# Properties

 Label 2523.1.h Level $2523$ Weight $1$ Character orbit 2523.h Rep. character $\chi_{2523}(236,\cdot)$ Character field $\Q(\zeta_{14})$ Dimension $36$ Newform subspaces $3$ Sturm bound $290$ Trace bound $2$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$2523 = 3 \cdot 29^{2}$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 2523.h (of order $$14$$ and degree $$6$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$87$$ Character field: $$\Q(\zeta_{14})$$ Newform subspaces: $$3$$ Sturm bound: $$290$$ Trace bound: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(2523, [\chi])$$.

Total New Old
Modular forms 216 192 24
Cusp forms 36 36 0
Eisenstein series 180 156 24

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 36 0 0 0

## Trace form

 $$36 q + 4 q^{4} + 2 q^{6} + 4 q^{7} + 2 q^{9} + O(q^{10})$$ $$36 q + 4 q^{4} + 2 q^{6} + 4 q^{7} + 2 q^{9} - 2 q^{16} - 2 q^{22} - 2 q^{24} - 6 q^{25} + 12 q^{28} + 2 q^{33} - 2 q^{34} - 4 q^{36} - 2 q^{42} - 2 q^{49} + 2 q^{51} + 2 q^{52} + 2 q^{54} + 12 q^{57} + 2 q^{64} - 2 q^{78} - 6 q^{81} + 4 q^{82} - 12 q^{88} - 6 q^{91} - 2 q^{93} - 2 q^{94} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(2523, [\chi])$$ into newform subspaces

Label Dim $A$ Field Image CM RM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
2523.1.h.a $6$ $1.259$ $$\Q(\zeta_{14})$$ $D_{3}$ $$\Q(\sqrt{-87})$$ None $$-1$$ $$1$$ $$0$$ $$1$$ $$q+\zeta_{14}^{6}q^{2}-\zeta_{14}^{2}q^{3}+\zeta_{14}q^{6}-\zeta_{14}^{2}q^{7}+\cdots$$
2523.1.h.b $6$ $1.259$ $$\Q(\zeta_{14})$$ $D_{3}$ $$\Q(\sqrt{-87})$$ None $$1$$ $$-1$$ $$0$$ $$1$$ $$q-\zeta_{14}^{6}q^{2}+\zeta_{14}^{2}q^{3}+\zeta_{14}q^{6}-\zeta_{14}^{2}q^{7}+\cdots$$
2523.1.h.c $24$ $1.259$ 24.0.$$\cdots$$.1 $D_{5}$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$0$$ $$2$$ $$q+\beta _{3}q^{3}-\beta _{13}q^{4}+(-\beta _{16}-\beta _{17}+\cdots)q^{7}+\cdots$$