# Properties

 Label 3700.1.bu Level $3700$ Weight $1$ Character orbit 3700.bu Rep. character $\chi_{3700}(2043,\cdot)$ Character field $\Q(\zeta_{12})$ Dimension $4$ Newform subspaces $1$ Sturm bound $570$ Trace bound $0$

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## Defining parameters

 Level: $$N$$ $$=$$ $$3700 = 2^{2} \cdot 5^{2} \cdot 37$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 3700.bu (of order $$12$$ and degree $$4$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$740$$ Character field: $$\Q(\zeta_{12})$$ Newform subspaces: $$1$$ Sturm bound: $$570$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(3700, [\chi])$$.

Total New Old
Modular forms 60 20 40
Cusp forms 12 4 8
Eisenstein series 48 16 32

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 4 0 0 0

## Trace form

 $$4 q + 2 q^{4} + O(q^{10})$$ $$4 q + 2 q^{4} - 2 q^{16} - 2 q^{17} + 2 q^{18} + 2 q^{29} + 6 q^{41} + 2 q^{53} - 4 q^{58} - 4 q^{61} - 4 q^{64} - 4 q^{68} - 2 q^{72} + 4 q^{73} - 4 q^{74} + 2 q^{81} - 2 q^{89} + 2 q^{98} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(3700, [\chi])$$ into newform subspaces

Label Dim $A$ Field Image CM RM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
3700.1.bu.a $4$ $1.847$ $$\Q(\zeta_{12})$$ $D_{12}$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{12}^{5}q^{2}-\zeta_{12}^{4}q^{4}-\zeta_{12}^{3}q^{8}+\cdots$$

## Decomposition of $$S_{1}^{\mathrm{old}}(3700, [\chi])$$ into lower level spaces

$$S_{1}^{\mathrm{old}}(3700, [\chi]) \simeq$$ $$S_{1}^{\mathrm{new}}(740, [\chi])$$$$^{\oplus 2}$$