# Properties

 Label 29.2.b Level 29 Weight 2 Character orbit b Rep. character $$\chi_{29}(28,\cdot)$$ Character field $$\Q$$ Dimension 2 Newform subspaces 1 Sturm bound 5 Trace bound 0

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$29$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 29.b (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$29$$ Character field: $$\Q$$ Newform subspaces: $$1$$ Sturm bound: $$5$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(29, [\chi])$$.

Total New Old
Modular forms 4 4 0
Cusp forms 2 2 0
Eisenstein series 2 2 0

## Trace form

 $$2q - 6q^{4} - 6q^{5} + 10q^{6} + 4q^{7} - 4q^{9} + O(q^{10})$$ $$2q - 6q^{4} - 6q^{5} + 10q^{6} + 4q^{7} - 4q^{9} - 2q^{13} - 2q^{16} + 18q^{20} - 10q^{22} + 12q^{23} - 10q^{24} + 8q^{25} - 12q^{28} - 6q^{29} - 30q^{30} + 10q^{33} + 20q^{34} - 12q^{35} + 12q^{36} + 20q^{42} + 12q^{45} - 6q^{49} - 20q^{51} + 6q^{52} - 18q^{53} + 10q^{54} - 20q^{58} + 12q^{59} - 30q^{62} - 8q^{63} + 26q^{64} + 6q^{65} + 16q^{67} - 10q^{78} + 6q^{80} - 22q^{81} + 20q^{82} - 12q^{83} + 30q^{86} + 20q^{87} + 10q^{88} - 4q^{91} - 36q^{92} + 30q^{93} - 10q^{94} - 30q^{96} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(29, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
29.2.b.a $$2$$ $$0.232$$ $$\Q(\sqrt{-5})$$ None $$0$$ $$0$$ $$-6$$ $$4$$ $$q+\beta q^{2}-\beta q^{3}-3q^{4}-3q^{5}+5q^{6}+\cdots$$

## Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ $$1 + T^{2} + 4 T^{4}$$
$3$ $$1 - T^{2} + 9 T^{4}$$
$5$ $$( 1 + 3 T + 5 T^{2} )^{2}$$
$7$ $$( 1 - 2 T + 7 T^{2} )^{2}$$
$11$ $$1 - 17 T^{2} + 121 T^{4}$$
$13$ $$( 1 + T + 13 T^{2} )^{2}$$
$17$ $$1 - 14 T^{2} + 289 T^{4}$$
$19$ $$( 1 - 19 T^{2} )^{2}$$
$23$ $$( 1 - 6 T + 23 T^{2} )^{2}$$
$29$ $$1 + 6 T + 29 T^{2}$$
$31$ $$1 - 17 T^{2} + 961 T^{4}$$
$37$ $$( 1 - 37 T^{2} )^{2}$$
$41$ $$( 1 - 12 T + 41 T^{2} )( 1 + 12 T + 41 T^{2} )$$
$43$ $$1 - 41 T^{2} + 1849 T^{4}$$
$47$ $$1 - 89 T^{2} + 2209 T^{4}$$
$53$ $$( 1 + 9 T + 53 T^{2} )^{2}$$
$59$ $$( 1 - 6 T + 59 T^{2} )^{2}$$
$61$ $$( 1 - 8 T + 61 T^{2} )( 1 + 8 T + 61 T^{2} )$$
$67$ $$( 1 - 8 T + 67 T^{2} )^{2}$$
$71$ $$( 1 + 71 T^{2} )^{2}$$
$73$ $$( 1 - 73 T^{2} )^{2}$$
$79$ $$1 - 113 T^{2} + 6241 T^{4}$$
$83$ $$( 1 + 6 T + 83 T^{2} )^{2}$$
$89$ $$1 - 158 T^{2} + 7921 T^{4}$$
$97$ $$1 - 14 T^{2} + 9409 T^{4}$$