# Properties

 Label 70.3.d Level 70 Weight 3 Character orbit d Rep. character $$\chi_{70}(69,\cdot)$$ Character field $$\Q$$ Dimension 8 Newform subspaces 1 Sturm bound 36 Trace bound 0

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$70 = 2 \cdot 5 \cdot 7$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 70.d (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$35$$ Character field: $$\Q$$ Newform subspaces: $$1$$ Sturm bound: $$36$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(70, [\chi])$$.

Total New Old
Modular forms 28 8 20
Cusp forms 20 8 12
Eisenstein series 8 0 8

## Trace form

 $$8q - 16q^{4} + 36q^{9} + O(q^{10})$$ $$8q - 16q^{4} + 36q^{9} - 60q^{11} + 4q^{14} + 4q^{15} + 32q^{16} + 56q^{21} - 92q^{29} - 104q^{30} + 52q^{35} - 72q^{36} + 204q^{39} + 120q^{44} + 104q^{46} - 284q^{49} + 192q^{50} - 212q^{51} - 8q^{56} - 8q^{60} - 64q^{64} - 292q^{65} - 4q^{70} + 504q^{71} - 112q^{74} + 692q^{79} - 136q^{81} - 112q^{84} + 92q^{85} - 280q^{86} - 44q^{91} - 176q^{95} - 944q^{99} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(70, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
70.3.d.a $$8$$ $$1.907$$ 8.0.$$\cdots$$.6 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{4}q^{2}-\beta _{5}q^{3}-2q^{4}+(\beta _{2}-\beta _{6}+\cdots)q^{5}+\cdots$$

## Decomposition of $$S_{3}^{\mathrm{old}}(70, [\chi])$$ into lower level spaces

$$S_{3}^{\mathrm{old}}(70, [\chi]) \cong$$ $$S_{3}^{\mathrm{new}}(35, [\chi])$$$$^{\oplus 2}$$

## Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ $$( 1 + 2 T^{2} )^{4}$$
$3$ $$( 1 + 9 T^{2} + 98 T^{4} + 729 T^{6} + 6561 T^{8} )^{2}$$
$5$ $$1 - 98 T^{4} + 390625 T^{8}$$
$7$ $$1 + 142 T^{2} + 9506 T^{4} + 340942 T^{6} + 5764801 T^{8}$$
$11$ $$( 1 + 15 T + 214 T^{2} + 1815 T^{3} + 14641 T^{4} )^{4}$$
$13$ $$( 1 + 355 T^{2} + 84500 T^{4} + 10139155 T^{6} + 815730721 T^{8} )^{2}$$
$17$ $$( 1 + 1027 T^{2} + 426596 T^{4} + 85776067 T^{6} + 6975757441 T^{8} )^{2}$$
$19$ $$( 1 - 396 T^{2} + 35638 T^{4} - 51607116 T^{6} + 16983563041 T^{8} )^{2}$$
$23$ $$( 1 - 1610 T^{2} + 1150754 T^{4} - 450544010 T^{6} + 78310985281 T^{8} )^{2}$$
$29$ $$( 1 + 23 T + 1056 T^{2} + 19343 T^{3} + 707281 T^{4} )^{4}$$
$31$ $$( 1 - 2748 T^{2} + 3729526 T^{4} - 2537835708 T^{6} + 852891037441 T^{8} )^{2}$$
$37$ $$( 1 - 3932 T^{2} + 7349270 T^{4} - 7369201052 T^{6} + 3512479453921 T^{8} )^{2}$$
$41$ $$( 1 + 3912 T^{2} + 9411406 T^{4} + 11054377032 T^{6} + 7984925229121 T^{8} )^{2}$$
$43$ $$( 1 - 5834 T^{2} + 14933666 T^{4} - 19945285034 T^{6} + 11688200277601 T^{8} )^{2}$$
$47$ $$( 1 + 3609 T^{2} + 6828178 T^{4} + 17610768729 T^{6} + 23811286661761 T^{8} )^{2}$$
$53$ $$( 1 - 3908 T^{2} + 9160166 T^{4} - 30835999748 T^{6} + 62259690411361 T^{8} )^{2}$$
$59$ $$( 1 - 3924 T^{2} + 14604166 T^{4} - 47548524564 T^{6} + 146830437604321 T^{8} )^{2}$$
$61$ $$( 1 - 10456 T^{2} + 54914478 T^{4} - 144772113496 T^{6} + 191707312997281 T^{8} )^{2}$$
$67$ $$( 1 - 17618 T^{2} + 117900386 T^{4} - 355022449778 T^{6} + 406067677556641 T^{8} )^{2}$$
$71$ $$( 1 - 126 T + 13714 T^{2} - 635166 T^{3} + 25411681 T^{4} )^{4}$$
$73$ $$( 1 + 9216 T^{2} + 58294078 T^{4} + 261718189056 T^{6} + 806460091894081 T^{8} )^{2}$$
$79$ $$( 1 - 173 T + 17858 T^{2} - 1079693 T^{3} + 38950081 T^{4} )^{4}$$
$83$ $$( 1 + 25678 T^{2} + 259012130 T^{4} + 1218634766638 T^{6} + 2252292232139041 T^{8} )^{2}$$
$89$ $$( 1 - 25980 T^{2} + 294219190 T^{4} - 1630043421180 T^{6} + 3936588805702081 T^{8} )^{2}$$
$97$ $$( 1 + 22275 T^{2} + 265834660 T^{4} + 1971989734275 T^{6} + 7837433594376961 T^{8} )^{2}$$