Properties

Label 14.5
Level 14
Weight 5
Dimension 8
Nonzero newspaces 2
Newform subspaces 2
Sturm bound 60
Trace bound 3

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Defining parameters

Level: \( N \) = \( 14 = 2 \cdot 7 \)
Weight: \( k \) = \( 5 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 2 \)
Sturm bound: \(60\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(\Gamma_1(14))\).

Total New Old
Modular forms 30 8 22
Cusp forms 18 8 10
Eisenstein series 12 0 12

Trace form

\( 8q - 18q^{3} + 16q^{4} + 54q^{5} - 104q^{7} - 168q^{9} + O(q^{10}) \) \( 8q - 18q^{3} + 16q^{4} + 54q^{5} - 104q^{7} - 168q^{9} - 96q^{10} + 306q^{11} + 144q^{12} - 288q^{14} - 324q^{15} + 128q^{16} + 918q^{17} + 768q^{18} + 30q^{19} + 390q^{21} - 960q^{22} - 1278q^{23} - 768q^{24} - 2872q^{25} - 1728q^{26} + 848q^{28} + 4464q^{29} + 5568q^{30} - 546q^{31} + 1062q^{33} + 2142q^{35} - 3360q^{36} - 4342q^{37} - 4320q^{38} - 4080q^{39} + 768q^{40} + 576q^{42} + 6032q^{43} + 2448q^{44} + 5724q^{45} + 6912q^{46} + 702q^{47} - 10744q^{49} - 10944q^{50} - 10818q^{51} - 384q^{52} + 8586q^{53} - 1440q^{54} - 2304q^{56} - 4596q^{57} + 7680q^{58} + 12366q^{59} + 5904q^{60} + 7686q^{61} + 9528q^{63} + 4096q^{64} - 7056q^{65} - 3456q^{66} - 6110q^{67} - 7344q^{68} - 3360q^{70} - 2736q^{71} + 6144q^{72} - 17274q^{73} - 7776q^{74} - 5220q^{75} + 8442q^{77} + 13632q^{78} + 13570q^{79} - 3456q^{80} - 33966q^{81} + 9984q^{82} + 1104q^{84} + 26892q^{85} - 21888q^{86} - 12276q^{87} - 9984q^{88} - 12474q^{89} + 8256q^{91} + 1440q^{92} + 56934q^{93} + 15168q^{94} + 45774q^{95} + 6144q^{96} + 21888q^{98} - 41040q^{99} + O(q^{100}) \)

Decomposition of \(S_{5}^{\mathrm{new}}(\Gamma_1(14))\)

We only show spaces with odd 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
14.5.b \(\chi_{14}(13, \cdot)\) 14.5.b.a 4 1
14.5.d \(\chi_{14}(3, \cdot)\) 14.5.d.a 4 2

