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Properties

Label 5077.2.a
Level 5077
Weight 2
Character orbit 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.

\(5077\)Dim.
\(+\)\(206\)
\(-\)\(216\)

Trace form

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

Display 100 coefficients 10 coefficients

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

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 5077
5077.2.a.a \(1\) \(40.540\) \(\Q\) None \(-2\) \(-3\) \(-4\) \(-4\) \(+\) \(q-2q^{2}-3q^{3}+2q^{4}-4q^{5}+6q^{6}+\cdots\)
5077.2.a.b \(205\) \(40.540\) None \(-25\) \(-59\) \(-44\) \(-30\) \(+\)
5077.2.a.c \(216\) \(40.540\) None \(25\) \(62\) \(46\) \(30\) \(-\)

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ (\( 1 + 2 T + 2 T^{2} \))
$3$ (\( 1 + 3 T + 3 T^{2} \))
$5$ (\( 1 + 4 T + 5 T^{2} \))
$7$ (\( 1 + 4 T + 7 T^{2} \))
$11$ (\( 1 + 6 T + 11 T^{2} \))
$13$ (\( 1 + 4 T + 13 T^{2} \))
$17$ (\( 1 + 4 T + 17 T^{2} \))
$19$ (\( 1 + 7 T + 19 T^{2} \))
$23$ (\( 1 + 6 T + 23 T^{2} \))
$29$ (\( 1 + 6 T + 29 T^{2} \))
$31$ (\( 1 + 2 T + 31 T^{2} \))
$37$ (\( 1 + 37 T^{2} \))
$41$ (\( 1 + 41 T^{2} \))
$43$ (\( 1 + 8 T + 43 T^{2} \))
$47$ (\( 1 + 9 T + 47 T^{2} \))
$53$ (\( 1 + 9 T + 53 T^{2} \))
$59$ (\( 1 + 11 T + 59 T^{2} \))
$61$ (\( 1 + 2 T + 61 T^{2} \))
$67$ (\( 1 + 12 T + 67 T^{2} \))
$71$ (\( 1 + 8 T + 71 T^{2} \))
$73$ (\( 1 + 14 T + 73 T^{2} \))
$79$ (\( 1 - 9 T + 79 T^{2} \))
$83$ (\( 1 + 2 T + 83 T^{2} \))
$89$ (\( 1 - 11 T + 89 T^{2} \))
$97$ (\( 1 - 6 T + 97 T^{2} \))
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