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

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