Properties

Label 501.2.c
Level 501
Weight 2
Character orbit c
Rep. character \(\chi_{501}(500,\cdot)\)
Character field \(\Q\)
Dimension 54
Newforms 2
Sturm bound 112
Trace bound 1

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Defining parameters

Level: \( N \) = \( 501 = 3 \cdot 167 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 501.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 501 \)
Character field: \(\Q\)
Newforms: \( 2 \)
Sturm bound: \(112\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(501, [\chi])\).

Total New Old
Modular forms 58 58 0
Cusp forms 54 54 0
Eisenstein series 4 4 0

Trace form

\(54q \) \(\mathstrut -\mathstrut 2q^{3} \) \(\mathstrut -\mathstrut 60q^{4} \) \(\mathstrut +\mathstrut 4q^{6} \) \(\mathstrut -\mathstrut 4q^{7} \) \(\mathstrut -\mathstrut 2q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(54q \) \(\mathstrut -\mathstrut 2q^{3} \) \(\mathstrut -\mathstrut 60q^{4} \) \(\mathstrut +\mathstrut 4q^{6} \) \(\mathstrut -\mathstrut 4q^{7} \) \(\mathstrut -\mathstrut 2q^{9} \) \(\mathstrut -\mathstrut 10q^{12} \) \(\mathstrut +\mathstrut 64q^{16} \) \(\mathstrut +\mathstrut 2q^{18} \) \(\mathstrut -\mathstrut 28q^{21} \) \(\mathstrut -\mathstrut 4q^{22} \) \(\mathstrut +\mathstrut 30q^{24} \) \(\mathstrut +\mathstrut 38q^{25} \) \(\mathstrut -\mathstrut 26q^{27} \) \(\mathstrut +\mathstrut 4q^{28} \) \(\mathstrut -\mathstrut 24q^{31} \) \(\mathstrut -\mathstrut 20q^{33} \) \(\mathstrut -\mathstrut 24q^{36} \) \(\mathstrut +\mathstrut 5q^{42} \) \(\mathstrut -\mathstrut 11q^{48} \) \(\mathstrut +\mathstrut 62q^{49} \) \(\mathstrut +\mathstrut 23q^{54} \) \(\mathstrut -\mathstrut 40q^{57} \) \(\mathstrut +\mathstrut 56q^{58} \) \(\mathstrut -\mathstrut 40q^{61} \) \(\mathstrut -\mathstrut 6q^{63} \) \(\mathstrut -\mathstrut 140q^{64} \) \(\mathstrut -\mathstrut 4q^{66} \) \(\mathstrut -\mathstrut 19q^{72} \) \(\mathstrut +\mathstrut 56q^{75} \) \(\mathstrut +\mathstrut 40q^{76} \) \(\mathstrut -\mathstrut 42q^{81} \) \(\mathstrut +\mathstrut 81q^{84} \) \(\mathstrut -\mathstrut 2q^{87} \) \(\mathstrut -\mathstrut 64q^{88} \) \(\mathstrut -\mathstrut 36q^{93} \) \(\mathstrut +\mathstrut 20q^{94} \) \(\mathstrut -\mathstrut 82q^{96} \) \(\mathstrut +\mathstrut 32q^{97} \) \(\mathstrut +\mathstrut 100q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(501, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
501.2.c.a \(22\) \(4.001\) \(\Q(\sqrt{-167}) \) \(0\) \(0\) \(0\) \(0\)
501.2.c.b \(32\) \(4.001\) None \(0\) \(-2\) \(0\) \(-4\)