# Properties

 Label 115.3.d Level $115$ Weight $3$ Character orbit 115.d Rep. character $\chi_{115}(91,\cdot)$ Character field $\Q$ Dimension $16$ Newform subspaces $2$ Sturm bound $36$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$115 = 5 \cdot 23$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 115.d (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$23$$ Character field: $$\Q$$ Newform subspaces: $$2$$ Sturm bound: $$36$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(115, [\chi])$$.

Total New Old
Modular forms 26 16 10
Cusp forms 22 16 6
Eisenstein series 4 0 4

## Trace form

 $$16 q - 4 q^{2} + 16 q^{4} + 26 q^{6} + 22 q^{8} + 32 q^{9} + O(q^{10})$$ $$16 q - 4 q^{2} + 16 q^{4} + 26 q^{6} + 22 q^{8} + 32 q^{9} - 30 q^{12} - 12 q^{13} - 8 q^{16} - 70 q^{18} + 34 q^{23} + 84 q^{24} - 80 q^{25} - 62 q^{26} + 96 q^{27} + 26 q^{29} + 10 q^{31} - 56 q^{32} - 50 q^{35} - 254 q^{36} - 76 q^{39} + 58 q^{41} + 96 q^{46} + 224 q^{47} - 226 q^{48} - 254 q^{49} + 20 q^{50} + 82 q^{52} - 26 q^{54} + 40 q^{55} + 174 q^{58} - 26 q^{59} - 130 q^{62} - 146 q^{64} + 280 q^{69} + 120 q^{70} + 18 q^{71} - 70 q^{72} + 168 q^{73} + 484 q^{77} - 106 q^{78} + 96 q^{81} - 2 q^{82} + 130 q^{85} - 44 q^{87} - 152 q^{92} - 76 q^{93} + 150 q^{94} + 80 q^{95} - 398 q^{96} + 692 q^{98} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(115, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
115.3.d.a $6$ $3.134$ $$\mathbb{Q}[x]/(x^{6} - \cdots)$$ None $$-6$$ $$2$$ $$0$$ $$0$$ $$q-q^{2}+\beta _{4}q^{3}-3q^{4}-\beta _{3}q^{5}-\beta _{4}q^{6}+\cdots$$
115.3.d.b $10$ $3.134$ $$\mathbb{Q}[x]/(x^{10} - \cdots)$$ None $$2$$ $$-2$$ $$0$$ $$0$$ $$q+\beta _{4}q^{2}-\beta _{7}q^{3}+(3+\beta _{6})q^{4}+\beta _{5}q^{5}+\cdots$$

## Decomposition of $$S_{3}^{\mathrm{old}}(115, [\chi])$$ into lower level spaces

$$S_{3}^{\mathrm{old}}(115, [\chi]) \cong$$ $$S_{3}^{\mathrm{new}}(23, [\chi])$$$$^{\oplus 2}$$