Properties

Label 64.6.b
Level 64
Weight 6
Character orbit b
Rep. character \(\chi_{64}(33,\cdot)\)
Character field \(\Q\)
Dimension 10
Newform subspaces 2
Sturm bound 48
Trace bound 1

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Defining parameters

Level: \( N \) \(=\) \( 64 = 2^{6} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 64.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 8 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(48\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(64, [\chi])\).

Total New Old
Modular forms 46 10 36
Cusp forms 34 10 24
Eisenstein series 12 0 12

Trace form

\( 10q - 810q^{9} + O(q^{10}) \) \( 10q - 810q^{9} - 1212q^{17} - 15598q^{25} + 17016q^{33} + 27396q^{41} - 5254q^{49} + 66648q^{57} - 11520q^{65} - 90028q^{73} - 267054q^{81} + 86388q^{89} + 302692q^{97} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(64, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
64.6.b.a \(2\) \(10.265\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-2}) \) \(0\) \(0\) \(0\) \(0\) \(q+iq^{3}+239q^{9}+237iq^{11}+1914q^{17}+\cdots\)
64.6.b.b \(8\) \(10.265\) 8.0.\(\cdots\).15 None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{3}q^{3}+\beta _{1}q^{5}-\beta _{6}q^{7}+(-161+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(64, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(64, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(8, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 2}\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ 1
$3$ (\( 1 - 482 T^{2} + 59049 T^{4} \))(\( ( 1 - 164 T^{2} + 99990 T^{4} - 9684036 T^{6} + 3486784401 T^{8} )^{2} \))
$5$ (\( ( 1 - 3125 T^{2} )^{2} \))(\( ( 1 - 788 T^{2} - 2662314 T^{4} - 7695312500 T^{6} + 95367431640625 T^{8} )^{2} \))
$7$ (\( ( 1 + 16807 T^{2} )^{2} \))(\( ( 1 + 26524 T^{2} + 612102054 T^{4} + 7492373504476 T^{6} + 79792266297612001 T^{8} )^{2} \))
$11$ (\( 1 - 97426 T^{2} + 25937424601 T^{4} \))(\( ( 1 - 457220 T^{2} + 102880261302 T^{4} - 11859109276069220 T^{6} + \)\(67\!\cdots\!01\)\( T^{8} )^{2} \))
$13$ (\( ( 1 - 371293 T^{2} )^{2} \))(\( ( 1 - 233908 T^{2} + 52296802614 T^{4} - 32246204111415892 T^{6} + \)\(19\!\cdots\!01\)\( T^{8} )^{2} \))
$17$ (\( ( 1 - 1914 T + 1419857 T^{2} )^{2} \))(\( ( 1 + 1260 T + 1225222 T^{2} + 1789019820 T^{3} + 2015993900449 T^{4} )^{4} \))
$19$ (\( 1 + 3353726 T^{2} + 6131066257801 T^{4} \))(\( ( 1 - 7777508 T^{2} + 27043670703318 T^{4} - 47684416868577339908 T^{6} + \)\(37\!\cdots\!01\)\( T^{8} )^{2} \))
$23$ (\( ( 1 + 6436343 T^{2} )^{2} \))(\( ( 1 + 11284700 T^{2} + 69827892672486 T^{4} + \)\(46\!\cdots\!00\)\( T^{6} + \)\(17\!\cdots\!01\)\( T^{8} )^{2} \))
