Properties

Label 483.2.u
Level $483$
Weight $2$
Character orbit 483.u
Rep. character $\chi_{483}(113,\cdot)$
Character field $\Q(\zeta_{22})$
Dimension $480$
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.u (of order \(22\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 69 \)
Character field: \(\Q(\zeta_{22})\)
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 680 480 200
Cusp forms 600 480 120
Eisenstein series 80 0 80

Trace form

\( 480q + 4q^{3} + 40q^{4} - 6q^{6} - 4q^{9} + O(q^{10}) \) \( 480q + 4q^{3} + 40q^{4} - 6q^{6} - 4q^{9} - 22q^{12} + 8q^{13} - 22q^{15} - 24q^{16} - 30q^{18} - 120q^{24} - 88q^{25} + 16q^{27} - 44q^{30} + 8q^{31} - 22q^{33} - 44q^{34} + 10q^{36} - 44q^{37} - 308q^{40} - 44q^{43} - 184q^{46} + 98q^{48} + 48q^{49} - 28q^{52} + 28q^{54} - 44q^{55} + 66q^{57} + 4q^{58} + 220q^{60} + 84q^{64} + 176q^{66} + 44q^{67} + 102q^{69} - 8q^{70} - 60q^{72} + 4q^{73} - 8q^{75} + 176q^{76} + 18q^{78} - 16q^{81} + 20q^{82} - 154q^{84} + 84q^{85} + 28q^{87} - 418q^{90} - 188q^{93} + 12q^{94} - 412q^{96} - 132q^{97} + O(q^{100}) \)

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.u.a \(480\) \(3.857\) None \(0\) \(4\) \(0\) \(0\)

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

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