# Properties

 Label 693.2.db Level 693 Weight 2 Character orbit db Rep. character $$\chi_{693}(5,\cdot)$$ 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.db (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

 $$736q - 9q^{3} + 170q^{4} - 9q^{5} - 12q^{6} - 3q^{7} + 3q^{9} + O(q^{10})$$ $$736q - 9q^{3} + 170q^{4} - 9q^{5} - 12q^{6} - 3q^{7} + 3q^{9} - 48q^{10} - 6q^{11} - 36q^{12} - 9q^{14} - 174q^{16} - 35q^{18} - 18q^{19} + 18q^{20} - 24q^{21} - 12q^{22} - 42q^{23} - 3q^{24} + 79q^{25} - 48q^{26} - 27q^{27} - 8q^{28} - 18q^{29} - 45q^{30} - 12q^{33} - 12q^{34} - 75q^{35} + 28q^{36} - 6q^{37} - 39q^{38} + 9q^{39} - 63q^{40} + 123q^{42} - 16q^{43} + 27q^{44} - 72q^{45} + 6q^{46} - 18q^{47} - 30q^{48} - 3q^{49} - 111q^{50} + 43q^{51} + 39q^{52} + 36q^{53} - 120q^{54} - 78q^{56} - 34q^{57} - 23q^{58} + 42q^{59} - 43q^{60} - 24q^{62} + 61q^{63} + 132q^{64} + 3q^{66} - 16q^{67} - 9q^{68} - 27q^{69} - 81q^{70} - 41q^{72} - 18q^{73} - 33q^{74} - 51q^{75} - 63q^{77} + 16q^{78} + 42q^{79} + 24q^{80} - 5q^{81} - 30q^{82} - 114q^{84} - 28q^{85} + 15q^{86} + 144q^{87} + 16q^{88} - 30q^{89} - 12q^{90} + 16q^{91} - 168q^{92} - 2q^{93} + 213q^{96} - 60q^{98} - 112q^{99} + O(q^{100})$$

## 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.db.a $$736$$ $$5.534$$ None $$0$$ $$-9$$ $$-9$$ $$-3$$

## Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database