Properties

 Label 3600.1.bo Level 3600 Weight 1 Character orbit bo Rep. character $$\chi_{3600}(451,\cdot)$$ Character field $$\Q(\zeta_{4})$$ Dimension 4 Newform subspaces 1 Sturm bound 720 Trace bound 0

Related objects

Defining parameters

 Level: $$N$$ $$=$$ $$3600 = 2^{4} \cdot 3^{2} \cdot 5^{2}$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 3600.bo (of order $$4$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$16$$ Character field: $$\Q(i)$$ Newform subspaces: $$1$$ Sturm bound: $$720$$ Trace bound: $$0$$

Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(3600, [\chi])$$.

Total New Old
Modular forms 52 10 42
Cusp forms 4 4 0
Eisenstein series 48 6 42

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

 $$4q + O(q^{10})$$ $$4q - 4q^{16} - 4q^{19} + 4q^{34} + 4q^{46} - 4q^{49} - 4q^{61} - 4q^{76} - 4q^{94} + O(q^{100})$$

Decomposition of $$S_{1}^{\mathrm{new}}(3600, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field Image CM RM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
3600.1.bo.a $$4$$ $$1.797$$ $$\Q(\zeta_{8})$$ $$D_{4}$$ $$\Q(\sqrt{-15})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}-\zeta_{8}^{3}q^{8}-q^{16}+\cdots$$

Hecke characteristic polynomials

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