Properties

Label 5.12
Level 5
Weight 12
Dimension 7
Nonzero newspaces 2
Newform subspaces 3
Sturm bound 24
Trace bound 1

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 5 \)
Weight: \( k \) = \( 12 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 3 \)
Sturm bound: \(24\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{12}(\Gamma_1(5))\).

Total New Old
Modular forms 13 9 4
Cusp forms 9 7 2
Eisenstein series 4 2 2

Trace form

\( 7q + 14q^{2} - 1012q^{3} + 6012q^{4} - 3425q^{5} + 31504q^{6} + 40344q^{7} - 346200q^{8} + 454723q^{9} + O(q^{10}) \) \( 7q + 14q^{2} - 1012q^{3} + 6012q^{4} - 3425q^{5} + 31504q^{6} + 40344q^{7} - 346200q^{8} + 454723q^{9} + 260150q^{10} - 1413316q^{11} - 1220576q^{12} + 3040218q^{13} + 1818264q^{14} + 1645700q^{15} - 5401168q^{16} - 2406346q^{17} + 2755958q^{18} + 20406740q^{19} + 10859900q^{20} - 63279336q^{21} - 105430632q^{22} + 26485848q^{23} + 275764320q^{24} + 188449375q^{25} - 419449996q^{26} - 242961400q^{27} + 179345712q^{28} + 380079610q^{29} + 117768400q^{30} - 268050976q^{31} - 476025056q^{32} - 70979744q^{33} + 584514364q^{34} + 158492400q^{35} - 772438948q^{36} - 270337326q^{37} + 928850600q^{38} - 321965704q^{39} + 181921000q^{40} + 458473294q^{41} + 1902541008q^{42} - 1129907292q^{43} - 1378140656q^{44} - 1294625525q^{45} + 3670019704q^{46} + 221408384q^{47} - 5130637952q^{48} - 5511437393q^{49} - 4484451250q^{50} + 13942147384q^{51} + 13174967064q^{52} + 493431938q^{53} - 22959047360q^{54} - 7305926100q^{55} + 8131081920q^{56} + 5021442800q^{57} + 9757106100q^{58} + 11444056220q^{59} + 10152654400q^{60} - 14725486366q^{61} - 22735073952q^{62} - 10750886232q^{63} + 3780862912q^{64} - 8608720550q^{65} - 7362926752q^{66} + 19529964204q^{67} - 1251711608q^{68} + 52825715016q^{69} + 34748023800q^{70} - 50363939096q^{71} - 63347763000q^{72} - 20102028402q^{73} + 53336626564q^{74} + 9449727500q^{75} - 53974552560q^{76} - 26504706672q^{77} + 120428573776q^{78} + 50566058960q^{79} + 48367377200q^{80} - 30124770233q^{81} - 68124845412q^{82} + 16503964428q^{83} - 104885035296q^{84} - 61874541850q^{85} - 77495824096q^{86} - 21134853400q^{87} - 33934826400q^{88} + 168774049830q^{89} + 123557259950q^{90} + 148769636064q^{91} + 232124189904q^{92} - 301987859184q^{93} - 271190537336q^{94} - 282533715500q^{95} + 299296601984q^{96} + 123413770134q^{97} + 73456940302q^{98} + 27251190476q^{99} + O(q^{100}) \)

Decomposition of \(S_{12}^{\mathrm{new}}(\Gamma_1(5))\)

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
5.12.a \(\chi_{5}(1, \cdot)\) 5.12.a.a 1 1
5.12.a.b 2
5.12.b \(\chi_{5}(4, \cdot)\) 5.12.b.a 4 1

