(6,\cdot)$$ Character field $$\Q$$ Dimension 1 Newforms 1 Sturm bound 2 Trace bound 0

Related objects

Defining parameters

 Level: $$N$$ = $$7$$ Weight: $$k$$ = $$3$$ Character orbit: $$[\chi]$$ = 7.b (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$7$$ Character field: $$\Q$$ Newforms: $$1$$ Sturm bound: $$2$$ Trace bound: $$0$$

Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(7, [\chi])$$.

Total New Old
Modular forms 3 3 0
Cusp forms 1 1 0
Eisenstein series 2 2 0

Trace form

 $$q - 3q^{2} + 5q^{4} - 7q^{7} - 3q^{8} + 9q^{9} + O(q^{10})$$ $$q - 3q^{2} + 5q^{4} - 7q^{7} - 3q^{8} + 9q^{9} - 6q^{11} + 21q^{14} - 11q^{16} - 27q^{18} + 18q^{22} + 18q^{23} + 25q^{25} - 35q^{28} - 54q^{29} + 45q^{32} + 45q^{36} - 38q^{37} + 58q^{43} - 30q^{44} - 54q^{46} + 49q^{49} - 75q^{50} - 6q^{53} + 21q^{56} + 162q^{58} - 63q^{63} - 91q^{64} - 118q^{67} + 114q^{71} - 27q^{72} + 114q^{74} + 42q^{77} - 94q^{79} + 81q^{81} - 174q^{86} + 18q^{88} + 90q^{92} - 147q^{98} - 54q^{99} + O(q^{100})$$

Decomposition of $$S_{3}^{\mathrm{new}}(7, [\chi])$$ into irreducible Hecke orbits

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
7.3.b.a $$1$$ $$0.191$$ $$\Q$$ $$\Q(\sqrt{-7})$$ $$-3$$ $$0$$ $$0$$ $$-7$$ $$q-3q^{2}+5q^{4}-7q^{7}-3q^{8}+9q^{9}+\cdots$$