Properties

Label 483.2.j
Level $483$
Weight $2$
Character orbit 483.j
Rep. character $\chi_{483}(229,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $64$
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.j (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 161 \)
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 64 72
Cusp forms 120 64 56
Eisenstein series 16 0 16

Trace form

\( 64q + 4q^{2} - 36q^{4} - 24q^{8} + 32q^{9} + O(q^{10}) \) \( 64q + 4q^{2} - 36q^{4} - 24q^{8} + 32q^{9} - 44q^{16} - 4q^{18} - 16q^{23} - 12q^{25} + 84q^{26} + 24q^{29} - 12q^{31} + 8q^{32} + 32q^{35} - 72q^{36} - 8q^{46} - 12q^{47} + 8q^{49} - 96q^{50} - 108q^{52} - 24q^{58} + 36q^{59} + 168q^{64} - 40q^{70} - 16q^{71} - 12q^{72} + 48q^{73} - 48q^{75} - 32q^{78} - 32q^{81} - 24q^{82} + 88q^{85} + 36q^{87} + 152q^{92} + 24q^{93} - 108q^{94} - 44q^{95} + 60q^{96} + 112q^{98} + O(q^{100}) \)

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.j.a \(64\) \(3.857\) None \(4\) \(0\) \(0\) \(0\)

Decomposition of \(S_{2}^{\mathrm{old}}(483, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(483, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(161, [\chi])\)\(^{\oplus 2}\)