# Properties

 Label 5.4.a Level 5 Weight 4 Character orbit a Rep. character $$\chi_{5}(1,\cdot)$$ Character field $$\Q$$ Dimension 1 Newform subspaces 1 Sturm bound 2 Trace bound 0

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$5$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 5.a (trivial) Character field: $$\Q$$ Newform subspaces: $$1$$ Sturm bound: $$2$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(\Gamma_0(5))$$.

Total New Old
Modular forms 3 1 2
Cusp forms 1 1 0
Eisenstein series 2 0 2

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

$$5$$Dim.
$$+$$$$1$$

## Trace form

 $$q - 4q^{2} + 2q^{3} + 8q^{4} - 5q^{5} - 8q^{6} + 6q^{7} - 23q^{9} + O(q^{10})$$ $$q - 4q^{2} + 2q^{3} + 8q^{4} - 5q^{5} - 8q^{6} + 6q^{7} - 23q^{9} + 20q^{10} + 32q^{11} + 16q^{12} - 38q^{13} - 24q^{14} - 10q^{15} - 64q^{16} + 26q^{17} + 92q^{18} + 100q^{19} - 40q^{20} + 12q^{21} - 128q^{22} - 78q^{23} + 25q^{25} + 152q^{26} - 100q^{27} + 48q^{28} - 50q^{29} + 40q^{30} - 108q^{31} + 256q^{32} + 64q^{33} - 104q^{34} - 30q^{35} - 184q^{36} + 266q^{37} - 400q^{38} - 76q^{39} + 22q^{41} - 48q^{42} + 442q^{43} + 256q^{44} + 115q^{45} + 312q^{46} - 514q^{47} - 128q^{48} - 307q^{49} - 100q^{50} + 52q^{51} - 304q^{52} + 2q^{53} + 400q^{54} - 160q^{55} + 200q^{57} + 200q^{58} + 500q^{59} - 80q^{60} - 518q^{61} + 432q^{62} - 138q^{63} - 512q^{64} + 190q^{65} - 256q^{66} + 126q^{67} + 208q^{68} - 156q^{69} + 120q^{70} + 412q^{71} - 878q^{73} - 1064q^{74} + 50q^{75} + 800q^{76} + 192q^{77} + 304q^{78} + 600q^{79} + 320q^{80} + 421q^{81} - 88q^{82} + 282q^{83} + 96q^{84} - 130q^{85} - 1768q^{86} - 100q^{87} - 150q^{89} - 460q^{90} - 228q^{91} - 624q^{92} - 216q^{93} + 2056q^{94} - 500q^{95} + 512q^{96} + 386q^{97} + 1228q^{98} - 736q^{99} + O(q^{100})$$

## Decomposition of $$S_{4}^{\mathrm{new}}(\Gamma_0(5))$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces A-L signs $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$ 5
5.4.a.a $$1$$ $$0.295$$ $$\Q$$ None $$-4$$ $$2$$ $$-5$$ $$6$$ $$+$$ $$q-4q^{2}+2q^{3}+8q^{4}-5q^{5}-8q^{6}+\cdots$$

## Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ $$1 + 4 T + 8 T^{2}$$
$3$ $$1 - 2 T + 27 T^{2}$$
$5$ $$1 + 5 T$$
$7$ $$1 - 6 T + 343 T^{2}$$
$11$ $$1 - 32 T + 1331 T^{2}$$
$13$ $$1 + 38 T + 2197 T^{2}$$
$17$ $$1 - 26 T + 4913 T^{2}$$
$19$ $$1 - 100 T + 6859 T^{2}$$
$23$ $$1 + 78 T + 12167 T^{2}$$
$29$ $$1 + 50 T + 24389 T^{2}$$
$31$ $$1 + 108 T + 29791 T^{2}$$
$37$ $$1 - 266 T + 50653 T^{2}$$
$41$ $$1 - 22 T + 68921 T^{2}$$
$43$ $$1 - 442 T + 79507 T^{2}$$
$47$ $$1 + 514 T + 103823 T^{2}$$
$53$ $$1 - 2 T + 148877 T^{2}$$
$59$ $$1 - 500 T + 205379 T^{2}$$
$61$ $$1 + 518 T + 226981 T^{2}$$
$67$ $$1 - 126 T + 300763 T^{2}$$
$71$ $$1 - 412 T + 357911 T^{2}$$
$73$ $$1 + 878 T + 389017 T^{2}$$
$79$ $$1 - 600 T + 493039 T^{2}$$
$83$ $$1 - 282 T + 571787 T^{2}$$
$89$ $$1 + 150 T + 704969 T^{2}$$
$97$ $$1 - 386 T + 912673 T^{2}$$