Properties

Label 144.2.l
Level 144
Weight 2
Character orbit l
Rep. character \(\chi_{144}(35,\cdot)\)
Character field \(\Q(\zeta_{4})\)
Dimension 16
Newform subspaces 1
Sturm bound 48
Trace bound 0

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) \(=\) \( 144 = 2^{4} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 144.l (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 48 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 1 \)
Sturm bound: \(48\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(144, [\chi])\).

Total New Old
Modular forms 56 16 40
Cusp forms 40 16 24
Eisenstein series 16 0 16

Trace form

\( 16q + O(q^{10}) \) \( 16q - 8q^{10} - 16q^{16} + 16q^{19} - 40q^{22} - 24q^{28} + 24q^{34} + 72q^{40} - 32q^{43} + 40q^{46} + 16q^{49} + 24q^{52} - 64q^{55} + 24q^{58} - 32q^{61} - 48q^{64} - 16q^{67} - 72q^{70} + 80q^{82} - 32q^{85} + 48q^{88} + 48q^{91} + 72q^{94} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(144, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
144.2.l.a \(16\) \(1.150\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{11}q^{2}-\beta _{7}q^{4}+\beta _{6}q^{5}+(-\beta _{4}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(144, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(144, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 2}\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( 1 + 4 T^{4} + 8 T^{6} + 4 T^{8} + 32 T^{10} + 64 T^{12} + 256 T^{16} \)
$3$ 1
$5$ \( 1 - 8 T^{4} - 804 T^{8} + 2376 T^{12} + 502406 T^{16} + 1485000 T^{20} - 314062500 T^{24} - 1953125000 T^{28} + 152587890625 T^{32} \)
$7$ \( ( 1 + 12 T^{2} + 16 T^{3} + 74 T^{4} + 112 T^{5} + 588 T^{6} + 2401 T^{8} )^{4} \)
$11$ \( 1 - 184 T^{4} + 8796 T^{8} + 2616696 T^{12} - 490804602 T^{16} + 38311046136 T^{20} + 1885500717276 T^{24} - 577470821316664 T^{28} + 45949729863572161 T^{32} \)
$13$ \( ( 1 + 64 T^{3} - 36 T^{4} - 704 T^{5} + 2048 T^{6} + 384 T^{7} - 43930 T^{8} + 4992 T^{9} + 346112 T^{10} - 1546688 T^{11} - 1028196 T^{12} + 23762752 T^{13} + 815730721 T^{16} )^{2} \)
$17$ \( ( 1 - 64 T^{2} + 1956 T^{4} - 40128 T^{6} + 697542 T^{8} - 11596992 T^{10} + 163367076 T^{12} - 1544804416 T^{14} + 6975757441 T^{16} )^{2} \)
$19$ \( ( 1 - 8 T + 32 T^{2} - 184 T^{3} + 388 T^{4} + 1992 T^{5} - 11424 T^{6} + 82616 T^{7} - 538074 T^{8} + 1569704 T^{9} - 4124064 T^{10} + 13663128 T^{11} + 50564548 T^{12} - 455602216 T^{13} + 1505468192 T^{14} - 7150973912 T^{15} + 16983563041 T^{16} )^{2} \)
$23$ \( ( 1 - 88 T^{2} + 3004 T^{4} - 46440 T^{6} + 546118 T^{8} - 24566760 T^{10} + 840642364 T^{12} - 13027158232 T^{14} + 78310985281 T^{16} )^{2} \)
$29$ \( 1 - 1672 T^{4} + 1133916 T^{8} - 595679544 T^{12} + 410245939974 T^{16} - 421312823559864 T^{20} + 567237411599085276 T^{24} - \)\(59\!\cdots\!52\)\( T^{28} + \)\(25\!\cdots\!21\)\( T^{32} \)
$31$ \( ( 1 - 56 T^{2} + 3492 T^{4} - 137064 T^{6} + 4924550 T^{8} - 131718504 T^{10} + 3224935332 T^{12} - 49700206136 T^{14} + 852891037441 T^{16} )^{2} \)
