Properties

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

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Defining parameters

Level: \( N \) = \( 463 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 463.a (trivial)
Character field: \(\Q\)
Newforms: \( 2 \)
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

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

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(463))\) into irreducible Hecke orbits

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 \(8\) \(4\) \(14\) \(2\) \(-\)