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Properties

Label 14.4.c
Level 14
Weight 4
Character orbit c
Rep. character \(\chi_{14}(9,\cdot)\)
Character field \(\Q(\zeta_{3})\)
Dimension 4
Newform subspaces 2
Sturm bound 8
Trace bound 2

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Defining parameters

Level: \( N \) = \( 14 = 2 \cdot 7 \)
Weight: \( k \) = \( 4 \)
Character orbit: \([\chi]\) = 14.c (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 2 \)
Sturm bound: \(8\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(14, [\chi])\).

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

Trace form

\( 4q + 6q^{3} - 8q^{4} + 2q^{5} - 16q^{6} - 48q^{7} + 28q^{9} + O(q^{10}) \) \( 4q + 6q^{3} - 8q^{4} + 2q^{5} - 16q^{6} - 48q^{7} + 28q^{9} + 32q^{10} + 22q^{11} + 24q^{12} - 8q^{13} + 104q^{14} + 76q^{15} - 32q^{16} - 110q^{17} - 48q^{18} - 142q^{19} - 16q^{20} - 2q^{21} - 368q^{22} - 62q^{23} + 32q^{24} + 120q^{25} + 272q^{26} + 396q^{27} + 120q^{28} + 440q^{29} - 104q^{30} - 98q^{31} - 250q^{33} - 32q^{34} - 434q^{35} - 224q^{36} + 242q^{37} + 264q^{38} - 284q^{39} + 128q^{40} - 1080q^{41} + 240q^{42} + 272q^{43} + 88q^{44} + 164q^{45} - 152q^{46} - 30q^{47} - 192q^{48} - 188q^{49} + 128q^{50} + 314q^{51} + 16q^{52} + 810q^{53} - 184q^{54} + 1516q^{55} - 64q^{56} - 324q^{57} - 16q^{58} - 202q^{59} - 152q^{60} + 658q^{61} - 208q^{62} + 372q^{63} + 256q^{64} - 1092q^{65} - 640q^{66} - 858q^{67} - 440q^{68} - 676q^{69} - 392q^{70} - 1760q^{71} - 192q^{72} + 18q^{73} + 528q^{74} - 296q^{75} + 1136q^{76} + 1694q^{77} + 1664q^{78} + 34q^{79} + 32q^{80} + 22q^{81} - 912q^{82} + 688q^{83} - 632q^{84} - 92q^{85} + 768q^{86} + 676q^{87} + 736q^{88} + 1890q^{89} + 800q^{90} + 640q^{91} + 496q^{92} + 190q^{93} - 744q^{94} - 914q^{95} + 128q^{96} - 4248q^{97} - 2640q^{98} - 1592q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(14, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
14.4.c.a \(2\) \(0.826\) \(\Q(\sqrt{-3}) \) None \(-2\) \(5\) \(9\) \(-28\) \(q+(-2+2\zeta_{6})q^{2}+5\zeta_{6}q^{3}-4\zeta_{6}q^{4}+\cdots\)
14.4.c.b \(2\) \(0.826\) \(\Q(\sqrt{-3}) \) None \(2\) \(1\) \(-7\) \(-20\) \(q+(2-2\zeta_{6})q^{2}+\zeta_{6}q^{3}-4\zeta_{6}q^{4}+(-7+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(14, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(14, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ (\( 1 + 2 T + 4 T^{2} \))(\( 1 - 2 T + 4 T^{2} \))
$3$ (\( 1 - 5 T - 2 T^{2} - 135 T^{3} + 729 T^{4} \))(\( 1 - T - 26 T^{2} - 27 T^{3} + 729 T^{4} \))
$5$ (\( 1 - 9 T - 44 T^{2} - 1125 T^{3} + 15625 T^{4} \))(\( 1 + 7 T - 76 T^{2} + 875 T^{3} + 15625 T^{4} \))
