Properties

Label 501.2.c
Level $501$
Weight $2$
Character orbit 501.c
Rep. character $\chi_{501}(500,\cdot)$
Character field $\Q$
Dimension $54$
Newform subspaces $2$
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: \(\Q\)
Newform subspaces: \( 2 \)
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

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

Decomposition of \(S_{2}^{\mathrm{new}}(501, [\chi])\) into newform subspaces

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 \(0\) \(-2\) \(0\) \(-4\)

Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database