Properties

Label 14.4
Level 14
Weight 4
Dimension 6
Nonzero newspaces 2
Newform subspaces 4
Sturm bound 48
Trace bound 1

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Defining parameters

Level: \( N \) = \( 14 = 2 \cdot 7 \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 4 \)
Sturm bound: \(48\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(14))\).

Total New Old
Modular forms 24 6 18
Cusp forms 12 6 6
Eisenstein series 12 0 12

Trace form

\( 6q + 12q^{3} - 24q^{5} - 36q^{6} - 48q^{7} + 42q^{9} + O(q^{10}) \) \( 6q + 12q^{3} - 24q^{5} - 36q^{6} - 48q^{7} + 42q^{9} + 36q^{10} + 42q^{11} + 48q^{12} + 66q^{13} + 132q^{14} - 12q^{15} - 150q^{17} - 168q^{18} - 60q^{19} - 120q^{20} - 72q^{21} - 216q^{22} - 294q^{23} - 48q^{24} + 210q^{25} + 348q^{26} + 576q^{27} + 120q^{28} + 576q^{29} + 168q^{30} + 210q^{31} - 570q^{33} - 408q^{34} - 420q^{35} - 168q^{36} + 42q^{37} + 108q^{38} - 252q^{39} + 144q^{40} - 792q^{41} + 324q^{42} - 516q^{43} + 168q^{44} - 78q^{45} - 168q^{46} - 18q^{47} - 96q^{48} - 90q^{49} + 24q^{50} + 1134q^{51} + 312q^{52} + 1302q^{53} - 144q^{54} + 1332q^{55} + 48q^{56} + 312q^{57} - 504q^{58} - 264q^{59} - 504q^{60} + 840q^{61} + 120q^{62} - 48q^{63} + 384q^{64} - 2016q^{65} - 384q^{66} - 2058q^{67} - 600q^{68} - 1332q^{69} - 756q^{70} - 792q^{71} - 672q^{72} - 594q^{73} + 1512q^{74} + 234q^{75} + 1464q^{76} + 2226q^{77} + 1152q^{78} + 1050q^{79} - 384q^{80} + 84q^{81} - 984q^{82} - 6q^{83} - 912q^{84} + 240q^{85} + 840q^{86} + 2304q^{87} + 1344q^{88} + 2310q^{89} + 2388q^{90} + 906q^{91} - 432q^{92} + 294q^{93} - 816q^{94} - 2058q^{95} - 192q^{96} - 4224q^{97} - 2640q^{98} - 3732q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(14))\)

We only show spaces with even parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
14.4.a \(\chi_{14}(1, \cdot)\) 14.4.a.a 1 1
14.4.a.b 1
14.4.c \(\chi_{14}(9, \cdot)\) 14.4.c.a 2 2
14.4.c.b 2