$7$ (\( 1 + 28 T + 343 T^{2} \))(\( 1 + 20 T + 343 T^{2} \))
$11$ (\( 1 - 57 T + 1918 T^{2} - 75867 T^{3} + 1771561 T^{4} \))(\( 1 + 35 T - 106 T^{2} + 46585 T^{3} + 1771561 T^{4} \))
$13$ (\( ( 1 + 70 T + 2197 T^{2} )^{2} \))(\( ( 1 - 66 T + 2197 T^{2} )^{2} \))
$17$ (\( 1 + 51 T - 2312 T^{2} + 250563 T^{3} + 24137569 T^{4} \))(\( 1 + 59 T - 1432 T^{2} + 289867 T^{3} + 24137569 T^{4} \))
$19$ (\( 1 + 5 T - 6834 T^{2} + 34295 T^{3} + 47045881 T^{4} \))(\( 1 + 137 T + 11910 T^{2} + 939683 T^{3} + 47045881 T^{4} \))
$23$ (\( 1 + 69 T - 7406 T^{2} + 839523 T^{3} + 148035889 T^{4} \))(\( 1 - 7 T - 12118 T^{2} - 85169 T^{3} + 148035889 T^{4} \))
$29$ (\( ( 1 - 114 T + 24389 T^{2} )^{2} \))(\( ( 1 - 106 T + 24389 T^{2} )^{2} \))
$31$ (\( 1 + 23 T - 29262 T^{2} + 685193 T^{3} + 887503681 T^{4} \))(\( 1 + 75 T - 24166 T^{2} + 2234325 T^{3} + 887503681 T^{4} \))
$37$ (\( 1 - 253 T + 13356 T^{2} - 12815209 T^{3} + 2565726409 T^{4} \))(\( 1 + 11 T - 50532 T^{2} + 557183 T^{3} + 2565726409 T^{4} \))
$41$ (\( ( 1 + 42 T + 68921 T^{2} )^{2} \))(\( ( 1 + 498 T + 68921 T^{2} )^{2} \))
$43$ (\( ( 1 + 124 T + 79507 T^{2} )^{2} \))(\( ( 1 - 260 T + 79507 T^{2} )^{2} \))
$47$ (\( 1 + 201 T - 63422 T^{2} + 20868423 T^{3} + 10779215329 T^{4} \))(\( 1 - 171 T - 74582 T^{2} - 17753733 T^{3} + 10779215329 T^{4} \))
$53$ (\( 1 - 393 T + 5572 T^{2} - 58508661 T^{3} + 22164361129 T^{4} \))(\( 1 - 417 T + 25012 T^{2} - 62081709 T^{3} + 22164361129 T^{4} \))
$59$ (\( 1 + 219 T - 157418 T^{2} + 44978001 T^{3} + 42180533641 T^{4} \))(\( 1 - 17 T - 205090 T^{2} - 3491443 T^{3} + 42180533641 T^{4} \))
$61$ (\( 1 - 709 T + 275700 T^{2} - 160929529 T^{3} + 51520374361 T^{4} \))(\( 1 + 51 T - 224380 T^{2} + 11576031 T^{3} + 51520374361 T^{4} \))
$67$ (\( 1 + 419 T - 125202 T^{2} + 126019697 T^{3} + 90458382169 T^{4} \))(\( 1 + 439 T - 108042 T^{2} + 132034957 T^{3} + 90458382169 T^{4} \))
$71$ (\( ( 1 + 96 T + 357911 T^{2} )^{2} \))(\( ( 1 + 784 T + 357911 T^{2} )^{2} \))
$73$ (\( 1 - 313 T - 291048 T^{2} - 121762321 T^{3} + 151334226289 T^{4} \))(\( 1 + 295 T - 301992 T^{2} + 114760015 T^{3} + 151334226289 T^{4} \))
$79$ (\( 1 + 461 T - 280518 T^{2} + 227290979 T^{3} + 243087455521 T^{4} \))(\( 1 - 495 T - 248014 T^{2} - 244054305 T^{3} + 243087455521 T^{4} \))
$83$ (\( ( 1 + 588 T + 571787 T^{2} )^{2} \))(\( ( 1 - 932 T + 571787 T^{2} )^{2} \))
$89$ (\( 1 - 1017 T + 329320 T^{2} - 716953473 T^{3} + 496981290961 T^{4} \))(\( 1 - 873 T + 57160 T^{2} - 615437937 T^{3} + 496981290961 T^{4} \))
$97$ (\( ( 1 + 1834 T + 912673 T^{2} )^{2} \))(\( ( 1 + 290 T + 912673 T^{2} )^{2} \))
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