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Properties

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

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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

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

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 5077
5077.2.a.a 5077.a 1.a $1$ $40.540$ \(\Q\) None \(-2\) \(-3\) \(-4\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q-2q^{2}-3q^{3}+2q^{4}-4q^{5}+6q^{6}+\cdots\)
5077.2.a.b 5077.a 1.a $205$ $40.540$ None \(-25\) \(-59\) \(-44\) \(-30\) $+$ $\mathrm{SU}(2)$
5077.2.a.c 5077.a 1.a $216$ $40.540$ None \(25\) \(62\) \(46\) \(30\) $-$ $\mathrm{SU}(2)$