# Properties

 Label 100.2.c Level $100$ Weight $2$ Character orbit 100.c Rep. character $\chi_{100}(49,\cdot)$ Character field $\Q$ Dimension $2$ Newform subspaces $1$ Sturm bound $30$ Trace bound $0$

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## Defining parameters

 Level: $$N$$ $$=$$ $$100 = 2^{2} \cdot 5^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 100.c (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$5$$ Character field: $$\Q$$ Newform subspaces: $$1$$ Sturm bound: $$30$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(100, [\chi])$$.

Total New Old
Modular forms 24 2 22
Cusp forms 6 2 4
Eisenstein series 18 0 18

## Trace form

 $$2 q - 2 q^{9} + O(q^{10})$$ $$2 q - 2 q^{9} + 8 q^{19} - 8 q^{21} - 12 q^{29} - 8 q^{31} + 8 q^{39} + 12 q^{41} + 6 q^{49} + 24 q^{51} - 24 q^{59} + 4 q^{61} + 24 q^{69} - 24 q^{71} - 16 q^{79} - 22 q^{81} + 12 q^{89} + 8 q^{91} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(100, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
100.2.c.a $2$ $0.799$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{3}+iq^{7}-q^{9}-iq^{13}-3iq^{17}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(100, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(100, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(50, [\chi])$$$$^{\oplus 2}$$