# Properties

 Label 145.2.d Level $145$ Weight $2$ Character orbit 145.d Rep. character $\chi_{145}(144,\cdot)$ Character field $\Q$ Dimension $12$ Newform subspaces $3$ Sturm bound $30$ Trace bound $2$

# Related objects

## Defining parameters

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

## Dimensions

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

Total New Old
Modular forms 16 16 0
Cusp forms 12 12 0
Eisenstein series 4 4 0

## Trace form

 $$12 q + 4 q^{4} + 2 q^{5} - 4 q^{6} + O(q^{10})$$ $$12 q + 4 q^{4} + 2 q^{5} - 4 q^{6} - 12 q^{16} - 18 q^{20} + 12 q^{24} - 26 q^{25} + 12 q^{29} + 14 q^{30} + 24 q^{34} + 4 q^{35} - 48 q^{36} + 4 q^{45} - 28 q^{49} + 8 q^{51} - 28 q^{54} + 40 q^{59} + 4 q^{64} + 22 q^{65} + 48 q^{71} - 16 q^{74} - 2 q^{80} - 20 q^{81} + 60 q^{86} + 56 q^{91} + 36 q^{94} - 20 q^{96} + O(q^{100})$$

## 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.d.a $4$ $1.158$ $$\Q(\sqrt{-3}, \sqrt{17})$$ None $$-4$$ $$2$$ $$3$$ $$0$$ $$q-q^{2}-\beta _{2}q^{3}-q^{4}+(1+\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots$$
145.2.d.b $4$ $1.158$ $$\Q(i, \sqrt{5})$$ None $$0$$ $$0$$ $$-4$$ $$0$$ $$q-\beta _{3}q^{2}+3q^{4}+(-1-\beta _{1})q^{5}+\beta _{1}q^{7}+\cdots$$
145.2.d.c $4$ $1.158$ $$\Q(\sqrt{-3}, \sqrt{17})$$ None $$4$$ $$-2$$ $$3$$ $$0$$ $$q+q^{2}+(-1+\beta _{2})q^{3}-q^{4}+(1-\beta _{1}+\cdots)q^{5}+\cdots$$