Decomposition of \(S_{5}^{\mathrm{old}}(\Gamma_1(14))\) into lower level spaces

\( S_{5}^{\mathrm{old}}(\Gamma_1(14)) \cong \) \(S_{5}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 2}\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ (\( ( 1 - 8 T^{2} )^{2} \))(\( 1 + 8 T^{2} + 64 T^{4} \))
$3$ (\( 1 - 36 T^{2} + 13158 T^{4} - 236196 T^{6} + 43046721 T^{8} \))(\( 1 + 18 T + 201 T^{2} + 1674 T^{3} + 10836 T^{4} + 135594 T^{5} + 1318761 T^{6} + 9565938 T^{7} + 43046721 T^{8} \))
$5$ (\( 1 - 100 T^{2} + 345702 T^{4} - 39062500 T^{6} + 152587890625 T^{8} \))(\( 1 - 54 T + 2369 T^{2} - 75438 T^{3} + 2168484 T^{4} - 47148750 T^{5} + 925390625 T^{6} - 13183593750 T^{7} + 152587890625 T^{8} \))
$7$ (\( 1 + 76 T + 3654 T^{2} + 182476 T^{3} + 5764801 T^{4} \))(\( ( 1 + 14 T + 2401 T^{2} )^{2} \))
$11$ (\( ( 1 - 180 T + 27014 T^{2} - 2635380 T^{3} + 214358881 T^{4} )^{2} \))(\( 1 + 54 T - 26807 T^{2} + 23814 T^{3} + 626404692 T^{4} + 348660774 T^{5} - 5746318522967 T^{6} + 169475132342934 T^{7} + 45949729863572161 T^{8} \))
$13$ (\( 1 - 111460 T^{2} + 4736358630 T^{4} - 90921346162660 T^{6} + 665416609183179841 T^{8} \))(\( 1 - 51652 T^{2} + 2274555846 T^{4} - 42134123201092 T^{6} + 665416609183179841 T^{8} \))
$17$ (\( 1 - 217348 T^{2} + 25123879686 T^{4} - 1516166928286468 T^{6} + 48661191875666868481 T^{8} \))(\( 1 - 918 T + 493601 T^{2} - 195252174 T^{3} + 61724271876 T^{4} - 16307656824654 T^{5} + 3443240848635041 T^{6} - 534847213776920598 T^{7} + 48661191875666868481 T^{8} \))
$19$ (\( 1 - 150436 T^{2} + 9183572838 T^{4} - 2554939289635876 T^{6} + \)\(28\!\cdots\!81\)\( T^{8} \))(\( 1 - 30 T + 66617 T^{2} - 1989510 T^{3} - 12546522252 T^{4} - 259274932710 T^{5} + 1131394019102297 T^{6} - 66399447571984830 T^{7} + \)\(28\!\cdots\!81\)\( T^{8} \))
$23$ (\( ( 1 + 396 T + 525158 T^{2} + 110817036 T^{3} + 78310985281 T^{4} )^{2} \))(\( 1 + 486 T + 78265 T^{2} - 195250986 T^{3} - 119466109356 T^{4} - 54639231173226 T^{5} + 6129009263017465 T^{6} + 10650507473961876006 T^{7} + \)\(61\!\cdots\!61\)\( T^{8} \))
$29$ (\( ( 1 - 612 T + 1092326 T^{2} - 432855972 T^{3} + 500246412961 T^{4} )^{2} \))(\( ( 1 - 1620 T + 2066054 T^{2} - 1145795220 T^{3} + 500246412961 T^{4} )^{2} \))
$31$ (\( 1 - 1703428 T^{2} + 1577900136966 T^{4} - 1452838474126047748 T^{6} + \)\(72\!\cdots\!81\)\( T^{8} \))(\( 1 + 546 T + 1193657 T^{2} + 597479610 T^{3} + 436340752596 T^{4} + 551784966906810 T^{5} + 1018059357078711737 T^{6} + \)\(43\!\cdots\!06\)\( T^{7} + \)\(72\!\cdots\!81\)\( T^{8} \))
$37$ (\( ( 1 + 1948 T + 4603686 T^{2} + 3650865628 T^{3} + 3512479453921 T^{4} )^{2} \))(\( 1 + 446 T - 3015935 T^{2} - 237928066 T^{3} + 6449986888804 T^{4} - 445915502102626 T^{5} - 10593409721861231135 T^{6} + \)\(29\!\cdots\!26\)\( T^{7} + \)\(12\!\cdots\!41\)\( T^{8} \))
$41$ (\( 1 - 7851268 T^{2} + 31379741059206 T^{4} - 62691787933790375428 T^{6} + \)\(63\!\cdots\!41\)\( T^{8} \))(\( 1 - 9195268 T^{2} + 37043496050310 T^{4} - 73423527441728999428 T^{6} + \)\(63\!\cdots\!41\)\( T^{8} \))
$43$ (\( ( 1 - 1844 T + 6650886 T^{2} - 6304269044 T^{3} + 11688200277601 T^{4} )^{2} \))(\( ( 1 - 1172 T + 3821766 T^{2} - 4006834772 T^{3} + 11688200277601 T^{4} )^{2} \))
