# Properties

 Label 128.2.b Level $128$ Weight $2$ Character orbit 128.b Rep. character $\chi_{128}(65,\cdot)$ Character field $\Q$ Dimension $4$ Newform subspaces $2$ Sturm bound $32$ Trace bound $9$

# Learn more about

## Defining parameters

 Level: $$N$$ $$=$$ $$128 = 2^{7}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 128.b (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$8$$ Character field: $$\Q$$ Newform subspaces: $$2$$ Sturm bound: $$32$$ Trace bound: $$9$$ Distinguishing $$T_p$$: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(128, [\chi])$$.

Total New Old
Modular forms 24 4 20
Cusp forms 8 4 4
Eisenstein series 16 0 16

## Trace form

 $$4q - 4q^{9} + O(q^{10})$$ $$4q - 4q^{9} + 8q^{17} - 12q^{25} - 16q^{33} + 8q^{41} - 28q^{49} + 48q^{57} + 32q^{65} + 8q^{73} + 20q^{81} - 56q^{89} - 56q^{97} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(128, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
128.2.b.a $$2$$ $$1.022$$ $$\Q(\sqrt{-2})$$ $$\Q(\sqrt{-2})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta q^{3}-5q^{9}+\beta q^{11}+6q^{17}-3\beta q^{19}+\cdots$$
128.2.b.b $$2$$ $$1.022$$ $$\Q(\sqrt{-1})$$ $$\Q(\sqrt{-1})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{5}+3q^{9}-iq^{13}-2q^{17}-11q^{25}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(128, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(128, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(64, [\chi])$$$$^{\oplus 2}$$

## Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ 1
$3$ ($$( 1 - 2 T + 3 T^{2} )( 1 + 2 T + 3 T^{2} )$$)($$( 1 - 3 T^{2} )^{2}$$)
$5$ ($$( 1 - 5 T^{2} )^{2}$$)($$( 1 - 2 T + 5 T^{2} )( 1 + 2 T + 5 T^{2} )$$)
$7$ ($$( 1 + 7 T^{2} )^{2}$$)($$( 1 + 7 T^{2} )^{2}$$)
$11$ ($$( 1 - 6 T + 11 T^{2} )( 1 + 6 T + 11 T^{2} )$$)($$( 1 - 11 T^{2} )^{2}$$)
$13$ ($$( 1 - 13 T^{2} )^{2}$$)($$( 1 - 6 T + 13 T^{2} )( 1 + 6 T + 13 T^{2} )$$)
$17$ ($$( 1 - 6 T + 17 T^{2} )^{2}$$)($$( 1 + 2 T + 17 T^{2} )^{2}$$)
$19$ ($$( 1 - 2 T + 19 T^{2} )( 1 + 2 T + 19 T^{2} )$$)($$( 1 - 19 T^{2} )^{2}$$)
$23$ ($$( 1 + 23 T^{2} )^{2}$$)($$( 1 + 23 T^{2} )^{2}$$)
$29$ ($$( 1 - 29 T^{2} )^{2}$$)($$( 1 - 10 T + 29 T^{2} )( 1 + 10 T + 29 T^{2} )$$)
$31$ ($$( 1 + 31 T^{2} )^{2}$$)($$( 1 + 31 T^{2} )^{2}$$)
$37$ ($$( 1 - 37 T^{2} )^{2}$$)($$( 1 - 2 T + 37 T^{2} )( 1 + 2 T + 37 T^{2} )$$)
$41$ ($$( 1 + 6 T + 41 T^{2} )^{2}$$)($$( 1 - 10 T + 41 T^{2} )^{2}$$)
$43$ ($$( 1 - 10 T + 43 T^{2} )( 1 + 10 T + 43 T^{2} )$$)($$( 1 - 43 T^{2} )^{2}$$)
$47$ ($$( 1 + 47 T^{2} )^{2}$$)($$( 1 + 47 T^{2} )^{2}$$)
$53$ ($$( 1 - 53 T^{2} )^{2}$$)($$( 1 - 14 T + 53 T^{2} )( 1 + 14 T + 53 T^{2} )$$)
$59$ ($$( 1 - 6 T + 59 T^{2} )( 1 + 6 T + 59 T^{2} )$$)($$( 1 - 59 T^{2} )^{2}$$)
$61$ ($$( 1 - 61 T^{2} )^{2}$$)($$( 1 - 10 T + 61 T^{2} )( 1 + 10 T + 61 T^{2} )$$)
$67$ ($$( 1 - 14 T + 67 T^{2} )( 1 + 14 T + 67 T^{2} )$$)($$( 1 - 67 T^{2} )^{2}$$)
$71$ ($$( 1 + 71 T^{2} )^{2}$$)($$( 1 + 71 T^{2} )^{2}$$)
$73$ ($$( 1 + 2 T + 73 T^{2} )^{2}$$)($$( 1 - 6 T + 73 T^{2} )^{2}$$)
$79$ ($$( 1 + 79 T^{2} )^{2}$$)($$( 1 + 79 T^{2} )^{2}$$)
$83$ ($$( 1 - 18 T + 83 T^{2} )( 1 + 18 T + 83 T^{2} )$$)($$( 1 - 83 T^{2} )^{2}$$)
$89$ ($$( 1 + 18 T + 89 T^{2} )^{2}$$)($$( 1 + 10 T + 89 T^{2} )^{2}$$)
$97$ ($$( 1 + 10 T + 97 T^{2} )^{2}$$)($$( 1 + 18 T + 97 T^{2} )^{2}$$)
show more
show less