# Properties

 Label 463.2.a Level 463 Weight 2 Character orbit a Rep. character $$\chi_{463}(1,\cdot)$$ Character field $$\Q$$ Dimension 38 Newform subspaces 2 Sturm bound 77 Trace bound 1

# Related objects

## Defining parameters

 Level: $$N$$ = $$463$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 463.a (trivial) Character field: $$\Q$$ Newform subspaces: $$2$$ Sturm bound: $$77$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_0(463))$$.

Total New Old
Modular forms 39 39 0
Cusp forms 38 38 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.

$$463$$Dim.
$$+$$$$16$$
$$-$$$$22$$

## Trace form

 $$38q - q^{2} - 2q^{3} + 37q^{4} - 2q^{5} - 6q^{6} - 8q^{7} - 3q^{8} + 38q^{9} + O(q^{10})$$ $$38q - q^{2} - 2q^{3} + 37q^{4} - 2q^{5} - 6q^{6} - 8q^{7} - 3q^{8} + 38q^{9} + 6q^{10} - 4q^{11} - 4q^{12} - 4q^{13} - 10q^{15} + 39q^{16} + 10q^{17} - 11q^{18} - 4q^{19} - 8q^{20} - 10q^{21} - 4q^{22} - 16q^{23} - 16q^{24} + 34q^{25} + 16q^{26} - 26q^{27} - 24q^{28} - 2q^{29} - 8q^{30} - 7q^{32} + 10q^{33} + 26q^{34} + 4q^{35} + 37q^{36} - 2q^{38} - 10q^{39} + 34q^{40} - 8q^{41} - 4q^{42} + 8q^{43} - 8q^{44} - 20q^{45} + 2q^{46} - 4q^{47} - 16q^{48} - 2q^{49} - 47q^{50} + 14q^{51} - 40q^{52} - 10q^{53} - 24q^{54} - 34q^{55} - 34q^{56} - 32q^{57} - 34q^{58} + 14q^{59} - 66q^{60} - 6q^{61} + 2q^{62} - 20q^{63} + 33q^{64} + 26q^{65} + 34q^{66} - 8q^{67} + 12q^{68} - 10q^{69} + 40q^{70} + 18q^{71} - 11q^{72} + 10q^{73} - 2q^{74} - 4q^{75} + 6q^{76} - 14q^{77} + 10q^{78} - 14q^{79} - 4q^{80} + 30q^{81} + 46q^{82} + 8q^{83} - 10q^{84} + 24q^{85} - 64q^{86} - 40q^{87} - 28q^{88} - 24q^{89} + 32q^{90} - 38q^{91} - 10q^{92} + 10q^{93} + 2q^{94} + 70q^{95} - 10q^{96} - 20q^{97} + 85q^{98} - 28q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_0(463))$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces A-L signs $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$ 463
463.2.a.a $$16$$ $$3.697$$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$-9$$ $$-6$$ $$-16$$ $$-10$$ $$+$$ $$q+(-1+\beta _{1})q^{2}-\beta _{6}q^{3}+(1-\beta _{1}-\beta _{12}+\cdots)q^{4}+\cdots$$
463.2.a.b $$22$$ $$3.697$$ None $$8$$ $$4$$ $$14$$ $$2$$ $$-$$