Properties

Label 2016.3.g
Level 2016
Weight 3
Character orbit g
Rep. character \(\chi_{2016}(1135,\cdot)\)
Character field \(\Q\)
Dimension 60
Newform subspaces 4
Sturm bound 1152
Trace bound 11

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Defining parameters

Level: \( N \) \(=\) \( 2016 = 2^{5} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 2016.g (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 8 \)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(1152\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(2016, [\chi])\).

Total New Old
Modular forms 800 60 740
Cusp forms 736 60 676
Eisenstein series 64 0 64

Trace form

\( 60q + O(q^{10}) \) \( 60q + 16q^{11} - 8q^{17} + 64q^{19} - 324q^{25} - 8q^{41} - 176q^{43} - 420q^{49} + 288q^{59} + 96q^{65} - 16q^{67} + 120q^{73} - 160q^{83} - 200q^{89} - 72q^{97} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(2016, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
2016.3.g.a \(4\) \(54.932\) \(\Q(\sqrt{2}, \sqrt{-7})\) None \(0\) \(0\) \(0\) \(0\) \(q+(-\beta _{2}+2\beta _{3})q^{5}+\beta _{3}q^{7}+(4+6\beta _{1}+\cdots)q^{11}+\cdots\)
2016.3.g.b \(8\) \(54.932\) 8.0.\(\cdots\).3 None \(0\) \(0\) \(0\) \(0\) \(q+(\beta _{1}-\beta _{2}-\beta _{4})q^{5}+\beta _{2}q^{7}+(-4+\cdots)q^{11}+\cdots\)
2016.3.g.c \(24\) \(54.932\) None \(0\) \(0\) \(0\) \(0\)
2016.3.g.d \(24\) \(54.932\) None \(0\) \(0\) \(0\) \(0\)

