# Properties

 Label 1575.1.cp Level 1575 Weight 1 Character orbit cp Rep. character $$\chi_{1575}(193,\cdot)$$ Character field $$\Q(\zeta_{12})$$ Dimension 8 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.cp (of order $$12$$ and degree $$4$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$315$$ Character field: $$\Q(\zeta_{12})$$ 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 56 24 32
Cusp forms 8 8 0
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 0 8 0 0

## Trace form

 $$8q + 4q^{6} + O(q^{10})$$ $$8q + 4q^{6} - 4q^{16} + 8q^{21} - 4q^{26} + 4q^{31} - 4q^{41} + 4q^{51} - 8q^{56} - 4q^{61} - 16q^{71} - 8q^{81} - 8q^{86} + 4q^{91} + O(q^{100})$$

## 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.cp.a $$8$$ $$0.786$$ $$\Q(\zeta_{24})$$ $$A_{4}$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{24}^{11}q^{2}-\zeta_{24}^{9}q^{3}-\zeta_{24}^{8}q^{6}+\cdots$$

## Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ $$( 1 + T^{4} )^{2}( 1 - T^{4} + T^{8} )$$
$3$ $$( 1 + T^{4} )^{2}$$
$5$ 1
$7$ $$( 1 + T^{4} )^{2}$$
$11$ $$( 1 + T^{2} )^{8}$$
$13$ $$( 1 + T^{4} )^{2}( 1 - T^{4} + T^{8} )$$
$17$ $$( 1 + T^{4} )^{2}( 1 - T^{4} + T^{8} )$$
$19$ $$( 1 + T^{2} )^{4}( 1 - T^{2} + T^{4} )^{2}$$
$23$ $$( 1 + T^{4} )^{4}$$
$29$ $$( 1 + T^{2} )^{4}( 1 - T^{2} + T^{4} )^{2}$$
$31$ $$( 1 - T )^{8}( 1 + T + T^{2} )^{4}$$
$37$ $$( 1 + T^{4} )^{2}( 1 - T^{4} + T^{8} )$$
$41$ $$( 1 + T )^{8}( 1 - T + T^{2} )^{4}$$
$43$ $$( 1 + T^{4} )^{2}( 1 - T^{4} + T^{8} )$$
$47$ $$( 1 + T^{4} )^{2}( 1 - T^{4} + T^{8} )$$
$53$ $$( 1 + T^{4} )^{2}( 1 - T^{4} + T^{8} )$$
$59$ $$( 1 + T^{2} )^{4}( 1 - T^{2} + T^{4} )^{2}$$
$61$ $$( 1 + T )^{8}( 1 - T + T^{2} )^{4}$$
$67$ $$( 1 + T^{4} )^{2}( 1 - T^{4} + T^{8} )$$
$71$ $$( 1 + T )^{16}$$
$73$ $$( 1 + T^{4} )^{2}( 1 - T^{4} + T^{8} )$$
$79$ $$( 1 + T^{2} )^{4}( 1 - T^{2} + T^{4} )^{2}$$
$83$ $$( 1 + T^{4} )^{2}( 1 - T^{4} + T^{8} )$$
$89$ $$( 1 + T^{2} )^{4}( 1 - T^{2} + T^{4} )^{2}$$
$97$ $$( 1 + T^{4} )^{2}( 1 - T^{4} + T^{8} )$$