$37$ \( ( 1 - 512 T^{3} + 700 T^{4} + 9728 T^{5} + 131072 T^{6} - 437248 T^{7} - 3354522 T^{8} - 16178176 T^{9} + 179437568 T^{10} + 492752384 T^{11} + 1311912700 T^{12} - 35504105984 T^{13} + 3512479453921 T^{16} )^{2} \)
$41$ \( ( 1 + 160 T^{2} + 12772 T^{4} + 745952 T^{6} + 34631942 T^{8} + 1253945312 T^{10} + 36090619492 T^{12} + 760016678560 T^{14} + 7984925229121 T^{16} )^{2} \)
$43$ \( ( 1 + 16 T + 128 T^{2} + 1200 T^{3} + 6980 T^{4} - 80 T^{5} - 174720 T^{6} - 2568048 T^{7} - 25827098 T^{8} - 110426064 T^{9} - 323057280 T^{10} - 6360560 T^{11} + 23863230980 T^{12} + 176410131600 T^{13} + 809134470272 T^{14} + 4349097777712 T^{15} + 11688200277601 T^{16} )^{2} \)
$47$ \( ( 1 + 216 T^{2} + 24572 T^{4} + 1856872 T^{6} + 101744902 T^{8} + 4101830248 T^{10} + 119903521532 T^{12} + 2328310511064 T^{14} + 23811286661761 T^{16} )^{2} \)
$53$ \( 1 + 2936 T^{4} + 12654300 T^{8} + 22427423688 T^{12} + 91065624180102 T^{16} + 176963160489113928 T^{20} + \)\(78\!\cdots\!00\)\( T^{24} + \)\(14\!\cdots\!76\)\( T^{28} + \)\(38\!\cdots\!21\)\( T^{32} \)
$59$ \( 1 - 2360 T^{4} + 15662172 T^{8} - 90024948744 T^{12} + 175698504275846 T^{16} - 1090864802937544584 T^{20} + \)\(22\!\cdots\!12\)\( T^{24} - \)\(41\!\cdots\!60\)\( T^{28} + \)\(21\!\cdots\!41\)\( T^{32} \)
$61$ \( ( 1 + 16 T + 128 T^{2} + 1392 T^{3} + 16892 T^{4} + 124816 T^{5} + 803712 T^{6} + 7357296 T^{7} + 67536550 T^{8} + 448795056 T^{9} + 2990612352 T^{10} + 28330860496 T^{11} + 233883946172 T^{12} + 1175678050992 T^{13} + 6594607918208 T^{14} + 50283885376336 T^{15} + 191707312997281 T^{16} )^{2} \)
$67$ \( ( 1 + 8 T + 32 T^{2} + 1240 T^{3} + 5540 T^{4} - 65000 T^{5} + 71520 T^{6} - 2339576 T^{7} - 86245658 T^{8} - 156751592 T^{9} + 321053280 T^{10} - 19549595000 T^{11} + 111637210340 T^{12} + 1674155132680 T^{13} + 2894668229408 T^{14} + 48485692842584 T^{15} + 406067677556641 T^{16} )^{2} \)
$71$ \( ( 1 - 376 T^{2} + 67068 T^{4} - 7636296 T^{6} + 626574150 T^{8} - 38494568136 T^{10} + 1704310621308 T^{12} - 48165706754296 T^{14} + 645753531245761 T^{16} )^{2} \)
$73$ \( ( 1 - 408 T^{2} + 80156 T^{4} - 9970856 T^{6} + 862104454 T^{8} - 53134691624 T^{10} + 2276289405596 T^{12} - 61744364325912 T^{14} + 806460091894081 T^{16} )^{2} \)
$79$ \( ( 1 - 408 T^{2} + 84004 T^{4} - 11101576 T^{6} + 1033756678 T^{8} - 69284935816 T^{10} + 3271962604324 T^{12} - 99179681852568 T^{14} + 1517108809906561 T^{16} )^{2} \)
$83$ \( 1 - 5432 T^{4} + 103273180 T^{8} - 984945914120 T^{12} + 5200099763862790 T^{16} - 46743879359945392520 T^{20} + \)\(23\!\cdots\!80\)\( T^{24} - \)\(58\!\cdots\!52\)\( T^{28} + \)\(50\!\cdots\!81\)\( T^{32} \)
$89$ \( ( 1 + 512 T^{2} + 123588 T^{4} + 18716160 T^{6} + 1970104134 T^{8} + 148250703360 T^{10} + 7754188080708 T^{12} + 254454420972032 T^{14} + 3936588805702081 T^{16} )^{2} \)
$97$ \( ( 1 + 316 T^{2} - 256 T^{3} + 42310 T^{4} - 24832 T^{5} + 2973244 T^{6} + 88529281 T^{8} )^{4} \)
show more
show less