Properties

 Label 672.2.ch Level 672 Weight 2 Character orbit ch Rep. character $$\chi_{672}(11,\cdot)$$ Character field $$\Q(\zeta_{24})$$ Dimension 992 Newform subspaces 1 Sturm bound 256 Trace bound 0

Related objects

Defining parameters

 Level: $$N$$ $$=$$ $$672 = 2^{5} \cdot 3 \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 672.ch (of order $$24$$ and degree $$8$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$672$$ Character field: $$\Q(\zeta_{24})$$ Newform subspaces: $$1$$ Sturm bound: $$256$$ Trace bound: $$0$$

Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(672, [\chi])$$.

Total New Old
Modular forms 1056 1056 0
Cusp forms 992 992 0
Eisenstein series 64 64 0

Trace form

 $$992q - 4q^{3} - 8q^{4} - 16q^{6} - 16q^{7} - 4q^{9} + O(q^{10})$$ $$992q - 4q^{3} - 8q^{4} - 16q^{6} - 16q^{7} - 4q^{9} - 8q^{10} - 4q^{12} - 32q^{13} - 32q^{15} + 24q^{16} - 4q^{18} - 8q^{19} - 8q^{21} - 32q^{22} - 44q^{24} - 8q^{25} - 16q^{27} - 16q^{28} - 36q^{30} - 8q^{33} + 64q^{36} - 8q^{37} - 4q^{39} - 72q^{40} - 68q^{42} - 32q^{43} - 4q^{45} - 8q^{46} - 16q^{48} + 20q^{51} + 16q^{52} - 92q^{54} - 32q^{55} - 16q^{57} + 24q^{58} - 20q^{60} - 8q^{61} - 128q^{64} - 20q^{66} - 72q^{67} - 16q^{69} - 16q^{70} - 4q^{72} - 8q^{73} + 16q^{75} - 32q^{76} + 136q^{78} - 16q^{79} - 48q^{82} + 124q^{84} + 48q^{85} - 4q^{87} - 8q^{88} + 128q^{90} - 64q^{91} - 28q^{93} - 64q^{94} - 72q^{96} - 64q^{97} - 16q^{99} + O(q^{100})$$

Decomposition of $$S_{2}^{\mathrm{new}}(672, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
672.2.ch.a $$992$$ $$5.366$$ None $$0$$ $$-4$$ $$0$$ $$-16$$

Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database