Properties

Label 14.5.d
Level 14
Weight 5
Character orbit d
Rep. character \(\chi_{14}(3,\cdot)\)
Character field \(\Q(\zeta_{6})\)
Dimension 4
Newform subspaces 1
Sturm bound 10
Trace bound 0

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Defining parameters

Level: \( N \) \(=\) \( 14 = 2 \cdot 7 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 14.d (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(10\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(14, [\chi])\).

Total New Old
Modular forms 20 4 16
Cusp forms 12 4 8
Eisenstein series 8 0 8

Trace form

\( 4q - 18q^{3} - 16q^{4} + 54q^{5} - 28q^{7} + 84q^{9} + O(q^{10}) \) \( 4q - 18q^{3} - 16q^{4} + 54q^{5} - 28q^{7} + 84q^{9} - 96q^{10} - 54q^{11} + 144q^{12} - 708q^{15} - 128q^{16} + 918q^{17} + 576q^{18} + 30q^{19} - 378q^{21} + 192q^{22} - 486q^{23} - 768q^{24} - 572q^{25} - 1728q^{26} + 1456q^{28} + 3240q^{29} + 1152q^{30} - 546q^{31} + 1062q^{33} - 1890q^{35} - 1344q^{36} - 446q^{37} - 4320q^{38} - 3312q^{39} + 768q^{40} + 5376q^{42} + 2344q^{43} - 432q^{44} + 5724q^{45} + 3840q^{46} + 702q^{47} - 9212q^{49} - 3456q^{50} + 318q^{51} - 384q^{52} + 2754q^{53} - 1440q^{54} - 17460q^{57} + 384q^{58} + 12366q^{59} + 2832q^{60} + 7686q^{61} + 6468q^{63} + 2048q^{64} - 3024q^{65} - 3456q^{66} - 5062q^{67} - 7344q^{68} - 2016q^{70} + 18792q^{71} + 4608q^{72} - 17274q^{73} - 4320q^{74} - 5220q^{75} + 4914q^{77} + 8832q^{78} + 794q^{79} - 3456q^{80} - 4338q^{81} + 9984q^{82} - 5040q^{84} + 10380q^{85} - 10368q^{86} - 12276q^{87} - 768q^{88} - 12474q^{89} + 2688q^{91} + 7776q^{92} + 18918q^{93} + 15168q^{94} + 8910q^{95} + 6144q^{96} - 11448q^{99} + O(q^{100}) \)

Decomposition of \(S_{5}^{\mathrm{new}}(14, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
14.5.d.a \(4\) \(1.447\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(-18\) \(54\) \(-28\) \(q+\beta _{1}q^{2}+(-6+2\beta _{1}-3\beta _{2}-2\beta _{3})q^{3}+\cdots\)

