Properties

 Label 44.1.d Level 44 Weight 1 Character orbit d Rep. character $$\chi_{44}(21,\cdot)$$ Character field $$\Q$$ Dimension 1 Newform subspaces 1 Sturm bound 6 Trace bound 0

Related objects

Defining parameters

 Level: $$N$$ $$=$$ $$44 = 2^{2} \cdot 11$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 44.d (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$11$$ Character field: $$\Q$$ Newform subspaces: $$1$$ Sturm bound: $$6$$ Trace bound: $$0$$

Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(44, [\chi])$$.

Total New Old
Modular forms 4 1 3
Cusp forms 1 1 0
Eisenstein series 3 0 3

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 1 0 0 0

Trace form

 $$q - q^{3} - q^{5} + O(q^{10})$$ $$q - q^{3} - q^{5} + q^{11} + q^{15} - q^{23} + q^{27} - q^{31} - q^{33} - q^{37} + 2q^{47} + q^{49} + 2q^{53} - q^{55} - q^{59} - q^{67} + q^{69} - q^{71} - q^{81} - q^{89} + q^{93} - q^{97} + O(q^{100})$$

Decomposition of $$S_{1}^{\mathrm{new}}(44, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field Image CM RM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
44.1.d.a $$1$$ $$0.022$$ $$\Q$$ $$D_{3}$$ $$\Q(\sqrt{-11})$$ None $$0$$ $$-1$$ $$-1$$ $$0$$ $$q-q^{3}-q^{5}+q^{11}+q^{15}-q^{23}+q^{27}+\cdots$$

Hecke characteristic polynomials

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