Properties

Label 5.6
Level 5
Weight 6
Dimension 3
Nonzero newspaces 2
Newform subspaces 2
Sturm bound 12
Trace bound 1

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Defining parameters

Level: \( N \) = \( 5\( 5 \) \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 2 \)
Sturm bound: \(12\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(5))\).

Total New Old
Modular forms 7 5 2
Cusp forms 3 3 0
Eisenstein series 4 2 2

Trace form

\( 3q + 2q^{2} - 4q^{3} - 52q^{4} - 65q^{5} + 256q^{6} + 192q^{7} - 120q^{8} - 533q^{9} + O(q^{10}) \) \( 3q + 2q^{2} - 4q^{3} - 52q^{4} - 65q^{5} + 256q^{6} + 192q^{7} - 120q^{8} - 533q^{9} - 390q^{10} + 356q^{11} + 112q^{12} + 286q^{13} + 1176q^{14} + 1220q^{15} - 1872q^{16} - 1678q^{17} - 454q^{18} + 620q^{19} + 380q^{20} - 3144q^{21} - 296q^{22} + 2976q^{23} + 5760q^{24} + 2475q^{25} + 2156q^{26} + 1880q^{27} - 5376q^{28} - 17270q^{29} - 12080q^{30} + 11056q^{31} + 5152q^{32} + 592q^{33} + 5796q^{34} + 8760q^{35} + 10028q^{36} + 182q^{37} + 2120q^{38} - 5896q^{39} - 11800q^{40} - 9794q^{41} - 1536q^{42} - 1244q^{43} - 1904q^{44} + 8095q^{45} - 26344q^{46} - 12088q^{47} - 2624q^{48} + 46543q^{49} + 40850q^{50} - 20744q^{51} - 8008q^{52} + 23846q^{53} + 27520q^{54} - 26380q^{55} - 7200q^{56} - 4240q^{57} - 6820q^{58} - 69340q^{59} - 13040q^{60} + 20906q^{61} - 4896q^{62} - 43584q^{63} - 36672q^{64} + 15070q^{65} + 67712q^{66} + 60972q^{67} + 46984q^{68} + 84984q^{69} - 26040q^{70} + 74056q^{71} + 27240q^{72} - 38774q^{73} - 184964q^{74} - 121300q^{75} - 24400q^{76} - 28416q^{77} - 2288q^{78} + 70480q^{79} + 130160q^{80} - 97997q^{81} - 18796q^{82} + 16716q^{83} + 50016q^{84} + 3810q^{85} + 3056q^{86} + 13640q^{87} + 17760q^{88} + 81390q^{89} + 55970q^{90} + 40656q^{91} - 83328q^{92} + 9792q^{93} + 115656q^{94} + 46300q^{95} - 185344q^{96} - 119038q^{97} + 40114q^{98} - 43516q^{99} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(5))\)

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
5.6.a \(\chi_{5}(1, \cdot)\) 5.6.a.a 1 1
5.6.b \(\chi_{5}(4, \cdot)\) 5.6.b.a 2 1

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ (\( 1 - 2 T + 32 T^{2} \))(\( 1 - 20 T^{2} + 1024 T^{4} \))
$3$ (\( 1 + 4 T + 243 T^{2} \))(\( ( 1 - 24 T + 243 T^{2} )( 1 + 24 T + 243 T^{2} ) \))
$5$ (\( 1 - 25 T \))(\( 1 + 90 T + 3125 T^{2} \))
$7$ (\( 1 - 192 T + 16807 T^{2} \))(\( 1 - 30050 T^{2} + 282475249 T^{4} \))
$11$ (\( 1 + 148 T + 161051 T^{2} \))(\( ( 1 - 252 T + 161051 T^{2} )^{2} \))
$13$ (\( 1 - 286 T + 371293 T^{2} \))(\( 1 - 728330 T^{2} + 137858491849 T^{4} \))
$17$ (\( 1 + 1678 T + 1419857 T^{2} \))(\( 1 - 2363810 T^{2} + 2015993900449 T^{4} \))
$19$ (\( 1 - 1060 T + 2476099 T^{2} \))(\( ( 1 + 220 T + 2476099 T^{2} )^{2} \))
$23$ (\( 1 - 2976 T + 6436343 T^{2} \))(\( 1 - 6946370 T^{2} + 41426511213649 T^{4} \))
$29$ (\( 1 + 3410 T + 20511149 T^{2} \))(\( ( 1 + 6930 T + 20511149 T^{2} )^{2} \))
$31$ (\( 1 + 2448 T + 28629151 T^{2} \))(\( ( 1 - 6752 T + 28629151 T^{2} )^{2} \))
$37$ (\( 1 - 182 T + 69343957 T^{2} \))(\( 1 + 56462470 T^{2} + 4808584372417849 T^{4} \))
$41$ (\( 1 + 9398 T + 115856201 T^{2} \))(\( ( 1 + 198 T + 115856201 T^{2} )^{2} \))
$43$ (\( 1 + 1244 T + 147008443 T^{2} \))(\( 1 - 293842250 T^{2} + 21611482313284249 T^{4} \))
$47$ (\( 1 + 12088 T + 229345007 T^{2} \))(\( 1 - 347593490 T^{2} + 52599132235830049 T^{4} \))
$53$ (\( 1 - 23846 T + 418195493 T^{2} \))(\( 1 - 802472090 T^{2} + 174887470365513049 T^{4} \))
$59$ (\( 1 + 20020 T + 714924299 T^{2} \))(\( ( 1 + 24660 T + 714924299 T^{2} )^{2} \))
$61$ (\( 1 - 32302 T + 844596301 T^{2} \))(\( ( 1 + 5698 T + 844596301 T^{2} )^{2} \))
$67$ (\( 1 - 60972 T + 1350125107 T^{2} \))(\( 1 - 795787610 T^{2} + 1822837804551761449 T^{4} \))
$71$ (\( 1 + 32648 T + 1804229351 T^{2} \))(\( ( 1 - 53352 T + 1804229351 T^{2} )^{2} \))
$73$ (\( 1 + 38774 T + 2073071593 T^{2} \))(\( 1 + 883886830 T^{2} + 4297625829703557649 T^{4} \))
$79$ (\( 1 + 33360 T + 3077056399 T^{2} \))(\( ( 1 - 51920 T + 3077056399 T^{2} )^{2} \))
$83$ (\( 1 - 16716 T + 3939040643 T^{2} \))(\( 1 - 4053674810 T^{2} + 15516041187205853449 T^{4} \))
$89$ (\( 1 - 101370 T + 5584059449 T^{2} \))(\( ( 1 + 9990 T + 5584059449 T^{2} )^{2} \))
$97$ (\( 1 + 119038 T + 8587340257 T^{2} \))(\( 1 - 6923133890 T^{2} + 73742412689492826049 T^{4} \))
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