# Properties

 Label 5077.2.a Level 5077 Weight 2 Character orbit a Rep. character $$\chi_{5077}(1,\cdot)$$ Character field $$\Q$$ Dimension 422 Newform subspaces 3 Sturm bound 846 Trace bound 1

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$5077$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 5077.a (trivial) Character field: $$\Q$$ Newform subspaces: $$3$$ Sturm bound: $$846$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_0(5077))$$.

Total New Old
Modular forms 423 423 0
Cusp forms 422 422 0
Eisenstein series 1 1 0

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

$$5077$$Dim.
$$+$$$$206$$
$$-$$$$216$$

## Trace form

 $$422q - 2q^{2} + 420q^{4} - 2q^{5} + 6q^{6} - 4q^{7} + 426q^{9} + O(q^{10})$$ $$422q - 2q^{2} + 420q^{4} - 2q^{5} + 6q^{6} - 4q^{7} + 426q^{9} + 4q^{10} - 6q^{13} - 6q^{14} + 10q^{15} + 412q^{16} - 12q^{18} - 22q^{20} + 2q^{21} - 2q^{22} + 6q^{23} + 16q^{24} + 418q^{25} - 12q^{26} - 10q^{28} + 2q^{29} + 12q^{30} - 2q^{31} - 12q^{32} + 24q^{33} + 8q^{34} - 18q^{35} + 440q^{36} - 10q^{37} - 26q^{38} + 4q^{39} - 2q^{40} + 2q^{41} + 10q^{42} + 2q^{43} - 6q^{44} - 4q^{45} - 28q^{46} + 8q^{48} + 402q^{49} - 10q^{50} + 6q^{51} - 30q^{52} + 4q^{53} + 46q^{54} + 4q^{55} - 72q^{56} + 6q^{57} - 8q^{59} + 10q^{60} - 6q^{61} - 48q^{62} - 30q^{63} + 424q^{64} - 8q^{65} - 54q^{66} + 2q^{67} + 14q^{68} + 34q^{69} - 4q^{70} - 18q^{71} + 24q^{72} - 14q^{73} - 16q^{74} - 52q^{75} + 4q^{76} + 6q^{77} + 72q^{78} - 28q^{79} - 42q^{80} + 470q^{81} - 16q^{82} - 32q^{83} - 16q^{84} - 38q^{85} - 32q^{86} - 18q^{87} - 18q^{89} - 60q^{90} - 46q^{91} - 10q^{92} + 10q^{93} + 28q^{94} - 26q^{95} - 12q^{97} - 24q^{98} + 28q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_0(5077))$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces A-L signs $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$ 5077
5077.2.a.a $$1$$ $$40.540$$ $$\Q$$ None $$-2$$ $$-3$$ $$-4$$ $$-4$$ $$+$$ $$q-2q^{2}-3q^{3}+2q^{4}-4q^{5}+6q^{6}+\cdots$$
5077.2.a.b $$205$$ $$40.540$$ None $$-25$$ $$-59$$ $$-44$$ $$-30$$ $$+$$
5077.2.a.c $$216$$ $$40.540$$ None $$25$$ $$62$$ $$46$$ $$30$$ $$-$$

## Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ ($$1 + 2 T + 2 T^{2}$$)
$3$ ($$1 + 3 T + 3 T^{2}$$)
$5$ ($$1 + 4 T + 5 T^{2}$$)
$7$ ($$1 + 4 T + 7 T^{2}$$)
$11$ ($$1 + 6 T + 11 T^{2}$$)
$13$ ($$1 + 4 T + 13 T^{2}$$)
$17$ ($$1 + 4 T + 17 T^{2}$$)
$19$ ($$1 + 7 T + 19 T^{2}$$)
$23$ ($$1 + 6 T + 23 T^{2}$$)
$29$ ($$1 + 6 T + 29 T^{2}$$)
$31$ ($$1 + 2 T + 31 T^{2}$$)
$37$ ($$1 + 37 T^{2}$$)
$41$ ($$1 + 41 T^{2}$$)
$43$ ($$1 + 8 T + 43 T^{2}$$)
$47$ ($$1 + 9 T + 47 T^{2}$$)
$53$ ($$1 + 9 T + 53 T^{2}$$)
$59$ ($$1 + 11 T + 59 T^{2}$$)
$61$ ($$1 + 2 T + 61 T^{2}$$)
$67$ ($$1 + 12 T + 67 T^{2}$$)
$71$ ($$1 + 8 T + 71 T^{2}$$)
$73$ ($$1 + 14 T + 73 T^{2}$$)
$79$ ($$1 - 9 T + 79 T^{2}$$)
$83$ ($$1 + 2 T + 83 T^{2}$$)
$89$ ($$1 - 11 T + 89 T^{2}$$)
$97$ ($$1 - 6 T + 97 T^{2}$$)