# Properties

 Label 2624.1.h Level $2624$ Weight $1$ Character orbit 2624.h Rep. character $\chi_{2624}(2623,\cdot)$ Character field $\Q$ Dimension $7$ Newform subspaces $3$ Sturm bound $336$ Trace bound $1$

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## Defining parameters

 Level: $$N$$ $$=$$ $$2624 = 2^{6} \cdot 41$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 2624.h (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$164$$ Character field: $$\Q$$ Newform subspaces: $$3$$ Sturm bound: $$336$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(2624, [\chi])$$.

Total New Old
Modular forms 46 9 37
Cusp forms 34 7 27
Eisenstein series 12 2 10

The following table gives the dimensions of subspaces with specified projective image type.

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 7 0 0 0

## Trace form

 $$7 q + 2 q^{5} + 5 q^{9} + O(q^{10})$$ $$7 q + 2 q^{5} + 5 q^{9} + 4 q^{21} + 5 q^{25} - 4 q^{33} + 2 q^{37} - q^{41} + 6 q^{45} + 5 q^{49} - 4 q^{57} + 2 q^{61} - 2 q^{73} + 4 q^{77} + 3 q^{81} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(2624, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field Image CM RM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
2624.1.h.a $$1$$ $$1.310$$ $$\Q$$ $$D_{2}$$ $$\Q(\sqrt{-1})$$, $$\Q(\sqrt{-41})$$ $$\Q(\sqrt{41})$$ $$0$$ $$0$$ $$2$$ $$0$$ $$q+2q^{5}-q^{9}+3q^{25}+2q^{37}+q^{41}+\cdots$$
2624.1.h.b $$2$$ $$1.310$$ $$\Q(\sqrt{2})$$ $$D_{4}$$ $$\Q(\sqrt{-41})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta q^{3}-\beta q^{7}+q^{9}+\beta q^{11}-\beta q^{19}+\cdots$$
2624.1.h.c $$4$$ $$1.310$$ $$\Q(\zeta_{16})^+$$ $$D_{8}$$ $$\Q(\sqrt{-41})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{3}q^{3}-\beta _{2}q^{5}-\beta _{1}q^{7}+(1-\beta _{2}+\cdots)q^{9}+\cdots$$

## Decomposition of $$S_{1}^{\mathrm{old}}(2624, [\chi])$$ into lower level spaces

$$S_{1}^{\mathrm{old}}(2624, [\chi]) \cong$$ $$S_{1}^{\mathrm{new}}(164, [\chi])$$$$^{\oplus 5}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(656, [\chi])$$$$^{\oplus 3}$$