Properties

Label 160.6.c
Level 160
Weight 6
Character orbit c
Rep. character \(\chi_{160}(129,\cdot)\)
Character field \(\Q\)
Dimension 30
Newform subspaces 4
Sturm bound 144
Trace bound 9

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Defining parameters

Level: \( N \) \(=\) \( 160 = 2^{5} \cdot 5 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 160.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(144\)
Trace bound: \(9\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(160, [\chi])\).

Total New Old
Modular forms 128 30 98
Cusp forms 112 30 82
Eisenstein series 16 0 16

Trace form

\( 30q - 38q^{5} - 2430q^{9} + O(q^{10}) \) \( 30q - 38q^{5} - 2430q^{9} - 1640q^{21} - 1946q^{25} - 16524q^{29} - 2212q^{41} - 20634q^{45} - 48006q^{49} - 91580q^{61} + 29744q^{65} - 264232q^{69} + 83702q^{81} + 186272q^{85} - 143828q^{89} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(160, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
160.6.c.a \(2\) \(25.661\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(82\) \(0\) \(q+(41+19i)q^{5}+3^{5}q^{9}-122iq^{13}+\cdots\)
160.6.c.b \(4\) \(25.661\) \(\Q(i, \sqrt{5})\) \(\Q(\sqrt{-5}) \) \(0\) \(0\) \(0\) \(0\) \(q+(5\beta _{1}+\beta _{2})q^{3}+5\beta _{3}q^{5}+(46\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots\)
160.6.c.c \(12\) \(25.661\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(0\) \(-60\) \(0\) \(q+\beta _{4}q^{3}+(-5+\beta _{5}+\beta _{8})q^{5}-\beta _{9}q^{7}+\cdots\)
160.6.c.d \(12\) \(25.661\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(0\) \(-60\) \(0\) \(q+\beta _{2}q^{3}+(-5+\beta _{5})q^{5}+(-5\beta _{2}-3\beta _{3}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(160, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(160, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(5, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(10, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 2}\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ 1
$3$ (\( ( 1 - 243 T^{2} )^{2} \))(\( ( 1 - 38 T + 722 T^{2} - 9234 T^{3} + 59049 T^{4} )( 1 + 38 T + 722 T^{2} + 9234 T^{3} + 59049 T^{4} ) \))(\( ( 1 - 310 T^{2} + 120679 T^{4} - 26699028 T^{6} + 7125974271 T^{8} - 1080903164310 T^{10} + 205891132094649 T^{12} )^{2} \))(\( ( 1 - 662 T^{2} + 270567 T^{4} - 78508116 T^{6} + 15976710783 T^{8} - 2308251273462 T^{10} + 205891132094649 T^{12} )^{2} \))
$5$ (\( 1 - 82 T + 3125 T^{2} \))(\( ( 1 - 3125 T^{2} )^{2} \))(\( ( 1 + 30 T + 75 T^{2} - 123500 T^{3} + 234375 T^{4} + 292968750 T^{5} + 30517578125 T^{6} )^{2} \))(\( ( 1 + 30 T + 4555 T^{2} + 273300 T^{3} + 14234375 T^{4} + 292968750 T^{5} + 30517578125 T^{6} )^{2} \))
