# Properties

 Label 5.5 Level 5 Weight 5 Dimension 2 Nonzero newspaces 1 Newform subspaces 1 Sturm bound 10 Trace bound 0

## Defining parameters

 Level: $$N$$ = $$5\( 5$$ \) Weight: $$k$$ = $$5$$ Nonzero newspaces: $$1$$ Newform subspaces: $$1$$ Sturm bound: $$10$$ Trace bound: $$0$$

## Dimensions

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

Total New Old
Modular forms 6 6 0
Cusp forms 2 2 0
Eisenstein series 4 4 0

## Trace form

 $$2q - 2q^{2} - 12q^{3} + 40q^{5} + 24q^{6} - 52q^{7} - 60q^{8} + O(q^{10})$$ $$2q - 2q^{2} - 12q^{3} + 40q^{5} + 24q^{6} - 52q^{7} - 60q^{8} - 10q^{10} - 16q^{11} + 168q^{12} + 278q^{13} - 420q^{15} - 328q^{16} - 2q^{17} + 18q^{18} + 420q^{20} + 624q^{21} + 16q^{22} - 332q^{23} + 350q^{25} - 556q^{26} - 1080q^{27} - 728q^{28} + 480q^{30} + 1144q^{31} + 1288q^{32} + 96q^{33} - 260q^{35} + 252q^{36} - 502q^{37} + 360q^{38} - 2100q^{40} - 3376q^{41} - 624q^{42} + 2948q^{43} - 270q^{45} + 664q^{46} + 4948q^{47} + 1968q^{48} + 850q^{50} + 24q^{51} - 3892q^{52} - 6662q^{53} - 320q^{55} + 3120q^{56} - 2160q^{57} - 960q^{58} + 840q^{60} + 3184q^{61} - 1144q^{62} + 468q^{63} + 9730q^{65} - 192q^{66} + 1748q^{67} - 28q^{68} - 1560q^{70} - 12136q^{71} - 540q^{72} - 1582q^{73} - 9300q^{75} + 5040q^{76} + 416q^{77} + 3336q^{78} - 6560q^{80} + 11502q^{81} + 3376q^{82} + 11308q^{83} - 10q^{85} - 5896q^{86} + 5760q^{87} + 480q^{88} + 630q^{90} - 14456q^{91} + 4648q^{92} - 6864q^{93} - 5400q^{95} - 15456q^{96} - 13102q^{97} - 2098q^{98} + O(q^{100})$$

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

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
5.5.c $$\chi_{5}(2, \cdot)$$ 5.5.c.a 2 2

## Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ $$1 + 2 T + 2 T^{2} + 32 T^{3} + 256 T^{4}$$
$3$ $$1 + 12 T + 72 T^{2} + 972 T^{3} + 6561 T^{4}$$
$5$ $$1 - 40 T + 625 T^{2}$$
$7$ $$1 + 52 T + 1352 T^{2} + 124852 T^{3} + 5764801 T^{4}$$
$11$ $$( 1 + 8 T + 14641 T^{2} )^{2}$$
$13$ $$1 - 278 T + 38642 T^{2} - 7939958 T^{3} + 815730721 T^{4}$$
$17$ $$1 + 2 T + 2 T^{2} + 167042 T^{3} + 6975757441 T^{4}$$
$19$ $$1 - 228242 T^{2} + 16983563041 T^{4}$$
$23$ $$1 + 332 T + 55112 T^{2} + 92907212 T^{3} + 78310985281 T^{4}$$
$29$ $$1 - 1184162 T^{2} + 500246412961 T^{4}$$
$31$ $$( 1 - 572 T + 923521 T^{2} )^{2}$$
$37$ $$1 + 502 T + 126002 T^{2} + 940828822 T^{3} + 3512479453921 T^{4}$$
$41$ $$( 1 + 1688 T + 2825761 T^{2} )^{2}$$
$43$ $$1 - 2948 T + 4345352 T^{2} - 10078625348 T^{3} + 11688200277601 T^{4}$$
$47$ $$1 - 4948 T + 12241352 T^{2} - 24144661588 T^{3} + 23811286661761 T^{4}$$
$53$ $$1 + 6662 T + 22191122 T^{2} + 52566384422 T^{3} + 62259690411361 T^{4}$$
$59$ $$1 - 10839122 T^{2} + 146830437604321 T^{4}$$
$61$ $$( 1 - 1592 T + 13845841 T^{2} )^{2}$$
$67$ $$1 - 1748 T + 1527752 T^{2} - 35224159508 T^{3} + 406067677556641 T^{4}$$
$71$ $$( 1 + 6068 T + 25411681 T^{2} )^{2}$$
$73$ $$1 + 1582 T + 1251362 T^{2} + 44926017262 T^{3} + 806460091894081 T^{4}$$
$79$ $$1 + 5274238 T^{2} + 1517108809906561 T^{4}$$
$83$ $$1 - 11308 T + 63935432 T^{2} - 536658693868 T^{3} + 2252292232139041 T^{4}$$
$89$ $$1 - 120818882 T^{2} + 3936588805702081 T^{4}$$
$97$ $$1 + 13102 T + 85831202 T^{2} + 1159910639662 T^{3} + 7837433594376961 T^{4}$$