Properties

Label 483.2.m
Level $483$
Weight $2$
Character orbit 483.m
Rep. character $\chi_{483}(137,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $120$
Newform subspaces $1$
Sturm bound $128$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 483 = 3 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 483.m (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 483 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(128\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(483, [\chi])\).

Total New Old
Modular forms 136 136 0
Cusp forms 120 120 0
Eisenstein series 16 16 0

Trace form

\( 120q - 2q^{3} + 52q^{4} - 24q^{6} + 2q^{9} + O(q^{10}) \) \( 120q - 2q^{3} + 52q^{4} - 24q^{6} + 2q^{9} + 14q^{12} - 16q^{13} - 60q^{16} - 10q^{18} - 24q^{24} - 40q^{25} - 20q^{27} - 4q^{31} + 64q^{36} - 12q^{39} - 20q^{46} + 140q^{48} - 48q^{49} - 76q^{52} - 2q^{54} + 72q^{55} - 28q^{58} - 128q^{64} - 20q^{69} - 68q^{70} + 6q^{72} + 20q^{73} + 20q^{75} - 156q^{78} - 62q^{81} + 80q^{82} + 112q^{85} + 46q^{87} - 38q^{93} + 36q^{94} + 72q^{96} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(483, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
483.2.m.a \(120\) \(3.857\) None \(0\) \(-2\) \(0\) \(0\)