# Properties

 Label 145.2.b Level $145$ Weight $2$ Character orbit 145.b Rep. character $\chi_{145}(59,\cdot)$ Character field $\Q$ Dimension $14$ Newform subspaces $3$ Sturm bound $30$ Trace bound $4$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$145 = 5 \cdot 29$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 145.b (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$5$$ Character field: $$\Q$$ Newform subspaces: $$3$$ Sturm bound: $$30$$ Trace bound: $$4$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(145, [\chi])$$.

Total New Old
Modular forms 18 14 4
Cusp forms 14 14 0
Eisenstein series 4 0 4

## Trace form

 $$14 q - 18 q^{4} + 4 q^{6} - 10 q^{9} + O(q^{10})$$ $$14 q - 18 q^{4} + 4 q^{6} - 10 q^{9} + 2 q^{10} - 8 q^{11} + 8 q^{14} - 2 q^{15} + 18 q^{16} - 12 q^{19} + 4 q^{20} - 28 q^{24} + 16 q^{25} - 4 q^{26} + 6 q^{29} + 34 q^{30} - 8 q^{31} - 28 q^{34} + 8 q^{35} - 10 q^{36} + 36 q^{39} + 34 q^{40} + 4 q^{41} - 26 q^{45} - 40 q^{46} - 22 q^{49} + 14 q^{50} + 24 q^{51} - 20 q^{54} - 26 q^{55} + 16 q^{56} - 40 q^{59} + 26 q^{60} + 20 q^{61} - 26 q^{64} + 18 q^{65} + 4 q^{66} + 32 q^{69} + 48 q^{70} + 16 q^{71} + 4 q^{74} - 6 q^{75} - 20 q^{76} - 40 q^{79} - 64 q^{80} - 18 q^{81} + 40 q^{84} - 20 q^{85} - 36 q^{86} + 12 q^{89} - 24 q^{90} + 56 q^{91} + 20 q^{94} - 4 q^{95} + 28 q^{96} - 68 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(145, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
145.2.b.a $4$ $1.158$ $$\Q(\sqrt{-3}, \sqrt{-11})$$ None $$0$$ $$0$$ $$-3$$ $$0$$ $$q+\beta _{2}q^{2}+(-\beta _{1}-\beta _{3})q^{3}-q^{4}+(-1+\cdots)q^{5}+\cdots$$
145.2.b.b $4$ $1.158$ $$\Q(\sqrt{-2}, \sqrt{3})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+(\beta _{1}-\beta _{3})q^{3}+\beta _{2}q^{4}+(\beta _{1}+\cdots)q^{5}+\cdots$$
145.2.b.c $6$ $1.158$ 6.0.84345856.2 None $$0$$ $$0$$ $$3$$ $$0$$ $$q+\beta _{1}q^{2}+(-\beta _{1}+\beta _{5})q^{3}+(-3+\beta _{3}+\cdots)q^{4}+\cdots$$