Properties

 Label 360.1.u Level 360 Weight 1 Character orbit u Rep. character $$\chi_{360}(37,\cdot)$$ Character field $$\Q(\zeta_{4})$$ Dimension 4 Newform subspaces 1 Sturm bound 72 Trace bound 0

Related objects

Defining parameters

 Level: $$N$$ $$=$$ $$360 = 2^{3} \cdot 3^{2} \cdot 5$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 360.u (of order $$4$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$40$$ Character field: $$\Q(i)$$ Newform subspaces: $$1$$ Sturm bound: $$72$$ Trace bound: $$0$$

Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(360, [\chi])$$.

Total New Old
Modular forms 20 8 12
Cusp forms 4 4 0
Eisenstein series 16 4 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

 $$4q - 4q^{7} + O(q^{10})$$ $$4q - 4q^{7} + 4q^{10} - 4q^{16} + 4q^{22} - 4q^{28} - 4q^{55} - 4q^{58} - 4q^{70} + 4q^{73} + 4q^{88} - 4q^{97} + O(q^{100})$$

Decomposition of $$S_{1}^{\mathrm{new}}(360, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field Image CM RM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
360.1.u.a $$4$$ $$0.180$$ $$\Q(\zeta_{8})$$ $$D_{4}$$ $$\Q(\sqrt{-6})$$ None $$0$$ $$0$$ $$0$$ $$-4$$ $$q-\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}+\zeta_{8}q^{5}+(-1+\cdots)q^{7}+\cdots$$

Hecke characteristic polynomials

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