$29$ (\( ( 1 - 20511149 T^{2} )^{2} \))(\( ( 1 - 46615796 T^{2} + 1180167087778806 T^{4} - \)\(19\!\cdots\!96\)\( T^{6} + \)\(17\!\cdots\!01\)\( T^{8} )^{2} \))
$31$ (\( ( 1 + 28629151 T^{2} )^{2} \))(\( ( 1 + 84570748 T^{2} + 3405599639474310 T^{4} + \)\(69\!\cdots\!48\)\( T^{6} + \)\(67\!\cdots\!01\)\( T^{8} )^{2} \))
$37$ (\( ( 1 - 69343957 T^{2} )^{2} \))(\( ( 1 - 207752596 T^{2} + 19864489018719702 T^{4} - \)\(99\!\cdots\!04\)\( T^{6} + \)\(23\!\cdots\!01\)\( T^{8} )^{2} \))
$41$ (\( ( 1 + 13926 T + 115856201 T^{2} )^{2} \))(\( ( 1 - 13812 T + 278511286 T^{2} - 1600205848212 T^{3} + 13422659310152401 T^{4} )^{4} \))
$43$ (\( 1 + 214485614 T^{2} + 21611482313284249 T^{4} \))(\( ( 1 - 404372228 T^{2} + 75777916135242294 T^{4} - \)\(87\!\cdots\!72\)\( T^{6} + \)\(46\!\cdots\!01\)\( T^{8} )^{2} \))
$47$ (\( ( 1 + 229345007 T^{2} )^{2} \))(\( ( 1 + 193552316 T^{2} + 109332805721221830 T^{4} + \)\(10\!\cdots\!84\)\( T^{6} + \)\(27\!\cdots\!01\)\( T^{8} )^{2} \))
$53$ (\( ( 1 - 418195493 T^{2} )^{2} \))(\( ( 1 - 636002516 T^{2} + 183817193534771862 T^{4} - \)\(11\!\cdots\!84\)\( T^{6} + \)\(30\!\cdots\!01\)\( T^{8} )^{2} \))
$59$ (\( 1 + 921043598 T^{2} + 511116753300641401 T^{4} \))(\( ( 1 - 710599364 T^{2} + 399210125791716726 T^{4} - \)\(36\!\cdots\!64\)\( T^{6} + \)\(26\!\cdots\!01\)\( T^{8} )^{2} \))
$61$ (\( ( 1 - 844596301 T^{2} )^{2} \))(\( ( 1 - 592981876 T^{2} + 819511289079885174 T^{4} - \)\(42\!\cdots\!76\)\( T^{6} + \)\(50\!\cdots\!01\)\( T^{8} )^{2} \))
$67$ (\( 1 + 1813708382 T^{2} + 1822837804551761449 T^{4} \))(\( ( 1 - 2595461924 T^{2} + 4235124730923029142 T^{4} - \)\(47\!\cdots\!76\)\( T^{6} + \)\(33\!\cdots\!01\)\( T^{8} )^{2} \))
$71$ (\( ( 1 + 1804229351 T^{2} )^{2} \))(\( ( 1 + 6856248476 T^{2} + 18258947260812228774 T^{4} + \)\(22\!\cdots\!76\)\( T^{6} + \)\(10\!\cdots\!01\)\( T^{8} )^{2} \))
$73$ (\( ( 1 - 50402 T + 2073071593 T^{2} )^{2} \))(\( ( 1 + 47708 T + 3883557654 T^{2} + 98902099558844 T^{3} + 4297625829703557649 T^{4} )^{4} \))
$79$ (\( ( 1 + 3077056399 T^{2} )^{2} \))(\( ( 1 + 1040777788 T^{2} + 2897024027638170438 T^{4} + \)\(98\!\cdots\!88\)\( T^{6} + \)\(89\!\cdots\!01\)\( T^{8} )^{2} \))
$83$ (\( 1 + 96051518 T^{2} + 15516041187205853449 T^{4} \))(\( ( 1 - 9252333668 T^{2} + 44623630841831701206 T^{4} - \)\(14\!\cdots\!32\)\( T^{6} + \)\(24\!\cdots\!01\)\( T^{8} )^{2} \))
$89$ (\( ( 1 - 7218 T + 5584059449 T^{2} )^{2} \))(\( ( 1 - 17988 T + 11168331766 T^{2} - 100446061368612 T^{3} + 31181719929966183601 T^{4} )^{4} \))
$97$ (\( ( 1 - 85450 T + 8587340257 T^{2} )^{2} \))(\( ( 1 - 32948 T + 15595369062 T^{2} - 282935686787636 T^{3} + 73742412689492826049 T^{4} )^{4} \))
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