# Properties

 Label 115.3.c Level $115$ Weight $3$ Character orbit 115.c Rep. character $\chi_{115}(114,\cdot)$ Character field $\Q$ Dimension $22$ Newform subspaces $3$ Sturm bound $36$ Trace bound $5$

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## Defining parameters

 Level: $$N$$ $$=$$ $$115 = 5 \cdot 23$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 115.c (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$115$$ Character field: $$\Q$$ Newform subspaces: $$3$$ Sturm bound: $$36$$ Trace bound: $$5$$ Distinguishing $$T_p$$: $$2$$, $$7$$

## Dimensions

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

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

## Trace form

 $$22 q - 48 q^{4} - 8 q^{6} - 54 q^{9} + O(q^{10})$$ $$22 q - 48 q^{4} - 8 q^{6} - 54 q^{9} + 120 q^{16} + 44 q^{24} + 38 q^{25} - 56 q^{26} - 114 q^{29} + 130 q^{31} + 2 q^{35} + 40 q^{36} - 168 q^{39} + 58 q^{41} - 248 q^{46} + 152 q^{49} + 200 q^{50} - 196 q^{54} + 268 q^{55} + 62 q^{59} + 100 q^{64} + 376 q^{69} - 636 q^{70} - 142 q^{71} + 428 q^{75} - 826 q^{81} - 174 q^{85} + 276 q^{94} + 184 q^{95} - 264 q^{96} + O(q^{100})$$

## 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.c.a $1$ $3.134$ $$\Q$$ $$\Q(\sqrt{-115})$$ $$0$$ $$0$$ $$-5$$ $$9$$ $$q+4q^{4}-5q^{5}+9q^{7}+9q^{9}+2^{4}q^{16}+\cdots$$
115.3.c.b $1$ $3.134$ $$\Q$$ $$\Q(\sqrt{-115})$$ $$0$$ $$0$$ $$5$$ $$-9$$ $$q+4q^{4}+5q^{5}-9q^{7}+9q^{9}+2^{4}q^{16}+\cdots$$
115.3.c.c $20$ $3.134$ $$\mathbb{Q}[x]/(x^{20} + \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{3}q^{2}-\beta _{4}q^{3}+(-3+\beta _{7}-\beta _{8}+\cdots)q^{4}+\cdots$$