Decomposition of \(S_{5}^{\mathrm{old}}(14, [\chi])\) into lower level spaces

\( S_{5}^{\mathrm{old}}(14, [\chi]) \cong \) \(S_{5}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 2}\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( 1 + 8 T^{2} + 64 T^{4} \)
$3$ \( 1 + 18 T + 201 T^{2} + 1674 T^{3} + 10836 T^{4} + 135594 T^{5} + 1318761 T^{6} + 9565938 T^{7} + 43046721 T^{8} \)
$5$ \( 1 - 54 T + 2369 T^{2} - 75438 T^{3} + 2168484 T^{4} - 47148750 T^{5} + 925390625 T^{6} - 13183593750 T^{7} + 152587890625 T^{8} \)
$7$ \( ( 1 + 14 T + 2401 T^{2} )^{2} \)
$11$ \( 1 + 54 T - 26807 T^{2} + 23814 T^{3} + 626404692 T^{4} + 348660774 T^{5} - 5746318522967 T^{6} + 169475132342934 T^{7} + 45949729863572161 T^{8} \)
$13$ \( 1 - 51652 T^{2} + 2274555846 T^{4} - 42134123201092 T^{6} + 665416609183179841 T^{8} \)
$17$ \( 1 - 918 T + 493601 T^{2} - 195252174 T^{3} + 61724271876 T^{4} - 16307656824654 T^{5} + 3443240848635041 T^{6} - 534847213776920598 T^{7} + 48661191875666868481 T^{8} \)
$19$ \( 1 - 30 T + 66617 T^{2} - 1989510 T^{3} - 12546522252 T^{4} - 259274932710 T^{5} + 1131394019102297 T^{6} - 66399447571984830 T^{7} + \)\(28\!\cdots\!81\)\( T^{8} \)
$23$ \( 1 + 486 T + 78265 T^{2} - 195250986 T^{3} - 119466109356 T^{4} - 54639231173226 T^{5} + 6129009263017465 T^{6} + 10650507473961876006 T^{7} + \)\(61\!\cdots\!61\)\( T^{8} \)
$29$ \( ( 1 - 1620 T + 2066054 T^{2} - 1145795220 T^{3} + 500246412961 T^{4} )^{2} \)
$31$ \( 1 + 546 T + 1193657 T^{2} + 597479610 T^{3} + 436340752596 T^{4} + 551784966906810 T^{5} + 1018059357078711737 T^{6} + \)\(43\!\cdots\!06\)\( T^{7} + \)\(72\!\cdots\!81\)\( T^{8} \)
$37$ \( 1 + 446 T - 3015935 T^{2} - 237928066 T^{3} + 6449986888804 T^{4} - 445915502102626 T^{5} - 10593409721861231135 T^{6} + \)\(29\!\cdots\!26\)\( T^{7} + \)\(12\!\cdots\!41\)\( T^{8} \)
$41$ \( 1 - 9195268 T^{2} + 37043496050310 T^{4} - 73423527441728999428 T^{6} + \)\(63\!\cdots\!41\)\( T^{8} \)
$43$ \( ( 1 - 1172 T + 3821766 T^{2} - 4006834772 T^{3} + 11688200277601 T^{4} )^{2} \)
$47$ \( 1 - 702 T + 7568153 T^{2} - 5197527270 T^{3} + 31807801869972 T^{4} - 25362275066400870 T^{5} + \)\(18\!\cdots\!33\)\( T^{6} - \)\(81\!\cdots\!82\)\( T^{7} + \)\(56\!\cdots\!21\)\( T^{8} \)
$53$ \( 1 - 2754 T - 5299967 T^{2} + 7976903166 T^{3} + 43904732373732 T^{4} + 62941602870162846 T^{5} - \)\(32\!\cdots\!87\)\( T^{6} - \)\(13\!\cdots\!14\)\( T^{7} + \)\(38\!\cdots\!21\)\( T^{8} \)
$59$ \( 1 - 12366 T + 87438953 T^{2} - 450942278166 T^{3} + 1800614696429652 T^{4} - 5464230374699839926 T^{5} + \)\(12\!\cdots\!13\)\( T^{6} - \)\(22\!\cdots\!46\)\( T^{7} + \)\(21\!\cdots\!41\)\( T^{8} \)
$61$ \( 1 - 7686 T + 39234641 T^{2} - 150208335774 T^{3} + 462871617507012 T^{4} - 2079760734001415934 T^{5} + \)\(75\!\cdots\!21\)\( T^{6} - \)\(20\!\cdots\!06\)\( T^{7} + \)\(36\!\cdots\!61\)\( T^{8} \)
$67$ \( 1 + 5062 T + 1333849 T^{2} - 81053994314 T^{3} - 332413001385740 T^{4} - 1633328846954725994 T^{5} + \)\(54\!\cdots\!09\)\( T^{6} + \)\(41\!\cdots\!82\)\( T^{7} + \)\(16\!\cdots\!81\)\( T^{8} \)
$71$ \( ( 1 - 9396 T + 71231078 T^{2} - 238768154676 T^{3} + 645753531245761 T^{4} )^{2} \)
$73$ \( 1 + 17274 T + 161686097 T^{2} + 1074829823970 T^{3} + 5889761488255716 T^{4} + 30523276375087636770 T^{5} + \)\(13\!\cdots\!57\)\( T^{6} + \)\(39\!\cdots\!54\)\( T^{7} + \)\(65\!\cdots\!61\)\( T^{8} \)
$79$ \( 1 - 794 T - 69869063 T^{2} + 5876126422 T^{3} + 3428515016079124 T^{4} + 228875600103140182 T^{5} - \)\(10\!\cdots\!43\)\( T^{6} - \)\(46\!\cdots\!54\)\( T^{7} + \)\(23\!\cdots\!21\)\( T^{8} \)
$83$ \( 1 - 153397060 T^{2} + 10369989980918982 T^{4} - \)\(34\!\cdots\!60\)\( T^{6} + \)\(50\!\cdots\!81\)\( T^{8} \)
$89$ \( 1 + 12474 T + 182683793 T^{2} + 1631810023074 T^{3} + 16430717819326692 T^{4} + \)\(10\!\cdots\!34\)\( T^{5} + \)\(71\!\cdots\!33\)\( T^{6} + \)\(30\!\cdots\!54\)\( T^{7} + \)\(15\!\cdots\!61\)\( T^{8} \)
$97$ \( 1 - 281924740 T^{2} + 35525126061727494 T^{4} - \)\(22\!\cdots\!40\)\( T^{6} + \)\(61\!\cdots\!21\)\( T^{8} \)
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