# Properties

 Label 206.2.a Level $206$ Weight $2$ Character orbit 206.a Rep. character $\chi_{206}(1,\cdot)$ Character field $\Q$ Dimension $9$ Newform subspaces $4$ Sturm bound $52$ Trace bound $3$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$206 = 2 \cdot 103$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 206.a (trivial) Character field: $$\Q$$ Newform subspaces: $$4$$ Sturm bound: $$52$$ Trace bound: $$3$$ Distinguishing $$T_p$$: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_0(206))$$.

Total New Old
Modular forms 28 9 19
Cusp forms 25 9 16
Eisenstein series 3 0 3

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

$$2$$$$103$$FrickeDim.
$$+$$$$-$$$$-$$$$5$$
$$-$$$$+$$$$-$$$$4$$
Plus space$$+$$$$0$$
Minus space$$-$$$$9$$

## Trace form

 $$9q - q^{2} + 2q^{3} + 9q^{4} + 2q^{6} + 4q^{7} - q^{8} + 17q^{9} + O(q^{10})$$ $$9q - q^{2} + 2q^{3} + 9q^{4} + 2q^{6} + 4q^{7} - q^{8} + 17q^{9} + 6q^{11} + 2q^{12} + 6q^{13} + 4q^{15} + 9q^{16} - 10q^{17} - 13q^{18} + 12q^{19} + 2q^{22} - 8q^{23} + 2q^{24} + 19q^{25} - 6q^{26} - 16q^{27} + 4q^{28} - 6q^{29} - 12q^{30} + 24q^{31} - q^{32} - 24q^{33} - 18q^{34} - 32q^{35} + 17q^{36} + 12q^{37} - 12q^{38} - 20q^{39} - 18q^{41} - 24q^{42} - 2q^{43} + 6q^{44} - 48q^{45} + 12q^{46} - 24q^{47} + 2q^{48} + 13q^{49} - 31q^{50} - 36q^{51} + 6q^{52} - 16q^{53} - 4q^{54} - 12q^{55} - 24q^{57} + 6q^{58} + 4q^{59} + 4q^{60} - 6q^{61} - 8q^{62} + 4q^{63} + 9q^{64} - 8q^{65} - 8q^{66} + 18q^{67} - 10q^{68} + 28q^{69} + 12q^{70} + 24q^{71} - 13q^{72} + 34q^{73} + 8q^{74} - 18q^{75} + 12q^{76} - 12q^{77} + 36q^{78} + 32q^{79} + 17q^{81} - 18q^{82} + 20q^{83} + 12q^{85} + 10q^{86} - 36q^{87} + 2q^{88} + 18q^{89} + 28q^{90} + 16q^{91} - 8q^{92} + 40q^{93} + 24q^{94} + 8q^{95} + 2q^{96} - 10q^{97} + 7q^{98} + 54q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_0(206))$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces A-L signs $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$ 2 103
206.2.a.a $$1$$ $$1.645$$ $$\Q$$ None $$-1$$ $$2$$ $$4$$ $$0$$ $$+$$ $$-$$ $$q-q^{2}+2q^{3}+q^{4}+4q^{5}-2q^{6}-q^{8}+\cdots$$
206.2.a.b $$2$$ $$1.645$$ $$\Q(\sqrt{13})$$ None $$-2$$ $$-3$$ $$-5$$ $$5$$ $$+$$ $$-$$ $$q-q^{2}+(-1-\beta )q^{3}+q^{4}+(-2-\beta )q^{5}+\cdots$$
206.2.a.c $$2$$ $$1.645$$ $$\Q(\sqrt{29})$$ None $$-2$$ $$1$$ $$1$$ $$-3$$ $$+$$ $$-$$ $$q-q^{2}+(1-\beta )q^{3}+q^{4}+\beta q^{5}+(-1+\cdots)q^{6}+\cdots$$
206.2.a.d $$4$$ $$1.645$$ 4.4.5744.1 None $$4$$ $$2$$ $$0$$ $$2$$ $$-$$ $$+$$ $$q+q^{2}+\beta _{2}q^{3}+q^{4}+\beta _{3}q^{5}+\beta _{2}q^{6}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_0(206))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_0(206)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_0(103))$$$$^{\oplus 2}$$