Properties

 Label 2583.1.f Level 2583 Weight 1 Character orbit f Rep. character $$\chi_{2583}(2008,\cdot)$$ Character field $$\Q$$ Dimension 6 Newform subspaces 2 Sturm bound 336 Trace bound 7

Related objects

Defining parameters

 Level: $$N$$ $$=$$ $$2583 = 3^{2} \cdot 7 \cdot 41$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 2583.f (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$287$$ Character field: $$\Q$$ Newform subspaces: $$2$$ Sturm bound: $$336$$ Trace bound: $$7$$

Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(2583, [\chi])$$.

Total New Old
Modular forms 32 8 24
Cusp forms 24 6 18
Eisenstein series 8 2 6

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 6 0 0 0

Trace form

 $$6q + 2q^{2} + 4q^{4} + 4q^{8} + O(q^{10})$$ $$6q + 2q^{2} + 4q^{4} + 4q^{8} + 2q^{16} + 2q^{23} + 6q^{25} + 6q^{32} - 2q^{37} - 2q^{43} - 4q^{46} + 6q^{49} + 2q^{50} - 10q^{74} + 4q^{86} - 2q^{91} - 8q^{92} + 2q^{98} + O(q^{100})$$

Decomposition of $$S_{1}^{\mathrm{new}}(2583, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field Image CM RM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
2583.1.f.a $$3$$ $$1.289$$ $$\Q(\zeta_{14})^+$$ $$D_{7}$$ $$\Q(\sqrt{-287})$$ None $$1$$ $$0$$ $$0$$ $$-3$$ $$q-\beta _{2}q^{2}+(\beta _{1}-\beta _{2})q^{4}-q^{7}+(\beta _{1}-\beta _{2})q^{8}+\cdots$$
2583.1.f.b $$3$$ $$1.289$$ $$\Q(\zeta_{14})^+$$ $$D_{7}$$ $$\Q(\sqrt{-287})$$ None $$1$$ $$0$$ $$0$$ $$3$$ $$q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+q^{7}+(1+\beta _{2})q^{8}+\cdots$$

Decomposition of $$S_{1}^{\mathrm{old}}(2583, [\chi])$$ into lower level spaces

$$S_{1}^{\mathrm{old}}(2583, [\chi]) \cong$$ $$S_{1}^{\mathrm{new}}(287, [\chi])$$$$^{\oplus 3}$$

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ ($$1 - T + T^{2} - T^{3} + T^{4} - T^{5} + T^{6}$$)($$1 - T + T^{2} - T^{3} + T^{4} - T^{5} + T^{6}$$)
$3$ 1
$5$ ($$( 1 - T )^{3}( 1 + T )^{3}$$)($$( 1 - T )^{3}( 1 + T )^{3}$$)
$7$ ($$( 1 + T )^{3}$$)($$( 1 - T )^{3}$$)
$11$ ($$( 1 - T )^{3}( 1 + T )^{3}$$)($$( 1 - T )^{3}( 1 + T )^{3}$$)
$13$ ($$1 - T + T^{2} - T^{3} + T^{4} - T^{5} + T^{6}$$)($$1 + T + T^{2} + T^{3} + T^{4} + T^{5} + T^{6}$$)
$17$ ($$1 + T + T^{2} + T^{3} + T^{4} + T^{5} + T^{6}$$)($$1 - T + T^{2} - T^{3} + T^{4} - T^{5} + T^{6}$$)
$19$ ($$1 - T + T^{2} - T^{3} + T^{4} - T^{5} + T^{6}$$)($$1 + T + T^{2} + T^{3} + T^{4} + T^{5} + T^{6}$$)
$23$ ($$1 - T + T^{2} - T^{3} + T^{4} - T^{5} + T^{6}$$)($$1 - T + T^{2} - T^{3} + T^{4} - T^{5} + T^{6}$$)
$29$ ($$( 1 - T )^{3}( 1 + T )^{3}$$)($$( 1 - T )^{3}( 1 + T )^{3}$$)
$31$ ($$( 1 - T )^{3}( 1 + T )^{3}$$)($$( 1 - T )^{3}( 1 + T )^{3}$$)
$37$ ($$1 + T + T^{2} + T^{3} + T^{4} + T^{5} + T^{6}$$)($$1 + T + T^{2} + T^{3} + T^{4} + T^{5} + T^{6}$$)
$41$ ($$( 1 - T )^{3}$$)($$( 1 + T )^{3}$$)
$43$ ($$1 + T + T^{2} + T^{3} + T^{4} + T^{5} + T^{6}$$)($$1 + T + T^{2} + T^{3} + T^{4} + T^{5} + T^{6}$$)
$47$ ($$1 + T + T^{2} + T^{3} + T^{4} + T^{5} + T^{6}$$)($$1 - T + T^{2} - T^{3} + T^{4} - T^{5} + T^{6}$$)
$53$ ($$( 1 - T )^{3}( 1 + T )^{3}$$)($$( 1 - T )^{3}( 1 + T )^{3}$$)
$59$ ($$( 1 - T )^{3}( 1 + T )^{3}$$)($$( 1 - T )^{3}( 1 + T )^{3}$$)
$61$ ($$( 1 - T )^{3}( 1 + T )^{3}$$)($$( 1 - T )^{3}( 1 + T )^{3}$$)
$67$ ($$( 1 - T )^{3}( 1 + T )^{3}$$)($$( 1 - T )^{3}( 1 + T )^{3}$$)
$71$ ($$( 1 - T )^{3}( 1 + T )^{3}$$)($$( 1 - T )^{3}( 1 + T )^{3}$$)
$73$ ($$( 1 - T )^{3}( 1 + T )^{3}$$)($$( 1 - T )^{3}( 1 + T )^{3}$$)
$79$ ($$( 1 - T )^{3}( 1 + T )^{3}$$)($$( 1 - T )^{3}( 1 + T )^{3}$$)
$83$ ($$( 1 - T )^{3}( 1 + T )^{3}$$)($$( 1 - T )^{3}( 1 + T )^{3}$$)
$89$ ($$1 + T + T^{2} + T^{3} + T^{4} + T^{5} + T^{6}$$)($$1 - T + T^{2} - T^{3} + T^{4} - T^{5} + T^{6}$$)
$97$ ($$1 - T + T^{2} - T^{3} + T^{4} - T^{5} + T^{6}$$)($$1 + T + T^{2} + T^{3} + T^{4} + T^{5} + T^{6}$$)