Properties

Label 503.2.a
Level $503$
Weight $2$
Character orbit 503.a
Rep. character $\chi_{503}(1,\cdot)$
Character field $\Q$
Dimension $42$
Newform subspaces $6$
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: \(\Q\)
Newform subspaces: \( 6 \)
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 and the Fricke involution.

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

Trace form

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

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(503))\) into newform subspaces

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 \(4\) \(4\) \(9\) \(11\) \(-\)