# Properties

 Label 115.2.b Level $115$ Weight $2$ Character orbit 115.b Rep. character $\chi_{115}(24,\cdot)$ Character field $\Q$ Dimension $10$ Newform subspaces $2$ Sturm bound $24$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$115 = 5 \cdot 23$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 115.b (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$5$$ Character field: $$\Q$$ Newform subspaces: $$2$$ Sturm bound: $$24$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(115, [\chi])$$.

Total New Old
Modular forms 14 10 4
Cusp forms 10 10 0
Eisenstein series 4 0 4

## Trace form

 $$10 q - 8 q^{4} - 2 q^{5} - 4 q^{6} - 10 q^{9} + O(q^{10})$$ $$10 q - 8 q^{4} - 2 q^{5} - 4 q^{6} - 10 q^{9} + 2 q^{10} + 4 q^{11} + 4 q^{14} + 10 q^{15} - 4 q^{16} - 8 q^{19} - 16 q^{20} + 24 q^{24} - 10 q^{25} + 20 q^{26} + 2 q^{29} + 14 q^{30} - 10 q^{31} - 8 q^{34} + 26 q^{35} - 12 q^{36} + 8 q^{39} - 10 q^{40} - 30 q^{41} - 12 q^{44} + 20 q^{45} - 4 q^{46} + 12 q^{49} + 12 q^{50} - 28 q^{54} - 16 q^{55} + 28 q^{56} - 6 q^{59} - 24 q^{60} - 28 q^{61} + 56 q^{64} - 10 q^{65} - 16 q^{66} + 8 q^{69} - 36 q^{70} - 22 q^{71} + 44 q^{74} + 16 q^{75} - 4 q^{76} - 20 q^{79} - 18 q^{80} - 6 q^{81} - 12 q^{84} + 22 q^{85} + 44 q^{86} + 44 q^{89} + 56 q^{91} + 92 q^{94} - 36 q^{95} + 28 q^{96} - 72 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(115, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
115.2.b.a $2$ $0.918$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$4$$ $$0$$ $$q+2iq^{2}-2iq^{3}-2q^{4}+(2+i)q^{5}+\cdots$$
115.2.b.b $8$ $0.918$ 8.0.527896576.2 None $$0$$ $$0$$ $$-6$$ $$0$$ $$q+\beta _{7}q^{2}+(-\beta _{1}-\beta _{3}+\beta _{5})q^{3}+(-1+\cdots)q^{4}+\cdots$$