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(14))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(14)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ (\( 1 + 2 T \))(\( 1 - 2 T \))(\( 1 + 2 T + 4 T^{2} \))(\( 1 - 2 T + 4 T^{2} \))
$3$ (\( 1 - 8 T + 27 T^{2} \))(\( 1 + 2 T + 27 T^{2} \))(\( 1 - 5 T - 2 T^{2} - 135 T^{3} + 729 T^{4} \))(\( 1 - T - 26 T^{2} - 27 T^{3} + 729 T^{4} \))
$5$ (\( 1 + 14 T + 125 T^{2} \))(\( 1 + 12 T + 125 T^{2} \))(\( 1 - 9 T - 44 T^{2} - 1125 T^{3} + 15625 T^{4} \))(\( 1 + 7 T - 76 T^{2} + 875 T^{3} + 15625 T^{4} \))
$7$ (\( 1 + 7 T \))(\( 1 - 7 T \))(\( 1 + 28 T + 343 T^{2} \))(\( 1 + 20 T + 343 T^{2} \))
$11$ (\( 1 + 28 T + 1331 T^{2} \))(\( 1 - 48 T + 1331 T^{2} \))(\( 1 - 57 T + 1918 T^{2} - 75867 T^{3} + 1771561 T^{4} \))(\( 1 + 35 T - 106 T^{2} + 46585 T^{3} + 1771561 T^{4} \))
$13$ (\( 1 - 18 T + 2197 T^{2} \))(\( 1 - 56 T + 2197 T^{2} \))(\( ( 1 + 70 T + 2197 T^{2} )^{2} \))(\( ( 1 - 66 T + 2197 T^{2} )^{2} \))
$17$ (\( 1 - 74 T + 4913 T^{2} \))(\( 1 + 114 T + 4913 T^{2} \))(\( 1 + 51 T - 2312 T^{2} + 250563 T^{3} + 24137569 T^{4} \))(\( 1 + 59 T - 1432 T^{2} + 289867 T^{3} + 24137569 T^{4} \))
$19$ (\( 1 - 80 T + 6859 T^{2} \))(\( 1 - 2 T + 6859 T^{2} \))(\( 1 + 5 T - 6834 T^{2} + 34295 T^{3} + 47045881 T^{4} \))(\( 1 + 137 T + 11910 T^{2} + 939683 T^{3} + 47045881 T^{4} \))
$23$ (\( 1 + 112 T + 12167 T^{2} \))(\( 1 + 120 T + 12167 T^{2} \))(\( 1 + 69 T - 7406 T^{2} + 839523 T^{3} + 148035889 T^{4} \))(\( 1 - 7 T - 12118 T^{2} - 85169 T^{3} + 148035889 T^{4} \))
$29$ (\( 1 - 190 T + 24389 T^{2} \))(\( 1 + 54 T + 24389 T^{2} \))(\( ( 1 - 114 T + 24389 T^{2} )^{2} \))(\( ( 1 - 106 T + 24389 T^{2} )^{2} \))
$31$ (\( 1 - 72 T + 29791 T^{2} \))(\( 1 - 236 T + 29791 T^{2} \))(\( 1 + 23 T - 29262 T^{2} + 685193 T^{3} + 887503681 T^{4} \))(\( 1 + 75 T - 24166 T^{2} + 2234325 T^{3} + 887503681 T^{4} \))
$37$ (\( 1 + 346 T + 50653 T^{2} \))(\( 1 - 146 T + 50653 T^{2} \))(\( 1 - 253 T + 13356 T^{2} - 12815209 T^{3} + 2565726409 T^{4} \))(\( 1 + 11 T - 50532 T^{2} + 557183 T^{3} + 2565726409 T^{4} \))
$41$ (\( 1 - 162 T + 68921 T^{2} \))(\( 1 - 126 T + 68921 T^{2} \))(\( ( 1 + 42 T + 68921 T^{2} )^{2} \))(\( ( 1 + 498 T + 68921 T^{2} )^{2} \))
$43$ (\( 1 + 412 T + 79507 T^{2} \))(\( 1 + 376 T + 79507 T^{2} \))(\( ( 1 + 124 T + 79507 T^{2} )^{2} \))(\( ( 1 - 260 T + 79507 T^{2} )^{2} \))
$47$ (\( 1 - 24 T + 103823 T^{2} \))(\( 1 + 12 T + 103823 T^{2} \))(\( 1 + 201 T - 63422 T^{2} + 20868423 T^{3} + 10779215329 T^{4} \))(\( 1 - 171 T - 74582 T^{2} - 17753733 T^{3} + 10779215329 T^{4} \))
$53$ (\( 1 - 318 T + 148877 T^{2} \))(\( 1 - 174 T + 148877 T^{2} \))(\( 1 - 393 T + 5572 T^{2} - 58508661 T^{3} + 22164361129 T^{4} \))(\( 1 - 417 T + 25012 T^{2} - 62081709 T^{3} + 22164361129 T^{4} \))
$59$ (\( 1 + 200 T + 205379 T^{2} \))(\( 1 - 138 T + 205379 T^{2} \))(\( 1 + 219 T - 157418 T^{2} + 44978001 T^{3} + 42180533641 T^{4} \))(\( 1 - 17 T - 205090 T^{2} - 3491443 T^{3} + 42180533641 T^{4} \))
$61$ (\( 1 + 198 T + 226981 T^{2} \))(\( 1 - 380 T + 226981 T^{2} \))(\( 1 - 709 T + 275700 T^{2} - 160929529 T^{3} + 51520374361 T^{4} \))(\( 1 + 51 T - 224380 T^{2} + 11576031 T^{3} + 51520374361 T^{4} \))
$67$ (\( 1 + 716 T + 300763 T^{2} \))(\( 1 + 484 T + 300763 T^{2} \))(\( 1 + 419 T - 125202 T^{2} + 126019697 T^{3} + 90458382169 T^{4} \))(\( 1 + 439 T - 108042 T^{2} + 132034957 T^{3} + 90458382169 T^{4} \))
$71$ (\( 1 - 392 T + 357911 T^{2} \))(\( 1 - 576 T + 357911 T^{2} \))(\( ( 1 + 96 T + 357911 T^{2} )^{2} \))(\( ( 1 + 784 T + 357911 T^{2} )^{2} \))
$73$ (\( 1 - 538 T + 389017 T^{2} \))(\( 1 + 1150 T + 389017 T^{2} \))(\( 1 - 313 T - 291048 T^{2} - 121762321 T^{3} + 151334226289 T^{4} \))(\( 1 + 295 T - 301992 T^{2} + 114760015 T^{3} + 151334226289 T^{4} \))
$79$ (\( 1 - 240 T + 493039 T^{2} \))(\( 1 - 776 T + 493039 T^{2} \))(\( 1 + 461 T - 280518 T^{2} + 227290979 T^{3} + 243087455521 T^{4} \))(\( 1 - 495 T - 248014 T^{2} - 244054305 T^{3} + 243087455521 T^{4} \))
$83$ (\( 1 + 1072 T + 571787 T^{2} \))(\( 1 - 378 T + 571787 T^{2} \))(\( ( 1 + 588 T + 571787 T^{2} )^{2} \))(\( ( 1 - 932 T + 571787 T^{2} )^{2} \))
$89$ (\( 1 - 810 T + 704969 T^{2} \))(\( 1 + 390 T + 704969 T^{2} \))(\( 1 - 1017 T + 329320 T^{2} - 716953473 T^{3} + 496981290961 T^{4} \))(\( 1 - 873 T + 57160 T^{2} - 615437937 T^{3} + 496981290961 T^{4} \))
$97$ (\( 1 - 1354 T + 912673 T^{2} \))(\( 1 + 1330 T + 912673 T^{2} \))(\( ( 1 + 1834 T + 912673 T^{2} )^{2} \))(\( ( 1 + 290 T + 912673 T^{2} )^{2} \))
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