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Properties

Label 483.2.n
Level $483$
Weight $2$
Character orbit 483.n
Rep. character $\chi_{483}(47,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $116$
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.n (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 21 \)
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 136 116 20
Cusp forms 120 116 4
Eisenstein series 16 0 16

Trace form

\( 116q + 56q^{4} - 10q^{7} - 4q^{9} + O(q^{10}) \) \( 116q + 56q^{4} - 10q^{7} - 4q^{9} - 12q^{10} - 30q^{12} + 20q^{15} - 52q^{16} - 10q^{18} + 6q^{19} - 6q^{21} - 16q^{22} - 66q^{25} + 16q^{28} - 32q^{30} - 42q^{31} - 30q^{33} + 8q^{36} - 2q^{37} - 22q^{39} - 36q^{40} + 46q^{42} + 20q^{43} + 30q^{45} - 22q^{49} + 12q^{51} + 48q^{52} - 54q^{54} - 44q^{57} + 52q^{58} + 32q^{60} + 36q^{61} - 38q^{63} - 160q^{64} + 10q^{67} - 20q^{70} + 62q^{72} + 18q^{73} + 78q^{75} + 12q^{78} + 10q^{79} - 28q^{81} + 32q^{84} - 32q^{85} - 30q^{87} - 36q^{88} + 50q^{91} + 60q^{94} + 84q^{96} + 24q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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.n.a \(116\) \(3.857\) None \(0\) \(0\) \(0\) \(-10\)

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

\( S_{2}^{\mathrm{old}}(483, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 2}\)