# Properties

 Label 11.3.b Level 11 Weight 3 Character orbit b Rep. character $$\chi_{11}(10,\cdot)$$ Character field $$\Q$$ Dimension 1 Newform subspaces 1 Sturm bound 3 Trace bound 0

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$11$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 11.b (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$11$$ Character field: $$\Q$$ Newform subspaces: $$1$$ Sturm bound: $$3$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(11, [\chi])$$.

Total New Old
Modular forms 3 3 0
Cusp forms 1 1 0
Eisenstein series 2 2 0

## Trace form

 $$q - 5q^{3} + 4q^{4} - q^{5} + 16q^{9} + O(q^{10})$$ $$q - 5q^{3} + 4q^{4} - q^{5} + 16q^{9} - 11q^{11} - 20q^{12} + 5q^{15} + 16q^{16} - 4q^{20} + 35q^{23} - 24q^{25} - 35q^{27} - 37q^{31} + 55q^{33} + 64q^{36} - 25q^{37} - 44q^{44} - 16q^{45} + 50q^{47} - 80q^{48} + 49q^{49} - 70q^{53} + 11q^{55} + 107q^{59} + 20q^{60} + 64q^{64} + 35q^{67} - 175q^{69} - 133q^{71} + 120q^{75} - 16q^{80} + 31q^{81} - 97q^{89} + 140q^{92} + 185q^{93} + 95q^{97} - 176q^{99} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(11, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
11.3.b.a $$1$$ $$0.300$$ $$\Q$$ $$\Q(\sqrt{-11})$$ $$0$$ $$-5$$ $$-1$$ $$0$$ $$q-5q^{3}+4q^{4}-q^{5}+2^{4}q^{9}-11q^{11}+\cdots$$

## Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ $$( 1 - 2 T )( 1 + 2 T )$$
$3$ $$1 + 5 T + 9 T^{2}$$
$5$ $$1 + T + 25 T^{2}$$
$7$ $$( 1 - 7 T )( 1 + 7 T )$$
$11$ $$1 + 11 T$$
$13$ $$( 1 - 13 T )( 1 + 13 T )$$
$17$ $$( 1 - 17 T )( 1 + 17 T )$$
$19$ $$( 1 - 19 T )( 1 + 19 T )$$
$23$ $$1 - 35 T + 529 T^{2}$$
$29$ $$( 1 - 29 T )( 1 + 29 T )$$
$31$ $$1 + 37 T + 961 T^{2}$$
$37$ $$1 + 25 T + 1369 T^{2}$$
$41$ $$( 1 - 41 T )( 1 + 41 T )$$
$43$ $$( 1 - 43 T )( 1 + 43 T )$$
$47$ $$1 - 50 T + 2209 T^{2}$$
$53$ $$1 + 70 T + 2809 T^{2}$$
$59$ $$1 - 107 T + 3481 T^{2}$$
$61$ $$( 1 - 61 T )( 1 + 61 T )$$
$67$ $$1 - 35 T + 4489 T^{2}$$
$71$ $$1 + 133 T + 5041 T^{2}$$
$73$ $$( 1 - 73 T )( 1 + 73 T )$$
$79$ $$( 1 - 79 T )( 1 + 79 T )$$
$83$ $$( 1 - 83 T )( 1 + 83 T )$$
$89$ $$1 + 97 T + 7921 T^{2}$$
$97$ $$1 - 95 T + 9409 T^{2}$$