# Properties

 Label 2001.1.i Level 2001 Weight 1 Character orbit i Rep. character $$\chi_{2001}(1172,\cdot)$$ Character field $$\Q(\zeta_{4})$$ Dimension 12 Newform subspaces 4 Sturm bound 240 Trace bound 2

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$2001 = 3 \cdot 23 \cdot 29$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 2001.i (of order $$4$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$2001$$ Character field: $$\Q(i)$$ Newform subspaces: $$4$$ Sturm bound: $$240$$ Trace bound: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(2001, [\chi])$$.

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

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 12 0 0 0

## Trace form

 $$12q + O(q^{10})$$ $$12q + 6q^{12} - 12q^{16} - 6q^{18} + 12q^{24} + 12q^{25} + 6q^{27} - 12q^{36} - 6q^{39} + 12q^{49} - 12q^{58} + 6q^{72} + 6q^{87} + 24q^{94} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(2001, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field Image CM RM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
2001.1.i.a $$2$$ $$0.999$$ $$\Q(\sqrt{-1})$$ $$D_{4}$$ $$\Q(\sqrt{-23})$$ None $$-2$$ $$2$$ $$0$$ $$0$$ $$q+(-1+i)q^{2}+q^{3}-iq^{4}+(-1+i+\cdots)q^{6}+\cdots$$
2001.1.i.b $$2$$ $$0.999$$ $$\Q(\sqrt{-1})$$ $$D_{4}$$ $$\Q(\sqrt{-23})$$ None $$2$$ $$0$$ $$0$$ $$0$$ $$q+(1-i)q^{2}+iq^{3}-iq^{4}+(1+i)q^{6}+\cdots$$
2001.1.i.c $$4$$ $$0.999$$ $$\Q(\zeta_{12})$$ $$D_{12}$$ $$\Q(\sqrt{-23})$$ None $$-2$$ $$0$$ $$0$$ $$0$$ $$q+(\zeta_{12}^{4}+\zeta_{12}^{5})q^{2}-\zeta_{12}^{5}q^{3}+(-\zeta_{12}^{2}+\cdots)q^{4}+\cdots$$
2001.1.i.d $$4$$ $$0.999$$ $$\Q(\zeta_{12})$$ $$D_{12}$$ $$\Q(\sqrt{-23})$$ None $$2$$ $$-2$$ $$0$$ $$0$$ $$q+(-\zeta_{12}+\zeta_{12}^{2})q^{2}-\zeta_{12}^{2}q^{3}+(\zeta_{12}^{2}+\cdots)q^{4}+\cdots$$

## Hecke characteristic polynomials

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