# Properties

 Label 693.2.co Level 693 Weight 2 Character orbit co Rep. character $$\chi_{693}(61,\cdot)$$ Character field $$\Q(\zeta_{30})$$ Dimension 736 Newform subspaces 1 Sturm bound 192 Trace bound 0

# Related objects

## Defining parameters

 Level: $$N$$ = $$693 = 3^{2} \cdot 7 \cdot 11$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 693.co (of order $$30$$ and degree $$8$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$693$$ Character field: $$\Q(\zeta_{30})$$ Newform subspaces: $$1$$ Sturm bound: $$192$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(693, [\chi])$$.

Total New Old
Modular forms 800 800 0
Cusp forms 736 736 0
Eisenstein series 64 64 0

## Trace form

 $$736q + 5q^{2} - 9q^{3} - 85q^{4} - 5q^{7} - 40q^{8} - 9q^{9} + O(q^{10})$$ $$736q + 5q^{2} - 9q^{3} - 85q^{4} - 5q^{7} - 40q^{8} - 9q^{9} - 4q^{11} - 24q^{12} + 5q^{14} - 24q^{15} + 87q^{16} - 30q^{17} - 5q^{18} - 30q^{19} - 66q^{20} - 12q^{22} - 4q^{23} - 15q^{24} + 146q^{25} - 66q^{26} + 27q^{27} - 20q^{28} - 10q^{29} + 25q^{30} - 9q^{31} - 84q^{33} + 12q^{34} + 5q^{35} - 44q^{36} - 6q^{37} - 45q^{39} - 90q^{41} - 57q^{42} - q^{44} - 24q^{45} - 30q^{46} - 9q^{47} + 30q^{48} - 3q^{49} + 15q^{50} + 35q^{51} - 38q^{53} + 102q^{56} - 60q^{57} - 26q^{58} + 21q^{59} + 99q^{60} - 15q^{61} - 35q^{63} + 132q^{64} + 90q^{66} + 8q^{67} - 27q^{69} - 68q^{70} - 40q^{71} - 65q^{72} - 30q^{73} - 290q^{74} - 69q^{75} + 21q^{77} - 136q^{78} + 5q^{79} + 150q^{80} + 47q^{81} - 30q^{82} - 5q^{84} - 10q^{85} - 14q^{86} - 32q^{88} - 78q^{89} + 30q^{90} - 40q^{91} - 72q^{92} + 123q^{93} - 15q^{94} - 35q^{95} - 135q^{96} - 80q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(693, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
693.2.co.a $$736$$ $$5.534$$ None $$5$$ $$-9$$ $$0$$ $$-5$$

## Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database