Properties

Label 503.2.a
Level 503
Weight 2
Character orbit a
Rep. character \(\chi_{503}(1,\cdot)\)
Character field \(\Q\)
Dimension 42
Newforms 6
Sturm bound 84
Trace bound 3

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Defining parameters

Level: \( N \) = \( 503 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 503.a (trivial)
Character field: \(\Q\)
Newforms: \( 6 \)
Sturm bound: \(84\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(2\), \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(503))\).

Total New Old
Modular forms 43 43 0
Cusp forms 42 42 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.

\(503\)Dim.
\(+\)\(11\)
\(-\)\(31\)

Trace form

\(42q \) \(\mathstrut +\mathstrut q^{2} \) \(\mathstrut +\mathstrut 2q^{3} \) \(\mathstrut +\mathstrut 41q^{4} \) \(\mathstrut -\mathstrut 2q^{6} \) \(\mathstrut +\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut 3q^{8} \) \(\mathstrut +\mathstrut 42q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(42q \) \(\mathstrut +\mathstrut q^{2} \) \(\mathstrut +\mathstrut 2q^{3} \) \(\mathstrut +\mathstrut 41q^{4} \) \(\mathstrut -\mathstrut 2q^{6} \) \(\mathstrut +\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut 3q^{8} \) \(\mathstrut +\mathstrut 42q^{9} \) \(\mathstrut +\mathstrut 16q^{12} \) \(\mathstrut +\mathstrut 8q^{13} \) \(\mathstrut -\mathstrut 4q^{14} \) \(\mathstrut +\mathstrut 4q^{15} \) \(\mathstrut +\mathstrut 43q^{16} \) \(\mathstrut +\mathstrut 10q^{17} \) \(\mathstrut +\mathstrut 5q^{18} \) \(\mathstrut -\mathstrut 2q^{19} \) \(\mathstrut -\mathstrut 14q^{20} \) \(\mathstrut -\mathstrut 4q^{21} \) \(\mathstrut +\mathstrut 18q^{22} \) \(\mathstrut +\mathstrut 14q^{23} \) \(\mathstrut -\mathstrut 10q^{24} \) \(\mathstrut +\mathstrut 60q^{25} \) \(\mathstrut +\mathstrut 6q^{26} \) \(\mathstrut +\mathstrut 26q^{27} \) \(\mathstrut -\mathstrut 10q^{28} \) \(\mathstrut -\mathstrut 4q^{29} \) \(\mathstrut -\mathstrut 20q^{30} \) \(\mathstrut -\mathstrut 3q^{32} \) \(\mathstrut +\mathstrut 6q^{33} \) \(\mathstrut -\mathstrut 30q^{34} \) \(\mathstrut -\mathstrut 16q^{35} \) \(\mathstrut +\mathstrut 43q^{36} \) \(\mathstrut +\mathstrut 24q^{37} \) \(\mathstrut -\mathstrut 30q^{38} \) \(\mathstrut +\mathstrut 2q^{39} \) \(\mathstrut -\mathstrut 26q^{40} \) \(\mathstrut -\mathstrut 38q^{42} \) \(\mathstrut +\mathstrut 14q^{43} \) \(\mathstrut -\mathstrut 20q^{44} \) \(\mathstrut -\mathstrut 6q^{45} \) \(\mathstrut -\mathstrut 12q^{46} \) \(\mathstrut -\mathstrut 8q^{47} \) \(\mathstrut +\mathstrut 14q^{48} \) \(\mathstrut +\mathstrut 40q^{49} \) \(\mathstrut -\mathstrut 13q^{50} \) \(\mathstrut -\mathstrut 2q^{51} \) \(\mathstrut +\mathstrut 26q^{52} \) \(\mathstrut +\mathstrut 14q^{53} \) \(\mathstrut -\mathstrut 48q^{54} \) \(\mathstrut -\mathstrut 14q^{55} \) \(\mathstrut -\mathstrut 6q^{56} \) \(\mathstrut +\mathstrut 6q^{57} \) \(\mathstrut +\mathstrut 44q^{58} \) \(\mathstrut -\mathstrut 2q^{59} \) \(\mathstrut -\mathstrut 56q^{60} \) \(\mathstrut +\mathstrut 4q^{61} \) \(\mathstrut -\mathstrut 12q^{62} \) \(\mathstrut +\mathstrut 12q^{63} \) \(\mathstrut +\mathstrut 61q^{64} \) \(\mathstrut -\mathstrut 12q^{65} \) \(\mathstrut -\mathstrut 10q^{66} \) \(\mathstrut +\mathstrut 18q^{67} \) \(\mathstrut +\mathstrut 30q^{68} \) \(\mathstrut -\mathstrut 42q^{69} \) \(\mathstrut +\mathstrut 16q^{70} \) \(\mathstrut -\mathstrut 26q^{71} \) \(\mathstrut -\mathstrut 35q^{72} \) \(\mathstrut +\mathstrut 36q^{73} \) \(\mathstrut -\mathstrut 54q^{74} \) \(\mathstrut +\mathstrut 34q^{75} \) \(\mathstrut -\mathstrut 14q^{76} \) \(\mathstrut -\mathstrut 16q^{77} \) \(\mathstrut -\mathstrut 40q^{78} \) \(\mathstrut +\mathstrut 20q^{79} \) \(\mathstrut -\mathstrut 68q^{80} \) \(\mathstrut +\mathstrut 58q^{81} \) \(\mathstrut -\mathstrut 28q^{82} \) \(\mathstrut -\mathstrut 6q^{83} \) \(\mathstrut -\mathstrut 94q^{84} \) \(\mathstrut +\mathstrut 16q^{85} \) \(\mathstrut +\mathstrut 2q^{86} \) \(\mathstrut -\mathstrut 10q^{87} \) \(\mathstrut +\mathstrut 72q^{88} \) \(\mathstrut -\mathstrut 6q^{89} \) \(\mathstrut -\mathstrut 132q^{90} \) \(\mathstrut -\mathstrut 2q^{91} \) \(\mathstrut +\mathstrut 36q^{92} \) \(\mathstrut -\mathstrut 8q^{94} \) \(\mathstrut +\mathstrut 50q^{95} \) \(\mathstrut -\mathstrut 66q^{96} \) \(\mathstrut +\mathstrut 76q^{97} \) \(\mathstrut -\mathstrut 17q^{98} \) \(\mathstrut -\mathstrut 10q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(503))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 503
503.2.a.a \(1\) \(4.016\) \(\Q\) None \(-1\) \(1\) \(-4\) \(-3\) \(-\) \(q-q^{2}+q^{3}-q^{4}-4q^{5}-q^{6}-3q^{7}+\cdots\)
503.2.a.b \(1\) \(4.016\) \(\Q\) None \(1\) \(1\) \(-2\) \(-3\) \(+\) \(q+q^{2}+q^{3}-q^{4}-2q^{5}+q^{6}-3q^{7}+\cdots\)
503.2.a.c \(1\) \(4.016\) \(\Q\) None \(1\) \(3\) \(-2\) \(3\) \(-\) \(q+q^{2}+3q^{3}-q^{4}-2q^{5}+3q^{6}+3q^{7}+\cdots\)
503.2.a.d \(3\) \(4.016\) 3.3.257.1 None \(0\) \(1\) \(0\) \(1\) \(-\) \(q+\beta _{2}q^{2}+\beta _{1}q^{3}+(1+\beta _{1}-\beta _{2})q^{4}+\cdots\)
503.2.a.e \(10\) \(4.016\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(-4\) \(-8\) \(-1\) \(-5\) \(+\) \(q-\beta _{9}q^{2}+(-1+\beta _{1})q^{3}+\beta _{5}q^{4}-\beta _{2}q^{5}+\cdots\)
503.2.a.f \(26\) \(4.016\) None \(4\) \(4\) \(9\) \(11\) \(-\)