# Properties

 Label 133.2.a Level $133$ Weight $2$ Character orbit 133.a Rep. character $\chi_{133}(1,\cdot)$ Character field $\Q$ Dimension $9$ Newform subspaces $4$ Sturm bound $26$ Trace bound $2$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$133 = 7 \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 133.a (trivial) Character field: $$\Q$$ Newform subspaces: $$4$$ Sturm bound: $$26$$ Trace bound: $$2$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_0(133))$$.

Total New Old
Modular forms 14 9 5
Cusp forms 11 9 2
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.

$$7$$$$19$$FrickeDim
$$+$$$$+$$$+$$$2$$
$$+$$$$-$$$-$$$3$$
$$-$$$$+$$$-$$$2$$
$$-$$$$-$$$+$$$2$$
Plus space$$+$$$$4$$
Minus space$$-$$$$5$$

## Trace form

 $$9 q - q^{2} + 11 q^{4} - 6 q^{5} - q^{7} - 9 q^{8} + 9 q^{9} + O(q^{10})$$ $$9 q - q^{2} + 11 q^{4} - 6 q^{5} - q^{7} - 9 q^{8} + 9 q^{9} - 10 q^{10} - 8 q^{11} - 16 q^{12} - 6 q^{13} + q^{14} + 3 q^{16} - 2 q^{17} + 7 q^{18} + q^{19} + 6 q^{20} + 8 q^{22} + 20 q^{24} - q^{25} + 2 q^{26} - 12 q^{27} - 7 q^{28} + 2 q^{29} + 12 q^{30} - 8 q^{31} - 9 q^{32} + 36 q^{33} + 18 q^{34} - 2 q^{35} - 5 q^{36} - 22 q^{37} + 3 q^{38} - 20 q^{39} + 6 q^{40} + 10 q^{41} - 12 q^{42} - 20 q^{43} - 8 q^{44} - 18 q^{45} + 24 q^{46} + 12 q^{47} - 36 q^{48} + 9 q^{49} - 7 q^{50} + 36 q^{51} - 14 q^{52} - 10 q^{53} + 16 q^{54} + 12 q^{55} - 3 q^{56} + 10 q^{58} - 36 q^{60} - 6 q^{61} + 4 q^{62} + 3 q^{63} - q^{64} + 24 q^{65} - 24 q^{66} + 8 q^{67} - 42 q^{68} + 28 q^{69} + 18 q^{70} + 20 q^{71} - 57 q^{72} - 6 q^{73} + 46 q^{74} - 4 q^{75} + 7 q^{76} - 4 q^{77} - 12 q^{78} - 16 q^{79} + 26 q^{80} + 41 q^{81} + 18 q^{82} + 20 q^{83} + 12 q^{84} + 12 q^{86} + 52 q^{87} + 48 q^{88} - 14 q^{89} - 102 q^{90} - 6 q^{91} + 12 q^{92} - 40 q^{93} - 12 q^{94} - 10 q^{95} + 16 q^{96} - 10 q^{97} - q^{98} - 52 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_0(133))$$ into newform subspaces

Label Dim $A$ Field CM Traces A-L signs $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 7 19
133.2.a.a $2$ $1.062$ $$\Q(\sqrt{5})$$ None $$-3$$ $$-3$$ $$0$$ $$-2$$ $+$ $+$ $$q+(-1-\beta )q^{2}+(-1-\beta )q^{3}+3\beta q^{4}+\cdots$$
133.2.a.b $2$ $1.062$ $$\Q(\sqrt{13})$$ None $$-1$$ $$-3$$ $$-6$$ $$2$$ $-$ $-$ $$q-\beta q^{2}+(-2+\beta )q^{3}+(1+\beta )q^{4}-3q^{5}+\cdots$$
133.2.a.c $2$ $1.062$ $$\Q(\sqrt{5})$$ None $$1$$ $$3$$ $$2$$ $$2$$ $-$ $+$ $$q+\beta q^{2}+(2-\beta )q^{3}+(-1+\beta )q^{4}+q^{5}+\cdots$$
133.2.a.d $3$ $1.062$ 3.3.229.1 None $$2$$ $$3$$ $$-2$$ $$-3$$ $+$ $-$ $$q+(1+\beta _{2})q^{2}+(1-\beta _{1})q^{3}+(2+\beta _{1}+\cdots)q^{4}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_0(133))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_0(133)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_0(19))$$$$^{\oplus 2}$$