Properties

 Label 1224.1.cb Level $1224$ Weight $1$ Character orbit 1224.cb Rep. character $\chi_{1224}(115,\cdot)$ Character field $\Q(\zeta_{12})$ Dimension $8$ Newform subspaces $2$ Sturm bound $216$ Trace bound $3$

Related objects

Defining parameters

 Level: $$N$$ $$=$$ $$1224 = 2^{3} \cdot 3^{2} \cdot 17$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 1224.cb (of order $$12$$ and degree $$4$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$1224$$ Character field: $$\Q(\zeta_{12})$$ Newform subspaces: $$2$$ Sturm bound: $$216$$ Trace bound: $$3$$

Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(1224, [\chi])$$.

Total New Old
Modular forms 24 24 0
Cusp forms 8 8 0
Eisenstein series 16 16 0

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 8 0 0 0

Trace form

 $$8q + 2q^{3} + 4q^{4} + 2q^{6} + O(q^{10})$$ $$8q + 2q^{3} + 4q^{4} + 2q^{6} + 2q^{11} + 4q^{12} - 4q^{16} - 2q^{22} - 2q^{24} - 4q^{27} + 4q^{33} - 2q^{34} + 4q^{38} - 2q^{41} + 4q^{44} + 2q^{48} - 4q^{50} - 4q^{51} - 2q^{54} + 2q^{57} - 8q^{64} + 4q^{73} - 2q^{75} - 4q^{81} - 4q^{82} + 2q^{88} - 4q^{96} + 2q^{97} - 8q^{98} + O(q^{100})$$

Decomposition of $$S_{1}^{\mathrm{new}}(1224, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field Image CM RM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
1224.1.cb.a $$4$$ $$0.611$$ $$\Q(\zeta_{12})$$ $$D_{12}$$ $$\Q(\sqrt{-2})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{12}q^{2}+\zeta_{12}q^{3}+\zeta_{12}^{2}q^{4}+\zeta_{12}^{2}q^{6}+\cdots$$
1224.1.cb.b $$4$$ $$0.611$$ $$\Q(\zeta_{12})$$ $$D_{12}$$ $$\Q(\sqrt{-2})$$ None $$0$$ $$2$$ $$0$$ $$0$$ $$q+\zeta_{12}q^{2}-\zeta_{12}^{4}q^{3}+\zeta_{12}^{2}q^{4}-\zeta_{12}^{5}q^{6}+\cdots$$

Hecke characteristic polynomials

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