# Properties

 Label 476.2.b Level $476$ Weight $2$ Character orbit 476.b Rep. character $\chi_{476}(169,\cdot)$ Character field $\Q$ Dimension $8$ Newform subspaces $1$ Sturm bound $144$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$476 = 2^{2} \cdot 7 \cdot 17$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 476.b (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$17$$ Character field: $$\Q$$ Newform subspaces: $$1$$ Sturm bound: $$144$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(476, [\chi])$$.

Total New Old
Modular forms 78 8 70
Cusp forms 66 8 58
Eisenstein series 12 0 12

## Trace form

 $$8 q - 12 q^{9} + O(q^{10})$$ $$8 q - 12 q^{9} + 20 q^{13} + 12 q^{19} - 8 q^{21} - 12 q^{25} - 4 q^{33} - 4 q^{35} - 12 q^{43} + 24 q^{47} - 8 q^{49} - 20 q^{51} + 20 q^{53} - 4 q^{55} - 24 q^{59} - 4 q^{67} + 44 q^{69} + 16 q^{77} + 16 q^{81} + 4 q^{83} - 44 q^{85} + 52 q^{87} - 16 q^{93} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(476, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
476.2.b.a $8$ $3.801$ 8.0.980441344.2 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\beta _{4}+\beta _{7})q^{3}+\beta _{3}q^{5}+\beta _{4}q^{7}+(-1+\cdots)q^{9}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(476, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(476, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(34, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(68, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(119, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(238, [\chi])$$$$^{\oplus 2}$$