# Properties

 Label 35.2.a Level $35$ Weight $2$ Character orbit 35.a Rep. character $\chi_{35}(1,\cdot)$ Character field $\Q$ Dimension $3$ Newform subspaces $2$ Sturm bound $8$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$35 = 5 \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 35.a (trivial) Character field: $$\Q$$ Newform subspaces: $$2$$ Sturm bound: $$8$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_0(35))$$.

Total New Old
Modular forms 6 3 3
Cusp forms 3 3 0
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.

$$5$$$$7$$FrickeDim
$$+$$$$-$$$-$$$1$$
$$-$$$$+$$$-$$$2$$
Plus space$$+$$$$0$$
Minus space$$-$$$$3$$

## Trace form

 $$3 q - q^{2} + 3 q^{4} + q^{5} - 8 q^{6} - q^{7} - 9 q^{8} + q^{9} + O(q^{10})$$ $$3 q - q^{2} + 3 q^{4} + q^{5} - 8 q^{6} - q^{7} - 9 q^{8} + q^{9} - q^{10} - 2 q^{11} + 4 q^{12} + 10 q^{13} + q^{14} - 2 q^{15} + 7 q^{16} - 2 q^{17} + 7 q^{18} - 4 q^{19} + 7 q^{20} + 2 q^{21} + 8 q^{22} - 8 q^{23} - 4 q^{24} + 3 q^{25} + 6 q^{26} - 12 q^{27} - 7 q^{28} + 4 q^{29} - 8 q^{30} - 4 q^{31} - 9 q^{32} - 12 q^{33} - 6 q^{34} - 3 q^{35} + 3 q^{36} + 14 q^{37} + 20 q^{38} - 6 q^{39} - 9 q^{40} - 10 q^{41} + 8 q^{42} + 5 q^{45} - 16 q^{46} + 4 q^{47} + 28 q^{48} + 3 q^{49} - q^{50} + 14 q^{51} - 6 q^{52} + 10 q^{53} + 12 q^{54} + 4 q^{55} + 9 q^{56} - 12 q^{57} - 26 q^{58} - 8 q^{59} + 8 q^{60} + 14 q^{61} - 5 q^{63} - q^{64} - 4 q^{66} - 10 q^{68} + 12 q^{69} + q^{70} + 16 q^{71} - 5 q^{72} - 6 q^{73} - 6 q^{74} - 36 q^{76} - 4 q^{77} - 20 q^{78} - 10 q^{79} - q^{80} - 13 q^{81} - 18 q^{82} + 20 q^{83} - 8 q^{84} - 8 q^{85} + 12 q^{86} + 28 q^{87} + 4 q^{88} - 6 q^{89} + 7 q^{90} + 24 q^{92} - 4 q^{93} + 28 q^{94} - 8 q^{95} - 4 q^{96} - 10 q^{97} - q^{98} + 16 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_0(35))$$ into newform subspaces

Label Dim $A$ Field CM Traces A-L signs $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 5 7
35.2.a.a $1$ $0.279$ $$\Q$$ None $$0$$ $$1$$ $$-1$$ $$1$$ $+$ $-$ $$q+q^{3}-2q^{4}-q^{5}+q^{7}-2q^{9}-3q^{11}+\cdots$$
35.2.a.b $2$ $0.279$ $$\Q(\sqrt{17})$$ None $$-1$$ $$-1$$ $$2$$ $$-2$$ $-$ $+$ $$q-\beta q^{2}+(-1+\beta )q^{3}+(2+\beta )q^{4}+q^{5}+\cdots$$