Decomposition of \(S_{12}^{\mathrm{old}}(\Gamma_1(5))\) into lower level spaces

\( S_{12}^{\mathrm{old}}(\Gamma_1(5)) \cong \) \(S_{12}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ (\( 1 - 34 T + 2048 T^{2} \))(\( 1 + 20 T - 1240 T^{2} + 40960 T^{3} + 4194304 T^{4} \))(\( 1 - 4060 T^{2} + 10737408 T^{4} - 17028874240 T^{6} + 17592186044416 T^{8} \))
$3$ (\( 1 + 792 T + 177147 T^{2} \))(\( 1 + 220 T + 211770 T^{2} + 38972340 T^{3} + 31381059609 T^{4} \))(\( 1 - 367020 T^{2} + 85656582918 T^{4} - 11517476497695180 T^{6} + \)\(98\!\cdots\!81\)\( T^{8} \))
$5$ (\( 1 - 3125 T \))(\( ( 1 + 3125 T )^{2} \))(\( 1 + 300 T - 79531250 T^{2} + 14648437500 T^{3} + 2384185791015625 T^{4} \))
$7$ (\( 1 + 17556 T + 1977326743 T^{2} \))(\( 1 - 57900 T + 4624370450 T^{2} - 114487218419700 T^{3} + 3909821048582988049 T^{4} \))(\( 1 - 3004330300 T^{2} + 6149134474446008598 T^{4} - \)\(11\!\cdots\!00\)\( T^{6} + \)\(15\!\cdots\!01\)\( T^{8} \))
$11$ (\( 1 + 468788 T + 285311670611 T^{2} \))(\( 1 + 618176 T + 245194892966 T^{2} + 176372827291625536 T^{3} + \)\(81\!\cdots\!21\)\( T^{4} \))(\( ( 1 + 163176 T + 491510302966 T^{2} + 46556017163620536 T^{3} + \)\(81\!\cdots\!21\)\( T^{4} )^{2} \))
$13$ (\( 1 + 374042 T + 1792160394037 T^{2} \))(\( 1 - 3414260 T + 6398662197390 T^{2} - 6118901546944767620 T^{3} + \)\(32\!\cdots\!69\)\( T^{4} \))(\( 1 - 735603341140 T^{2} + \)\(27\!\cdots\!38\)\( T^{4} - \)\(23\!\cdots\!60\)\( T^{6} + \)\(10\!\cdots\!61\)\( T^{8} \))
$17$ (\( 1 + 3724286 T + 34271896307633 T^{2} \))(\( 1 - 1317940 T + 59308395866630 T^{2} - 45168303019681836020 T^{3} + \)\(11\!\cdots\!89\)\( T^{4} \))(\( 1 - 78202046986180 T^{2} + \)\(38\!\cdots\!78\)\( T^{4} - \)\(91\!\cdots\!20\)\( T^{6} + \)\(13\!\cdots\!21\)\( T^{8} \))
$19$ (\( 1 + 379460 T + 116490258898219 T^{2} \))(\( 1 - 5325320 T + 194538827137638 T^{2} - \)\(62\!\cdots\!80\)\( T^{3} + \)\(13\!\cdots\!61\)\( T^{4} \))(\( ( 1 - 7730440 T + 149933775923238 T^{2} - \)\(90\!\cdots\!60\)\( T^{3} + \)\(13\!\cdots\!61\)\( T^{4} )^{2} \))
$23$ (\( 1 + 32458092 T + 952809757913927 T^{2} \))(\( 1 - 58943940 T + 2773540471931410 T^{2} - \)\(56\!\cdots\!80\)\( T^{3} + \)\(90\!\cdots\!29\)\( T^{4} \))(\( 1 - 1406189031164860 T^{2} + \)\(99\!\cdots\!58\)\( T^{4} - \)\(12\!\cdots\!40\)\( T^{6} + \)\(82\!\cdots\!41\)\( T^{8} \))