$7$ (\( ( 1 - 16807 T^{2} )^{2} \))(\( ( 1 - 366 T + 66978 T^{2} - 6151362 T^{3} + 282475249 T^{4} )( 1 + 366 T + 66978 T^{2} + 6151362 T^{3} + 282475249 T^{4} ) \))(\( ( 1 - 42334 T^{2} + 748334111 T^{4} - 10497411086308 T^{6} + 211385864339918639 T^{8} - \)\(33\!\cdots\!34\)\( T^{10} + \)\(22\!\cdots\!49\)\( T^{12} )^{2} \))(\( ( 1 - 54910 T^{2} + 1199559327 T^{4} - 18786317442980 T^{6} + 338845819584597423 T^{8} - \)\(43\!\cdots\!10\)\( T^{10} + \)\(22\!\cdots\!49\)\( T^{12} )^{2} \))
$11$ (\( ( 1 + 161051 T^{2} )^{2} \))(\( ( 1 + 161051 T^{2} )^{4} \))(\( ( 1 + 220194 T^{2} + 46554422967 T^{4} + 4986677846505148 T^{6} + \)\(12\!\cdots\!67\)\( T^{8} + \)\(14\!\cdots\!94\)\( T^{10} + \)\(17\!\cdots\!01\)\( T^{12} )^{2} \))(\( ( 1 + 311650 T^{2} + 88422679991 T^{4} + 16030422126529084 T^{6} + \)\(22\!\cdots\!91\)\( T^{8} + \)\(20\!\cdots\!50\)\( T^{10} + \)\(17\!\cdots\!01\)\( T^{12} )^{2} \))
$13$ (\( ( 1 - 1194 T + 371293 T^{2} )( 1 + 1194 T + 371293 T^{2} ) \))(\( ( 1 - 371293 T^{2} )^{4} \))(\( ( 1 - 921822 T^{2} + 378030377607 T^{4} - 125995996576493956 T^{6} + \)\(52\!\cdots\!43\)\( T^{8} - \)\(17\!\cdots\!22\)\( T^{10} + \)\(26\!\cdots\!49\)\( T^{12} )^{2} \))(\( ( 1 - 183262 T^{2} + 260173900423 T^{4} - 19831011157232516 T^{6} + \)\(35\!\cdots\!27\)\( T^{8} - \)\(34\!\cdots\!62\)\( T^{10} + \)\(26\!\cdots\!49\)\( T^{12} )^{2} \))
$17$ (\( ( 1 - 2242 T + 1419857 T^{2} )( 1 + 2242 T + 1419857 T^{2} ) \))(\( ( 1 - 1419857 T^{2} )^{4} \))(\( ( 1 - 7508390 T^{2} + 24616526523247 T^{4} - 45351621021996027220 T^{6} + \)\(49\!\cdots\!03\)\( T^{8} - \)\(30\!\cdots\!90\)\( T^{10} + \)\(81\!\cdots\!49\)\( T^{12} )^{2} \))(\( ( 1 + 1156442 T^{2} + 502148271983 T^{4} - 1980542974409409364 T^{6} + \)\(10\!\cdots\!67\)\( T^{8} + \)\(47\!\cdots\!42\)\( T^{10} + \)\(81\!\cdots\!49\)\( T^{12} )^{2} \))
$19$ (\( ( 1 + 2476099 T^{2} )^{2} \))(\( ( 1 + 2476099 T^{2} )^{4} \))(\( ( 1 + 8862994 T^{2} + 40251921150215 T^{4} + \)\(12\!\cdots\!80\)\( T^{6} + \)\(24\!\cdots\!15\)\( T^{8} + \)\(33\!\cdots\!94\)\( T^{10} + \)\(23\!\cdots\!01\)\( T^{12} )^{2} \))(\( ( 1 + 3143250 T^{2} + 17341223849991 T^{4} + 36134402435803900316 T^{6} + \)\(10\!\cdots\!91\)\( T^{8} + \)\(11\!\cdots\!50\)\( T^{10} + \)\(23\!\cdots\!01\)\( T^{12} )^{2} \))
$23$ (\( ( 1 - 6436343 T^{2} )^{2} \))(\( ( 1 - 4838 T + 11703122 T^{2} - 31139027434 T^{3} + 41426511213649 T^{4} )( 1 + 4838 T + 11703122 T^{2} + 31139027434 T^{3} + 41426511213649 T^{4} ) \))(\( ( 1 - 27906430 T^{2} + 367961637958719 T^{4} - \)\(29\!\cdots\!08\)\( T^{6} + \)\(15\!\cdots\!31\)\( T^{8} - \)\(47\!\cdots\!30\)\( T^{10} + \)\(71\!\cdots\!49\)\( T^{12} )^{2} \))(\( ( 1 - 2071710 T^{2} + 29683977204927 T^{4} - \)\(44\!\cdots\!80\)\( T^{6} + \)\(12\!\cdots\!23\)\( T^{8} - \)\(35\!\cdots\!10\)\( T^{10} + \)\(71\!\cdots\!49\)\( T^{12} )^{2} \))
