Properties

Label 483.2.e
Level $483$
Weight $2$
Character orbit 483.e
Rep. character $\chi_{483}(344,\cdot)$
Character field $\Q$
Dimension $48$
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.e (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 69 \)
Character field: \(\Q\)
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 68 48 20
Cusp forms 60 48 12
Eisenstein series 8 0 8

Trace form

\( 48q - 4q^{3} - 40q^{4} + 6q^{6} + 4q^{9} + O(q^{10}) \) \( 48q - 4q^{3} - 40q^{4} + 6q^{6} + 4q^{9} + 22q^{12} - 8q^{13} + 24q^{16} - 14q^{18} - 12q^{24} + 88q^{25} - 16q^{27} - 8q^{31} - 10q^{36} + 8q^{46} - 98q^{48} - 48q^{49} + 28q^{52} - 28q^{54} - 92q^{58} + 92q^{64} + 8q^{69} + 8q^{70} + 60q^{72} + 40q^{73} - 80q^{75} + 114q^{78} - 28q^{81} - 20q^{82} - 40q^{85} - 28q^{87} - 76q^{93} - 12q^{94} - 6q^{96} + O(q^{100}) \)

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.e.a \(48\) \(3.857\) None \(0\) \(-4\) \(0\) \(0\)

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

\( S_{2}^{\mathrm{old}}(483, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(69, [\chi])\)\(^{\oplus 2}\)