$47$ (\( 1 - 10858756 T^{2} + 58650967963398 T^{4} - \)\(25\!\cdots\!16\)\( T^{6} + \)\(56\!\cdots\!21\)\( T^{8} \))(\( 1 - 702 T + 7568153 T^{2} - 5197527270 T^{3} + 31807801869972 T^{4} - 25362275066400870 T^{5} + \)\(18\!\cdots\!33\)\( T^{6} - \)\(81\!\cdots\!82\)\( T^{7} + \)\(56\!\cdots\!21\)\( T^{8} \))
$53$ (\( ( 1 - 2916 T + 9386534 T^{2} - 23008642596 T^{3} + 62259690411361 T^{4} )^{2} \))(\( 1 - 2754 T - 5299967 T^{2} + 7976903166 T^{3} + 43904732373732 T^{4} + 62941602870162846 T^{5} - \)\(32\!\cdots\!87\)\( T^{6} - \)\(13\!\cdots\!14\)\( T^{7} + \)\(38\!\cdots\!21\)\( T^{8} \))
$59$ (\( 1 - 42750244 T^{2} + 750538168343526 T^{4} - \)\(62\!\cdots\!24\)\( T^{6} + \)\(21\!\cdots\!41\)\( T^{8} \))(\( 1 - 12366 T + 87438953 T^{2} - 450942278166 T^{3} + 1800614696429652 T^{4} - 5464230374699839926 T^{5} + \)\(12\!\cdots\!13\)\( T^{6} - \)\(22\!\cdots\!46\)\( T^{7} + \)\(21\!\cdots\!41\)\( T^{8} \))
$61$ (\( 1 - 28277476 T^{2} + 401277478909158 T^{4} - \)\(54\!\cdots\!56\)\( T^{6} + \)\(36\!\cdots\!61\)\( T^{8} \))(\( 1 - 7686 T + 39234641 T^{2} - 150208335774 T^{3} + 462871617507012 T^{4} - 2079760734001415934 T^{5} + \)\(75\!\cdots\!21\)\( T^{6} - \)\(20\!\cdots\!06\)\( T^{7} + \)\(36\!\cdots\!61\)\( T^{8} \))
$67$ (\( ( 1 + 524 T + 39707334 T^{2} + 10559187404 T^{3} + 406067677556641 T^{4} )^{2} \))(\( 1 + 5062 T + 1333849 T^{2} - 81053994314 T^{3} - 332413001385740 T^{4} - 1633328846954725994 T^{5} + \)\(54\!\cdots\!09\)\( T^{6} + \)\(41\!\cdots\!82\)\( T^{7} + \)\(16\!\cdots\!81\)\( T^{8} \))
$71$ (\( ( 1 + 10764 T + 70144454 T^{2} + 273531334284 T^{3} + 645753531245761 T^{4} )^{2} \))(\( ( 1 - 9396 T + 71231078 T^{2} - 238768154676 T^{3} + 645753531245761 T^{4} )^{2} \))
$73$ (\( 1 - 62983684 T^{2} + 1969418053172358 T^{4} - \)\(50\!\cdots\!04\)\( T^{6} + \)\(65\!\cdots\!61\)\( T^{8} \))(\( 1 + 17274 T + 161686097 T^{2} + 1074829823970 T^{3} + 5889761488255716 T^{4} + 30523276375087636770 T^{5} + \)\(13\!\cdots\!57\)\( T^{6} + \)\(39\!\cdots\!54\)\( T^{7} + \)\(65\!\cdots\!61\)\( T^{8} \))
$79$ (\( ( 1 - 6388 T + 73521798 T^{2} - 248813117428 T^{3} + 1517108809906561 T^{4} )^{2} \))(\( 1 - 794 T - 69869063 T^{2} + 5876126422 T^{3} + 3428515016079124 T^{4} + 228875600103140182 T^{5} - \)\(10\!\cdots\!43\)\( T^{6} - \)\(46\!\cdots\!54\)\( T^{7} + \)\(23\!\cdots\!21\)\( T^{8} \))
$83$ (\( 1 - 129024292 T^{2} + 7865129580692070 T^{4} - \)\(29\!\cdots\!72\)\( T^{6} + \)\(50\!\cdots\!81\)\( T^{8} \))(\( 1 - 153397060 T^{2} + 10369989980918982 T^{4} - \)\(34\!\cdots\!60\)\( T^{6} + \)\(50\!\cdots\!81\)\( T^{8} \))
$89$ (\( 1 - 228854020 T^{2} + 20924407354852230 T^{4} - \)\(90\!\cdots\!20\)\( T^{6} + \)\(15\!\cdots\!61\)\( T^{8} \))(\( 1 + 12474 T + 182683793 T^{2} + 1631810023074 T^{3} + 16430717819326692 T^{4} + \)\(10\!\cdots\!34\)\( T^{5} + \)\(71\!\cdots\!33\)\( T^{6} + \)\(30\!\cdots\!54\)\( T^{7} + \)\(15\!\cdots\!61\)\( T^{8} \))
$97$ (\( 1 - 150468100 T^{2} + 16842128301249030 T^{4} - \)\(11\!\cdots\!00\)\( T^{6} + \)\(61\!\cdots\!21\)\( T^{8} \))(\( 1 - 281924740 T^{2} + 35525126061727494 T^{4} - \)\(22\!\cdots\!40\)\( T^{6} + \)\(61\!\cdots\!21\)\( T^{8} \))
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