# Properties

 Label 672.2.cl Level 672 Weight 2 Character orbit cl Rep. character $$\chi_{672}(5,\cdot)$$ 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.cl (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

 $$992q - 12q^{3} - 8q^{4} - 16q^{7} - 4q^{9} + O(q^{10})$$ $$992q - 12q^{3} - 8q^{4} - 16q^{7} - 4q^{9} - 24q^{10} - 12q^{12} + 24q^{16} - 4q^{18} - 24q^{19} - 8q^{21} - 32q^{22} - 12q^{24} - 8q^{25} - 16q^{28} + 28q^{30} - 48q^{31} - 24q^{33} - 96q^{36} - 8q^{37} - 4q^{39} - 24q^{40} - 68q^{42} - 32q^{43} - 12q^{45} - 8q^{46} - 28q^{51} - 96q^{52} - 12q^{54} - 16q^{57} - 40q^{58} + 12q^{60} - 24q^{61} - 16q^{63} + 64q^{64} - 12q^{66} - 72q^{67} - 16q^{70} - 4q^{72} - 24q^{73} - 72q^{75} + 136q^{78} + 96q^{82} - 140q^{84} - 112q^{85} - 12q^{87} - 8q^{88} + 32q^{91} - 28q^{93} - 96q^{94} + 192q^{96} - 16q^{99} + O(q^{100})$$

## 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.cl.a $$992$$ $$5.366$$ None $$0$$ $$-12$$ $$0$$ $$-16$$

## Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database