$29$ (\( 1 - 69696710 T + 12200509765705829 T^{2} \))(\( 1 - 94140380 T + 23426350431097358 T^{2} - \)\(11\!\cdots\!20\)\( T^{3} + \)\(14\!\cdots\!41\)\( T^{4} \))(\( ( 1 - 108121260 T + 27294876383478958 T^{2} - \)\(13\!\cdots\!40\)\( T^{3} + \)\(14\!\cdots\!41\)\( T^{4} )^{2} \))
$31$ (\( 1 - 171448632 T + 25408476896404831 T^{2} \))(\( 1 - 244543464 T + 34393316207729486 T^{2} - \)\(62\!\cdots\!84\)\( T^{3} + \)\(64\!\cdots\!61\)\( T^{4} \))(\( ( 1 + 342021536 T + 69944161934199486 T^{2} + \)\(86\!\cdots\!16\)\( T^{3} + \)\(64\!\cdots\!61\)\( T^{4} )^{2} \))
$37$ (\( 1 + 291340546 T + 177917621779460413 T^{2} \))(\( 1 - 21003220 T + 137126715218410590 T^{2} - \)\(37\!\cdots\!60\)\( T^{3} + \)\(31\!\cdots\!69\)\( T^{4} \))(\( 1 - 709399019409252340 T^{2} + \)\(18\!\cdots\!38\)\( T^{4} - \)\(22\!\cdots\!60\)\( T^{6} + \)\(10\!\cdots\!61\)\( T^{8} \))
$41$ (\( 1 - 191343242 T + 550329031716248441 T^{2} \))(\( 1 + 745743316 T + 929792912462405846 T^{2} + \)\(41\!\cdots\!56\)\( T^{3} + \)\(30\!\cdots\!81\)\( T^{4} \))(\( ( 1 - 506436684 T + 842443730768515846 T^{2} - \)\(27\!\cdots\!44\)\( T^{3} + \)\(30\!\cdots\!81\)\( T^{4} )^{2} \))
$43$ (\( 1 + 1759857392 T + 929293739471222707 T^{2} \))(\( 1 - 629950100 T + 1840945003918927050 T^{2} - \)\(58\!\cdots\!00\)\( T^{3} + \)\(86\!\cdots\!49\)\( T^{4} \))(\( 1 - 2973974160400621900 T^{2} + \)\(39\!\cdots\!98\)\( T^{4} - \)\(25\!\cdots\!00\)\( T^{6} + \)\(74\!\cdots\!01\)\( T^{8} \))
$47$ (\( 1 - 1623469924 T + 2472159215084012303 T^{2} \))(\( 1 + 1402061540 T + 5181805952108806370 T^{2} + \)\(34\!\cdots\!20\)\( T^{3} + \)\(61\!\cdots\!09\)\( T^{4} \))(\( 1 - 5406315144808526620 T^{2} + \)\(15\!\cdots\!18\)\( T^{4} - \)\(33\!\cdots\!80\)\( T^{6} + \)\(37\!\cdots\!81\)\( T^{8} \))
$53$ (\( 1 + 644888642 T + 9269035929372191597 T^{2} \))(\( 1 - 1138320580 T - 2203723231625575330 T^{2} - \)\(10\!\cdots\!60\)\( T^{3} + \)\(85\!\cdots\!09\)\( T^{4} \))(\( 1 - 17888513867443911220 T^{2} + \)\(22\!\cdots\!18\)\( T^{4} - \)\(15\!\cdots\!80\)\( T^{6} + \)\(73\!\cdots\!81\)\( T^{8} \))
$59$ (\( 1 - 925569220 T + 30155888444737842659 T^{2} \))(\( 1 - 7317515560 T + 55027608950440780118 T^{2} - \)\(22\!\cdots\!40\)\( T^{3} + \)\(90\!\cdots\!81\)\( T^{4} \))(\( ( 1 - 1600485720 T + 59001356645161802518 T^{2} - \)\(48\!\cdots\!80\)\( T^{3} + \)\(90\!\cdots\!81\)\( T^{4} )^{2} \))
