# Properties

 Label 1575.1.y Level $1575$ Weight $1$ Character orbit 1575.y Rep. character $\chi_{1575}(76,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $4$ Newform subspaces $1$ Sturm bound $240$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1575 = 3^{2} \cdot 5^{2} \cdot 7$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 1575.y (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$63$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$1$$ Sturm bound: $$240$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(1575, [\chi])$$.

Total New Old
Modular forms 28 16 12
Cusp forms 4 4 0
Eisenstein series 24 12 12

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

 $$4q + 2q^{4} - 4q^{9} + O(q^{10})$$ $$4q + 2q^{4} - 4q^{9} + 2q^{11} - 2q^{16} - 2q^{21} + 4q^{29} - 2q^{36} - 2q^{39} + 4q^{44} + 2q^{49} - 4q^{51} - 4q^{64} - 4q^{71} - 2q^{79} + 4q^{81} - 4q^{84} - 4q^{91} - 2q^{99} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(1575, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field Image CM RM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
1575.1.y.a $$4$$ $$0.786$$ $$\Q(\zeta_{12})$$ $$D_{3}$$ $$\Q(\sqrt{-35})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{12}^{3}q^{3}+\zeta_{12}^{2}q^{4}-\zeta_{12}q^{7}-q^{9}+\cdots$$

## Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ $$( 1 - T^{2} + T^{4} )^{2}$$
$3$ $$( 1 + T^{2} )^{2}$$
$5$ 1
$7$ $$1 - T^{2} + T^{4}$$
$11$ $$( 1 - T )^{4}( 1 + T + T^{2} )^{2}$$
$13$ $$( 1 + T^{2} )^{2}( 1 - T^{2} + T^{4} )$$
$17$ $$( 1 - T^{2} + T^{4} )^{2}$$
$19$ $$( 1 - T )^{4}( 1 + T )^{4}$$
$23$ $$( 1 - T^{2} + T^{4} )^{2}$$
$29$ $$( 1 - T + T^{2} )^{4}$$
$31$ $$( 1 - T + T^{2} )^{2}( 1 + T + T^{2} )^{2}$$
$37$ $$( 1 + T^{2} )^{4}$$
$41$ $$( 1 - T + T^{2} )^{2}( 1 + T + T^{2} )^{2}$$
$43$ $$( 1 - T^{2} + T^{4} )^{2}$$
$47$ $$( 1 + T^{2} )^{2}( 1 - T^{2} + T^{4} )$$
$53$ $$( 1 + T^{2} )^{4}$$
$59$ $$( 1 - T + T^{2} )^{2}( 1 + T + T^{2} )^{2}$$
$61$ $$( 1 - T + T^{2} )^{2}( 1 + T + T^{2} )^{2}$$
$67$ $$( 1 - T^{2} + T^{4} )^{2}$$
$71$ $$( 1 + T + T^{2} )^{4}$$
$73$ $$( 1 - T^{2} + T^{4} )^{2}$$
$79$ $$( 1 + T )^{4}( 1 - T + T^{2} )^{2}$$
$83$ $$( 1 + T^{2} )^{2}( 1 - T^{2} + T^{4} )$$
$89$ $$( 1 - T )^{4}( 1 + T )^{4}$$
$97$ $$( 1 + T^{2} )^{2}( 1 - T^{2} + T^{4} )$$