Properties

 Label 145.2.a Level $145$ Weight $2$ Character orbit 145.a Rep. character $\chi_{145}(1,\cdot)$ Character field $\Q$ Dimension $9$ Newform subspaces $4$ Sturm bound $30$ Trace bound $2$

Related objects

Defining parameters

 Level: $$N$$ $$=$$ $$145 = 5 \cdot 29$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 145.a (trivial) Character field: $$\Q$$ Newform subspaces: $$4$$ Sturm bound: $$30$$ Trace bound: $$2$$ Distinguishing $$T_p$$: $$2$$

Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_0(145))$$.

Total New Old
Modular forms 16 9 7
Cusp forms 13 9 4
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.

$$5$$$$29$$FrickeDim
$$+$$$$+$$$+$$$1$$
$$+$$$$-$$$-$$$3$$
$$-$$$$+$$$-$$$3$$
$$-$$$$-$$$+$$$2$$
Plus space$$+$$$$3$$
Minus space$$-$$$$6$$

Trace form

 $$9 q + q^{2} - 4 q^{3} + 7 q^{4} + q^{5} + 4 q^{6} - 4 q^{7} + 9 q^{8} + 5 q^{9} + O(q^{10})$$ $$9 q + q^{2} - 4 q^{3} + 7 q^{4} + q^{5} + 4 q^{6} - 4 q^{7} + 9 q^{8} + 5 q^{9} - 3 q^{10} - 16 q^{12} - 10 q^{13} - 8 q^{14} + 7 q^{16} - 6 q^{17} - 7 q^{18} - 16 q^{19} - q^{20} + 12 q^{22} + 20 q^{23} - 12 q^{24} + 9 q^{25} - 2 q^{26} + 8 q^{27} + 4 q^{28} + q^{29} - 4 q^{30} - 4 q^{31} + 9 q^{32} - 8 q^{33} - 18 q^{34} + 4 q^{35} - 21 q^{36} + 6 q^{37} - 12 q^{38} + 32 q^{39} - 15 q^{40} - 22 q^{41} + 8 q^{42} - 12 q^{43} + 5 q^{45} + 40 q^{46} + 8 q^{47} - 12 q^{48} + q^{49} + q^{50} - 8 q^{51} - 6 q^{52} + 14 q^{53} + 24 q^{54} - 4 q^{55} - 24 q^{56} - 8 q^{57} + q^{58} + 4 q^{59} - 12 q^{60} - 2 q^{61} + 40 q^{62} + 12 q^{63} + 15 q^{64} - 2 q^{65} - 16 q^{66} + 16 q^{67} - 38 q^{68} + 16 q^{69} + 12 q^{70} + 32 q^{71} - 31 q^{72} - 26 q^{73} - 46 q^{74} - 4 q^{75} + 16 q^{76} + 4 q^{77} - 24 q^{78} + 4 q^{79} - q^{80} - 15 q^{81} + 26 q^{82} + 16 q^{83} - 16 q^{84} - 2 q^{85} + 12 q^{86} - 8 q^{87} + 52 q^{88} + 26 q^{89} + 13 q^{90} - 24 q^{91} - 4 q^{92} + 8 q^{94} - 12 q^{95} + 4 q^{96} - 34 q^{97} + 69 q^{98} + 16 q^{99} + O(q^{100})$$

Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_0(145))$$ into newform subspaces

Label Dim $A$ Field CM Traces A-L signs $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 5 29
145.2.a.a $1$ $1.158$ $$\Q$$ None $$-1$$ $$0$$ $$-1$$ $$-2$$ $+$ $+$ $$q-q^{2}-q^{4}-q^{5}-2q^{7}+3q^{8}-3q^{9}+\cdots$$
145.2.a.b $2$ $1.158$ $$\Q(\sqrt{2})$$ None $$-2$$ $$-4$$ $$2$$ $$-4$$ $-$ $-$ $$q+(-1+\beta )q^{2}-2q^{3}+(1-2\beta )q^{4}+\cdots$$
145.2.a.c $3$ $1.158$ 3.3.148.1 None $$1$$ $$2$$ $$3$$ $$4$$ $-$ $+$ $$q+\beta _{1}q^{2}+(1-\beta _{1}-\beta _{2})q^{3}+(\beta _{1}+\beta _{2})q^{4}+\cdots$$
145.2.a.d $3$ $1.158$ 3.3.148.1 None $$3$$ $$-2$$ $$-3$$ $$-2$$ $+$ $-$ $$q+(1+\beta _{2})q^{2}+(-1+\beta _{1}+\beta _{2})q^{3}+\cdots$$

Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_0(145))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_0(145)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_0(29))$$$$^{\oplus 2}$$