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Properties

Label 463.2.a
Level $463$
Weight $2$
Character orbit 463.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 and the Fricke involution.

\(463\)Dim
\(+\)\(16\)
\(-\)\(22\)

Trace form

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

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 463
463.2.a.a 463.a 1.a $16$ $3.697$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(-9\) \(-6\) \(-16\) \(-10\) $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}-\beta _{6}q^{3}+(1-\beta _{1}-\beta _{12}+\cdots)q^{4}+\cdots\)
463.2.a.b 463.a 1.a $22$ $3.697$ None \(8\) \(4\) \(14\) \(2\) $-$ $\mathrm{SU}(2)$