# Properties

 Label 32.6.b Level 32 Weight 6 Character orbit b Rep. character $$\chi_{32}(17,\cdot)$$ Character field $$\Q$$ Dimension 4 Newform subspaces 1 Sturm bound 24 Trace bound 0

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$32 = 2^{5}$$ Weight: $$k$$ $$=$$ $$6$$ Character orbit: $$[\chi]$$ $$=$$ 32.b (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$8$$ Character field: $$\Q$$ Newform subspaces: $$1$$ Sturm bound: $$24$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{6}(32, [\chi])$$.

Total New Old
Modular forms 24 6 18
Cusp forms 16 4 12
Eisenstein series 8 2 6

## Trace form

 $$4q - 96q^{7} - 164q^{9} + O(q^{10})$$ $$4q - 96q^{7} - 164q^{9} + 416q^{15} + 200q^{17} - 2336q^{23} + 1556q^{25} + 12928q^{31} - 2352q^{33} - 35104q^{39} - 4568q^{41} + 54720q^{47} + 9828q^{49} - 85472q^{55} - 2032q^{57} + 153440q^{63} - 19520q^{65} - 206688q^{71} + 39976q^{73} + 247872q^{79} + 29684q^{81} - 307872q^{87} - 84632q^{89} + 259744q^{95} - 99576q^{97} + O(q^{100})$$

## Decomposition of $$S_{6}^{\mathrm{new}}(32, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
32.6.b.a $$4$$ $$5.132$$ 4.0.218489.1 None $$0$$ $$0$$ $$0$$ $$-96$$ $$q+\beta _{1}q^{3}+\beta _{2}q^{5}+(-24-\beta _{3})q^{7}+\cdots$$

## Decomposition of $$S_{6}^{\mathrm{old}}(32, [\chi])$$ into lower level spaces

$$S_{6}^{\mathrm{old}}(32, [\chi]) \cong$$ $$S_{6}^{\mathrm{new}}(8, [\chi])$$$$^{\oplus 3}$$

## Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ 1
$3$ $$1 - 404 T^{2} + 84150 T^{4} - 23855796 T^{6} + 3486784401 T^{8}$$
$5$ $$1 - 7028 T^{2} + 24404246 T^{4} - 68632812500 T^{6} + 95367431640625 T^{8}$$
$7$ $$( 1 + 48 T + 15502 T^{2} + 806736 T^{3} + 282475249 T^{4} )^{2}$$
$11$ $$1 - 296436 T^{2} + 49128544726 T^{4} - 7688786399022036 T^{6} +$$$$67\!\cdots\!01$$$$T^{8}$$
$13$ $$1 - 894228 T^{2} + 396323515894 T^{4} - 123276923449147572 T^{6} +$$$$19\!\cdots\!01$$$$T^{8}$$
$17$ $$( 1 - 100 T + 2767462 T^{2} - 141985700 T^{3} + 2015993900449 T^{4} )^{2}$$
$19$ $$1 - 6794580 T^{2} + 21506967947254 T^{4} - 41658020173929518580 T^{6} +$$$$37\!\cdots\!01$$$$T^{8}$$
$23$ $$( 1 + 1168 T + 10055470 T^{2} + 7517648624 T^{3} + 41426511213649 T^{4} )^{2}$$
$29$ $$1 - 31255380 T^{2} + 976386653995702 T^{4} -$$$$13\!\cdots\!80$$$$T^{6} +$$$$17\!\cdots\!01$$$$T^{8}$$
$31$ $$( 1 - 6464 T + 65013054 T^{2} - 185058832064 T^{3} + 819628286980801 T^{4} )^{2}$$
$37$ $$1 - 241262580 T^{2} + 24149916431784598 T^{4} -$$$$11\!\cdots\!20$$$$T^{6} +$$$$23\!\cdots\!01$$$$T^{8}$$
$41$ $$( 1 + 2284 T + 146603254 T^{2} + 264615563084 T^{3} + 13422659310152401 T^{4} )^{2}$$
$43$ $$1 - 466346868 T^{2} + 96250708269010006 T^{4} -$$$$10\!\cdots\!32$$$$T^{6} +$$$$46\!\cdots\!01$$$$T^{8}$$
$47$ $$( 1 - 27360 T + 591338206 T^{2} - 6274879391520 T^{3} + 52599132235830049 T^{4} )^{2}$$
$53$ $$1 - 1039152180 T^{2} + 595616955270391126 T^{4} -$$$$18\!\cdots\!20$$$$T^{6} +$$$$30\!\cdots\!01$$$$T^{8}$$
$59$ $$1 - 1537424180 T^{2} + 1399694789142612374 T^{4} -$$$$78\!\cdots\!80$$$$T^{6} +$$$$26\!\cdots\!01$$$$T^{8}$$
$61$ $$1 + 741098540 T^{2} + 1478044222094100534 T^{4} +$$$$52\!\cdots\!40$$$$T^{6} +$$$$50\!\cdots\!01$$$$T^{8}$$
$67$ $$1 - 1366835860 T^{2} + 3274116308996825526 T^{4} -$$$$24\!\cdots\!40$$$$T^{6} +$$$$33\!\cdots\!01$$$$T^{8}$$
$71$ $$( 1 + 103344 T + 6217736974 T^{2} + 186456278049744 T^{3} + 3255243551009881201 T^{4} )^{2}$$
$73$ $$( 1 - 19988 T + 2541602870 T^{2} - 41436555000884 T^{3} + 4297625829703557649 T^{4} )^{2}$$
$79$ $$( 1 - 123936 T + 9855929374 T^{2} - 381358061866464 T^{3} + 9468276082626847201 T^{4} )^{2}$$
$83$ $$1 - 10047855188 T^{2} + 55381071937674414326 T^{4} -$$$$15\!\cdots\!12$$$$T^{6} +$$$$24\!\cdots\!01$$$$T^{8}$$
$89$ $$( 1 + 42316 T + 4292401174 T^{2} + 236295059643884 T^{3} + 31181719929966183601 T^{4} )^{2}$$
$97$ $$( 1 + 49788 T + 16391371462 T^{2} + 427546496715516 T^{3} + 73742412689492826049 T^{4} )^{2}$$