$29$ (\( ( 1 - 2950 T + 20511149 T^{2} )^{2} \))(\( ( 1 - 1686 T + 20511149 T^{2} )^{4} \))(\( ( 1 + 5326 T + 46243827 T^{2} + 133362268948 T^{3} + 948514025927223 T^{4} + 2240686724556870526 T^{5} + \)\(86\!\cdots\!49\)\( T^{6} )^{4} \))(\( ( 1 + 1966 T + 38511987 T^{2} + 51339089236 T^{3} + 789925103643063 T^{4} + 827110420668195166 T^{5} + \)\(86\!\cdots\!49\)\( T^{6} )^{4} \))
$31$ (\( ( 1 + 28629151 T^{2} )^{2} \))(\( ( 1 + 28629151 T^{2} )^{4} \))(\( ( 1 + 10594234 T^{2} - 153174449706673 T^{4} + \)\(19\!\cdots\!88\)\( T^{6} - \)\(12\!\cdots\!73\)\( T^{8} + \)\(71\!\cdots\!34\)\( T^{10} + \)\(55\!\cdots\!01\)\( T^{12} )^{2} \))(\( ( 1 + 47574970 T^{2} + 2163796989249871 T^{4} + \)\(78\!\cdots\!04\)\( T^{6} + \)\(17\!\cdots\!71\)\( T^{8} + \)\(31\!\cdots\!70\)\( T^{10} + \)\(55\!\cdots\!01\)\( T^{12} )^{2} \))
$37$ (\( ( 1 - 12242 T + 69343957 T^{2} )( 1 + 12242 T + 69343957 T^{2} ) \))(\( ( 1 - 69343957 T^{2} )^{4} \))(\( ( 1 - 234974254 T^{2} + 32080895329334807 T^{4} - \)\(26\!\cdots\!92\)\( T^{6} + \)\(15\!\cdots\!43\)\( T^{8} - \)\(54\!\cdots\!54\)\( T^{10} + \)\(11\!\cdots\!49\)\( T^{12} )^{2} \))(\( ( 1 - 301201198 T^{2} + 42883739211630103 T^{4} - \)\(37\!\cdots\!24\)\( T^{6} + \)\(20\!\cdots\!47\)\( T^{8} - \)\(69\!\cdots\!98\)\( T^{10} + \)\(11\!\cdots\!49\)\( T^{12} )^{2} \))
$41$ (\( ( 1 - 20950 T + 115856201 T^{2} )^{2} \))(\( ( 1 - 211028098 T^{2} + 13422659310152401 T^{4} )^{2} \))(\( ( 1 + 27418 T + 531273543 T^{2} + 6402679071436 T^{3} + 61551334383790143 T^{4} + \)\(36\!\cdots\!18\)\( T^{5} + \)\(15\!\cdots\!01\)\( T^{6} )^{4} \))(\( ( 1 - 16390 T + 318388423 T^{2} - 3510238606580 T^{3} + 36887273131161023 T^{4} - \)\(21\!\cdots\!90\)\( T^{5} + \)\(15\!\cdots\!01\)\( T^{6} )^{4} \))
$43$ (\( ( 1 - 147008443 T^{2} )^{2} \))(\( ( 1 - 11862 T + 70353522 T^{2} - 1743814150866 T^{3} + 21611482313284249 T^{4} )( 1 + 11862 T + 70353522 T^{2} + 1743814150866 T^{3} + 21611482313284249 T^{4} ) \))(\( ( 1 - 613900486 T^{2} + 182904754783784951 T^{4} - \)\(33\!\cdots\!72\)\( T^{6} + \)\(39\!\cdots\!99\)\( T^{8} - \)\(28\!\cdots\!86\)\( T^{10} + \)\(10\!\cdots\!49\)\( T^{12} )^{2} \))(\( ( 1 - 640358182 T^{2} + 187647756282389367 T^{4} - \)\(33\!\cdots\!76\)\( T^{6} + \)\(40\!\cdots\!83\)\( T^{8} - \)\(29\!\cdots\!82\)\( T^{10} + \)\(10\!\cdots\!49\)\( T^{12} )^{2} \))