$61$ (\( 1 + 10898589338 T + 43513917611435838661 T^{2} \))(\( 1 + 1516425676 T + 85869525433683691566 T^{2} + \)\(65\!\cdots\!36\)\( T^{3} + \)\(18\!\cdots\!21\)\( T^{4} \))(\( ( 1 + 1155235676 T + 42416047619495221566 T^{2} + \)\(50\!\cdots\!36\)\( T^{3} + \)\(18\!\cdots\!21\)\( T^{4} )^{2} \))
$67$ (\( 1 - 3795674064 T + \)\(12\!\cdots\!83\)\( T^{2} \))(\( 1 - 15734290140 T + \)\(30\!\cdots\!30\)\( T^{2} - \)\(19\!\cdots\!20\)\( T^{3} + \)\(14\!\cdots\!89\)\( T^{4} \))(\( 1 - \)\(48\!\cdots\!80\)\( T^{2} + \)\(87\!\cdots\!78\)\( T^{4} - \)\(71\!\cdots\!20\)\( T^{6} + \)\(22\!\cdots\!21\)\( T^{8} \))
$71$ (\( 1 + 22966943728 T + \)\(23\!\cdots\!71\)\( T^{2} \))(\( 1 - 32938471544 T + \)\(73\!\cdots\!26\)\( T^{2} - \)\(76\!\cdots\!24\)\( T^{3} + \)\(53\!\cdots\!41\)\( T^{4} \))(\( ( 1 + 30167733456 T + \)\(58\!\cdots\!26\)\( T^{2} + \)\(69\!\cdots\!76\)\( T^{3} + \)\(53\!\cdots\!41\)\( T^{4} )^{2} \))
$73$ (\( 1 - 9880820458 T + \)\(31\!\cdots\!77\)\( T^{2} \))(\( 1 + 29982848860 T + \)\(78\!\cdots\!10\)\( T^{2} + \)\(94\!\cdots\!20\)\( T^{3} + \)\(98\!\cdots\!29\)\( T^{4} \))(\( 1 - \)\(81\!\cdots\!60\)\( T^{2} + \)\(34\!\cdots\!58\)\( T^{4} - \)\(80\!\cdots\!40\)\( T^{6} + \)\(96\!\cdots\!41\)\( T^{8} \))
$79$ (\( 1 + 20768886240 T + \)\(74\!\cdots\!79\)\( T^{2} \))(\( 1 + 3302823120 T + \)\(12\!\cdots\!58\)\( T^{2} + \)\(24\!\cdots\!80\)\( T^{3} + \)\(55\!\cdots\!41\)\( T^{4} \))(\( ( 1 - 37318884160 T + \)\(11\!\cdots\!58\)\( T^{2} - \)\(27\!\cdots\!40\)\( T^{3} + \)\(55\!\cdots\!41\)\( T^{4} )^{2} \))
$83$ (\( 1 - 3204862008 T + \)\(12\!\cdots\!67\)\( T^{2} \))(\( 1 - 13299102420 T + \)\(18\!\cdots\!30\)\( T^{2} - \)\(17\!\cdots\!40\)\( T^{3} + \)\(16\!\cdots\!89\)\( T^{4} \))(\( 1 - \)\(35\!\cdots\!80\)\( T^{2} + \)\(62\!\cdots\!78\)\( T^{4} - \)\(59\!\cdots\!20\)\( T^{6} + \)\(27\!\cdots\!21\)\( T^{8} \))
$89$ (\( 1 - 63176321130 T + \)\(27\!\cdots\!89\)\( T^{2} \))(\( 1 + 12674770860 T + \)\(43\!\cdots\!78\)\( T^{2} + \)\(35\!\cdots\!40\)\( T^{3} + \)\(77\!\cdots\!21\)\( T^{4} \))(\( ( 1 - 59136249780 T + \)\(53\!\cdots\!78\)\( T^{2} - \)\(16\!\cdots\!20\)\( T^{3} + \)\(77\!\cdots\!21\)\( T^{4} )^{2} \))
$97$ (\( 1 - 126494473874 T + \)\(71\!\cdots\!53\)\( T^{2} \))(\( 1 + 3080703740 T + \)\(18\!\cdots\!70\)\( T^{2} + \)\(22\!\cdots\!20\)\( T^{3} + \)\(51\!\cdots\!09\)\( T^{4} \))(\( 1 + \)\(10\!\cdots\!80\)\( T^{2} + \)\(10\!\cdots\!18\)\( T^{4} + \)\(53\!\cdots\!20\)\( T^{6} + \)\(26\!\cdots\!81\)\( T^{8} \))
show more
show less