# Properties

 Label 300.2.d Level $300$ Weight $2$ Character orbit 300.d Rep. character $\chi_{300}(49,\cdot)$ Character field $\Q$ Dimension $2$ Newform subspaces $1$ Sturm bound $120$ Trace bound $0$

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## Defining parameters

 Level: $$N$$ $$=$$ $$300 = 2^{2} \cdot 3 \cdot 5^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 300.d (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$5$$ Character field: $$\Q$$ Newform subspaces: $$1$$ Sturm bound: $$120$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(300, [\chi])$$.

Total New Old
Modular forms 78 2 76
Cusp forms 42 2 40
Eisenstein series 36 0 36

## Trace form

 $$2 q - 2 q^{9} + O(q^{10})$$ $$2 q - 2 q^{9} + 12 q^{11} - 10 q^{19} - 2 q^{21} + 12 q^{29} - 2 q^{31} - 10 q^{39} + 12 q^{49} - 12 q^{51} + 12 q^{59} - 26 q^{61} + 12 q^{69} - 16 q^{79} + 2 q^{81} - 10 q^{91} - 12 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(300, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
300.2.d.a $2$ $2.396$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{3}+iq^{7}-q^{9}+6q^{11}+5iq^{13}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(300, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(300, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(30, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(50, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(60, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(75, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(100, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(150, [\chi])$$$$^{\oplus 2}$$