$47$ (\( ( 1 - 229345007 T^{2} )^{2} \))(\( ( 1 - 33334 T + 555577778 T^{2} - 7644986463338 T^{3} + 52599132235830049 T^{4} )( 1 + 33334 T + 555577778 T^{2} + 7644986463338 T^{3} + 52599132235830049 T^{4} ) \))(\( ( 1 - 579920494 T^{2} + 165136673035562991 T^{4} - \)\(38\!\cdots\!48\)\( T^{6} + \)\(86\!\cdots\!59\)\( T^{8} - \)\(16\!\cdots\!94\)\( T^{10} + \)\(14\!\cdots\!49\)\( T^{12} )^{2} \))(\( ( 1 - 764642190 T^{2} + 310900354010297967 T^{4} - \)\(85\!\cdots\!20\)\( T^{6} + \)\(16\!\cdots\!83\)\( T^{8} - \)\(21\!\cdots\!90\)\( T^{10} + \)\(14\!\cdots\!49\)\( T^{12} )^{2} \))
$53$ (\( ( 1 - 7294 T + 418195493 T^{2} )( 1 + 7294 T + 418195493 T^{2} ) \))(\( ( 1 - 418195493 T^{2} )^{4} \))(\( ( 1 - 2026325390 T^{2} + 1866514545072595447 T^{4} - \)\(99\!\cdots\!20\)\( T^{6} + \)\(32\!\cdots\!03\)\( T^{8} - \)\(61\!\cdots\!90\)\( T^{10} + \)\(53\!\cdots\!49\)\( T^{12} )^{2} \))(\( ( 1 - 1611835534 T^{2} + 1232324270520828407 T^{4} - \)\(61\!\cdots\!84\)\( T^{6} + \)\(21\!\cdots\!43\)\( T^{8} - \)\(49\!\cdots\!34\)\( T^{10} + \)\(53\!\cdots\!49\)\( T^{12} )^{2} \))
$59$ (\( ( 1 + 714924299 T^{2} )^{2} \))(\( ( 1 + 714924299 T^{2} )^{4} \))(\( ( 1 + 55950786 T^{2} + 253972763776609047 T^{4} - \)\(45\!\cdots\!68\)\( T^{6} + \)\(12\!\cdots\!47\)\( T^{8} + \)\(14\!\cdots\!86\)\( T^{10} + \)\(13\!\cdots\!01\)\( T^{12} )^{2} \))(\( ( 1 + 2333761794 T^{2} + 3044701823751957015 T^{4} + \)\(26\!\cdots\!80\)\( T^{6} + \)\(15\!\cdots\!15\)\( T^{8} + \)\(60\!\cdots\!94\)\( T^{10} + \)\(13\!\cdots\!01\)\( T^{12} )^{2} \))
$61$ (\( ( 1 + 18950 T + 844596301 T^{2} )^{2} \))(\( ( 1 - 1041591898 T^{2} + 713342911662882601 T^{4} )^{2} \))(\( ( 1 - 16138 T + 744681843 T^{2} - 29097452426876 T^{3} + 628955530019662743 T^{4} - \)\(11\!\cdots\!38\)\( T^{5} + \)\(60\!\cdots\!01\)\( T^{6} )^{4} \))(\( ( 1 + 29558 T + 2350852083 T^{2} + 48603849831556 T^{3} + 1985520973499944983 T^{4} + \)\(21\!\cdots\!58\)\( T^{5} + \)\(60\!\cdots\!01\)\( T^{6} )^{4} \))
$67$ (\( ( 1 - 1350125107 T^{2} )^{2} \))(\( ( 1 - 100434 T + 5043494178 T^{2} - 135598464996438 T^{3} + 1822837804551761449 T^{4} )( 1 + 100434 T + 5043494178 T^{2} + 135598464996438 T^{3} + 1822837804551761449 T^{4} ) \))(\( ( 1 - 2173336374 T^{2} + 6882868324909910631 T^{4} - \)\(82\!\cdots\!68\)\( T^{6} + \)\(12\!\cdots\!19\)\( T^{8} - \)\(72\!\cdots\!74\)\( T^{10} + \)\(60\!\cdots\!49\)\( T^{12} )^{2} \))(\( ( 1 - 3741380758 T^{2} + 9572756841213379047 T^{4} - \)\(14\!\cdots\!84\)\( T^{6} + \)\(17\!\cdots\!03\)\( T^{8} - \)\(12\!\cdots\!58\)\( T^{10} + \)\(60\!\cdots\!49\)\( T^{12} )^{2} \))
$71$ (\( ( 1 + 1804229351 T^{2} )^{2} \))(\( ( 1 + 1804229351 T^{2} )^{4} \))(\( ( 1 + 942628714 T^{2} + 4622069102042239647 T^{4} + \)\(48\!\cdots\!68\)\( T^{6} + \)\(15\!\cdots\!47\)\( T^{8} + \)\(99\!\cdots\!14\)\( T^{10} + \)\(34\!\cdots\!01\)\( T^{12} )^{2} \))(\( ( 1 + 9793576042 T^{2} + 41626938509482688159 T^{4} + \)\(98\!\cdots\!36\)\( T^{6} + \)\(13\!\cdots\!59\)\( T^{8} + \)\(10\!\cdots\!42\)\( T^{10} + \)\(34\!\cdots\!01\)\( T^{12} )^{2} \))
