# Properties

 Label 693.2.cb Level 693 Weight 2 Character orbit cb Rep. character $$\chi_{693}(74,\cdot)$$ 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.cb (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

 $$736q - 3q^{3} - 182q^{4} - 9q^{5} - 20q^{6} - 5q^{7} - 9q^{9} + O(q^{10})$$ $$736q - 3q^{3} - 182q^{4} - 9q^{5} - 20q^{6} - 5q^{7} - 9q^{9} - 18q^{11} + 20q^{12} - 10q^{13} - 9q^{14} - 24q^{15} - 158q^{16} - 5q^{18} - 10q^{19} - 36q^{20} - 4q^{22} - 42q^{23} + 35q^{24} - 73q^{25} - 24q^{26} - 21q^{27} - 20q^{28} - 30q^{29} - 35q^{30} - 6q^{31} + 40q^{33} - 20q^{34} + 75q^{35} + 36q^{36} - 6q^{37} - 15q^{38} - 45q^{39} + 45q^{40} - 30q^{41} - 71q^{42} + 39q^{44} + 36q^{45} + 10q^{46} - 52q^{48} - 3q^{49} - 105q^{50} + 75q^{51} + 5q^{52} - 36q^{53} - 30q^{55} + 30q^{56} - 60q^{57} + 29q^{58} + 121q^{60} - 10q^{61} - 105q^{63} - 148q^{64} - 25q^{66} - 16q^{67} - 15q^{68} + 105q^{69} - 33q^{70} - 125q^{72} - 10q^{73} - 15q^{74} + 19q^{75} - 15q^{77} + 48q^{78} - 10q^{79} + 108q^{80} + 59q^{81} - 10q^{82} - 30q^{83} - 100q^{84} - 10q^{85} - 33q^{86} + 8q^{88} + 30q^{89} - 180q^{90} + 16q^{91} + 72q^{92} - 2q^{93} - 10q^{94} + 45q^{96} - 6q^{97} - 10q^{99} + O(q^{100})$$

## 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.cb.a $$736$$ $$5.534$$ None $$0$$ $$-3$$ $$-9$$ $$-5$$

## Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database