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Properties

Label 165.2.v
Level $165$
Weight $2$
Character orbit 165.v
Rep. character $\chi_{165}(38,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $160$
Newform subspaces $1$
Sturm bound $48$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 165 = 3 \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 165.v (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 165 \)
Character field: \(\Q(\zeta_{20})\)
Newform subspaces: \( 1 \)
Sturm bound: \(48\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(165, [\chi])\).

Total New Old
Modular forms 224 224 0
Cusp forms 160 160 0
Eisenstein series 64 64 0

Trace form

\( 160q - 8q^{3} - 12q^{6} - 20q^{7} + O(q^{10}) \) \( 160q - 8q^{3} - 12q^{6} - 20q^{7} - 40q^{10} - 68q^{12} - 4q^{13} - 14q^{15} - 8q^{16} + 2q^{18} - 24q^{21} - 20q^{22} - 48q^{25} - 14q^{27} + 8q^{28} - 26q^{30} - 8q^{31} + 38q^{33} - 124q^{36} + 16q^{37} + 52q^{40} + 74q^{42} - 28q^{45} + 34q^{48} - 116q^{51} + 12q^{52} + 8q^{55} + 30q^{57} + 112q^{58} + 10q^{60} - 14q^{63} - 20q^{66} + 128q^{67} + 40q^{70} + 92q^{72} - 80q^{73} - 46q^{75} - 176q^{76} + 20q^{78} + 52q^{81} + 12q^{82} - 12q^{85} - 36q^{87} - 276q^{88} + 16q^{90} + 128q^{91} - 8q^{93} + 152q^{96} - 96q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(165, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
165.2.v.a \(160\) \(1.318\) None \(0\) \(-8\) \(0\) \(-20\)