$73$ (\( ( 1 - 88806 T + 2073071593 T^{2} )( 1 + 88806 T + 2073071593 T^{2} ) \))(\( ( 1 - 2073071593 T^{2} )^{4} \))(\( ( 1 - 4736672630 T^{2} + 15959781190221205247 T^{4} - \)\(37\!\cdots\!40\)\( T^{6} + \)\(68\!\cdots\!03\)\( T^{8} - \)\(87\!\cdots\!30\)\( T^{10} + \)\(79\!\cdots\!49\)\( T^{12} )^{2} \))(\( ( 1 - 5477783158 T^{2} + 15527894807038343935 T^{4} - \)\(34\!\cdots\!40\)\( T^{6} + \)\(66\!\cdots\!15\)\( T^{8} - \)\(10\!\cdots\!58\)\( T^{10} + \)\(79\!\cdots\!49\)\( T^{12} )^{2} \))
$79$ (\( ( 1 + 3077056399 T^{2} )^{2} \))(\( ( 1 + 3077056399 T^{2} )^{4} \))(\( ( 1 + 454164826 T^{2} + 18487132928554429487 T^{4} - \)\(50\!\cdots\!28\)\( T^{6} + \)\(17\!\cdots\!87\)\( T^{8} + \)\(40\!\cdots\!26\)\( T^{10} + \)\(84\!\cdots\!01\)\( T^{12} )^{2} \))(\( ( 1 + 8854539610 T^{2} + 48426464203018517551 T^{4} + \)\(17\!\cdots\!76\)\( T^{6} + \)\(45\!\cdots\!51\)\( T^{8} + \)\(79\!\cdots\!10\)\( T^{10} + \)\(84\!\cdots\!01\)\( T^{12} )^{2} \))
$83$ (\( ( 1 - 3939040643 T^{2} )^{2} \))(\( ( 1 - 163262 T + 13327240322 T^{2} - 643095653457466 T^{3} + 15516041187205853449 T^{4} )( 1 + 163262 T + 13327240322 T^{2} + 643095653457466 T^{3} + 15516041187205853449 T^{4} ) \))(\( ( 1 - 11599602390 T^{2} + 72197091204656028039 T^{4} - \)\(31\!\cdots\!48\)\( T^{6} + \)\(11\!\cdots\!11\)\( T^{8} - \)\(27\!\cdots\!90\)\( T^{10} + \)\(37\!\cdots\!49\)\( T^{12} )^{2} \))(\( ( 1 - 17886738486 T^{2} + \)\(14\!\cdots\!27\)\( T^{4} - \)\(73\!\cdots\!08\)\( T^{6} + \)\(22\!\cdots\!23\)\( T^{8} - \)\(43\!\cdots\!86\)\( T^{10} + \)\(37\!\cdots\!49\)\( T^{12} )^{2} \))
$89$ (\( ( 1 - 51050 T + 5584059449 T^{2} )^{2} \))(\( ( 1 + 149286 T + 5584059449 T^{2} )^{4} \))(\( ( 1 + 930 T + 9446079447 T^{2} + 231471892494140 T^{3} + 52747469192025044703 T^{4} + \)\(28\!\cdots\!30\)\( T^{5} + \)\(17\!\cdots\!49\)\( T^{6} )^{4} \))(\( ( 1 - 88734 T + 11682221271 T^{2} - 581994460142148 T^{3} + 65234218073636339679 T^{4} - \)\(27\!\cdots\!34\)\( T^{5} + \)\(17\!\cdots\!49\)\( T^{6} )^{4} \))
$97$ (\( ( 1 - 92142 T + 8587340257 T^{2} )( 1 + 92142 T + 8587340257 T^{2} ) \))(\( ( 1 - 8587340257 T^{2} )^{4} \))(\( ( 1 - 35609466630 T^{2} + \)\(64\!\cdots\!47\)\( T^{4} - \)\(68\!\cdots\!40\)\( T^{6} + \)\(47\!\cdots\!03\)\( T^{8} - \)\(19\!\cdots\!30\)\( T^{10} + \)\(40\!\cdots\!49\)\( T^{12} )^{2} \))(\( ( 1 - 22620660742 T^{2} + \)\(25\!\cdots\!35\)\( T^{4} - \)\(22\!\cdots\!60\)\( T^{6} + \)\(18\!\cdots\!15\)\( T^{8} - \)\(12\!\cdots\!42\)\( T^{10} + \)\(40\!\cdots\!49\)\( T^{12} )^{2} \))
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