Decomposition of \(S_{3}^{\mathrm{old}}(2016, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(2016, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(8, [\chi])\)\(^{\oplus 18}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(168, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(224, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(288, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(504, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(672, [\chi])\)\(^{\oplus 2}\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ 1
$3$ 1
$5$ (\( 1 - 16 T^{2} - 254 T^{4} - 10000 T^{6} + 390625 T^{8} \))(\( 1 - 92 T^{2} + 5464 T^{4} - 211956 T^{6} + 6231214 T^{8} - 132472500 T^{10} + 2134375000 T^{12} - 22460937500 T^{14} + 152587890625 T^{16} \))
$7$ (\( ( 1 + 7 T^{2} )^{2} \))(\( ( 1 + 7 T^{2} )^{4} \))
$11$ (\( ( 1 - 8 T + 186 T^{2} - 968 T^{3} + 14641 T^{4} )^{2} \))(\( ( 1 + 16 T + 328 T^{2} + 4944 T^{3} + 49230 T^{4} + 598224 T^{5} + 4802248 T^{6} + 28344976 T^{7} + 214358881 T^{8} )^{2} \))
$13$ (\( 1 - 592 T^{2} + 143170 T^{4} - 16908112 T^{6} + 815730721 T^{8} \))(\( 1 - 444 T^{2} + 142936 T^{4} - 35361044 T^{6} + 6575436334 T^{8} - 1009946777684 T^{10} + 116597286336856 T^{12} - 10344349794381564 T^{14} + 665416609183179841 T^{16} \))
$17$ (\( ( 1 + 36 T + 870 T^{2} + 10404 T^{3} + 83521 T^{4} )^{2} \))(\( ( 1 - 40 T + 1308 T^{2} - 31512 T^{3} + 588230 T^{4} - 9106968 T^{5} + 109245468 T^{6} - 965502760 T^{7} + 6975757441 T^{8} )^{2} \))
$19$ (\( ( 1 + 4 T + 4 T^{2} + 1444 T^{3} + 130321 T^{4} )^{2} \))(\( ( 1 + 28 T + 1710 T^{2} + 31332 T^{3} + 975266 T^{4} + 11310852 T^{5} + 222848910 T^{6} + 1317284668 T^{7} + 16983563041 T^{8} )^{2} \))
$23$ (\( 1 - 268 T^{2} + 477286 T^{4} - 74997388 T^{6} + 78310985281 T^{8} \))(\( 1 - 1744 T^{2} + 1272156 T^{4} - 412076080 T^{6} + 99307893702 T^{8} - 115315782303280 T^{10} + 99623789791135836 T^{12} - 38219105009443439824 T^{14} + \)\(61\!\cdots\!61\)\( T^{16} \))
$29$ (\( ( 1 - 1178 T^{2} + 707281 T^{4} )^{2} \))(\( 1 - 3384 T^{2} + 6555580 T^{4} - 8754768776 T^{6} + 8490907402822 T^{8} - 6192081614658056 T^{10} + 3279405379878872380 T^{12} - \)\(11\!\cdots\!44\)\( T^{14} + \)\(25\!\cdots\!21\)\( T^{16} \))
$31$ (\( 1 - 1380 T^{2} + 1419974 T^{4} - 1274458980 T^{6} + 852891037441 T^{8} \))(\( 1 - 3944 T^{2} + 8438620 T^{4} - 12447428312 T^{6} + 13694235978694 T^{8} - 11495461442126552 T^{10} + 7197223366370371420 T^{12} - \)\(31\!\cdots\!84\)\( T^{14} + \)\(72\!\cdots\!81\)\( T^{16} \))
$37$ (\( 1 - 1780 T^{2} + 2031622 T^{4} - 3336006580 T^{6} + 3512479453921 T^{8} \))(\( 1 - 3512 T^{2} + 9188668 T^{4} - 18622781448 T^{6} + 27544347275206 T^{8} - 34902090701365128 T^{10} + 32275007558901367228 T^{12} - \)\(23\!\cdots\!72\)\( T^{14} + \)\(12\!\cdots\!41\)\( T^{16} \))
$41$ (\( ( 1 - 20 T + 3174 T^{2} - 33620 T^{3} + 2825761 T^{4} )^{2} \))(\( ( 1 + 64 T + 4956 T^{2} + 221760 T^{3} + 11848326 T^{4} + 372778560 T^{5} + 14004471516 T^{6} + 304006671424 T^{7} + 7984925229121 T^{8} )^{2} \))
$43$ (\( ( 1 - 40 T + 4090 T^{2} - 73960 T^{3} + 3418801 T^{4} )^{2} \))(\( ( 1 + 4680 T^{2} + 58016 T^{3} + 10251086 T^{4} + 107271584 T^{5} + 15999988680 T^{6} + 11688200277601 T^{8} )^{2} \))
$47$ (\( 1 - 7492 T^{2} + 23390470 T^{4} - 36558570052 T^{6} + 23811286661761 T^{8} \))(\( 1 - 8392 T^{2} + 39566748 T^{4} - 127207295352 T^{6} + 316693927920198 T^{8} - 620731022190542712 T^{10} + \)\(94\!\cdots\!28\)\( T^{12} - \)\(97\!\cdots\!72\)\( T^{14} + \)\(56\!\cdots\!21\)\( T^{16} \))
$53$ (\( 1 - 1604 T^{2} - 6155034 T^{4} - 12656331524 T^{6} + 62259690411361 T^{8} \))(\( 1 - 18920 T^{2} + 162796828 T^{4} - 840091728600 T^{6} + 2864724835962118 T^{8} - 6628727822775456600 T^{10} + \)\(10\!\cdots\!08\)\( T^{12} - \)\(92\!\cdots\!20\)\( T^{14} + \)\(38\!\cdots\!21\)\( T^{16} \))
$59$ (\( ( 1 - 92 T + 8836 T^{2} - 320252 T^{3} + 12117361 T^{4} )^{2} \))(\( ( 1 - 52 T + 2254 T^{2} + 207508 T^{3} - 19795230 T^{4} + 722335348 T^{5} + 27312531694 T^{6} - 2193387749332 T^{7} + 146830437604321 T^{8} )^{2} \))
$61$ (\( 1 - 13232 T^{2} + 71110338 T^{4} - 183208168112 T^{6} + 191707312997281 T^{8} \))(\( 1 - 16316 T^{2} + 140172120 T^{4} - 816942037524 T^{6} + 3499102878259502 T^{8} - 11311249557773337684 T^{10} + \)\(26\!\cdots\!20\)\( T^{12} - \)\(43\!\cdots\!36\)\( T^{14} + \)\(36\!\cdots\!61\)\( T^{16} \))
$67$ (\( ( 1 - 112 T + 11602 T^{2} - 502768 T^{3} + 20151121 T^{4} )^{2} \))(\( ( 1 + 152 T + 22224 T^{2} + 2037320 T^{3} + 158433022 T^{4} + 9145529480 T^{5} + 447838513104 T^{6} + 13749674089688 T^{7} + 406067677556641 T^{8} )^{2} \))
$71$ (\( 1 - 9412 T^{2} + 47279686 T^{4} - 239174741572 T^{6} + 645753531245761 T^{8} \))(\( 1 - 9864 T^{2} + 51888284 T^{4} - 294531431096 T^{6} + 1789421441990854 T^{8} - 7484538771485032376 T^{10} + \)\(33\!\cdots\!24\)\( T^{12} - \)\(16\!\cdots\!24\)\( T^{14} + \)\(41\!\cdots\!21\)\( T^{16} \))
$73$ (\( ( 1 - 116 T + 13894 T^{2} - 618164 T^{3} + 28398241 T^{4} )^{2} \))(\( ( 1 + 56 T + 18460 T^{2} + 736008 T^{3} + 138223494 T^{4} + 3922186632 T^{5} + 524231528860 T^{6} + 8474716672184 T^{7} + 806460091894081 T^{8} )^{2} \))
$79$ (\( 1 - 16900 T^{2} + 142880134 T^{4} - 658256368900 T^{6} + 1517108809906561 T^{8} \))(\( 1 - 24968 T^{2} + 330869788 T^{4} - 3106127956152 T^{6} + 22189846569597766 T^{8} - \)\(12\!\cdots\!12\)\( T^{10} + \)\(50\!\cdots\!68\)\( T^{12} - \)\(14\!\cdots\!88\)\( T^{14} + \)\(23\!\cdots\!21\)\( T^{16} \))
$83$ (\( ( 1 - 44 T + 13924 T^{2} - 303116 T^{3} + 47458321 T^{4} )^{2} \))(\( ( 1 - 36 T + 16478 T^{2} - 177884 T^{3} + 135298114 T^{4} - 1225442876 T^{5} + 782018213438 T^{6} - 11769853441284 T^{7} + 2252292232139041 T^{8} )^{2} \))
$89$ (\( ( 1 + 156 T + 20774 T^{2} + 1235676 T^{3} + 62742241 T^{4} )^{2} \))(\( ( 1 - 256 T + 48252 T^{2} - 6269952 T^{3} + 638304966 T^{4} - 49664289792 T^{5} + 3027438612732 T^{6} - 127227210486016 T^{7} + 3936588805702081 T^{8} )^{2} \))
$97$ (\( ( 1 + 68 T + 3046 T^{2} + 639812 T^{3} + 88529281 T^{4} )^{2} \))(\( ( 1 - 32 T + 19484 T^{2} - 1437536 T^{3} + 199130566 T^{4} - 13525776224 T^{5} + 1724904511004 T^{6} - 26655104157728 T^{7} + 7837433594376961 T^{8} )^{2} \))
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