Properties

Label 165.2.r
Level $165$
Weight $2$
Character orbit 165.r
Rep. character $\chi_{165}(29,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $80$
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.r (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 165 \)
Character field: \(\Q(\zeta_{10})\)
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 112 112 0
Cusp forms 80 80 0
Eisenstein series 32 32 0

Trace form

\( 80 q + 4 q^{4} - 10 q^{6} - 10 q^{9} + O(q^{10}) \) \( 80 q + 4 q^{4} - 10 q^{6} - 10 q^{9} - 2 q^{15} - 60 q^{16} - 20 q^{19} - 30 q^{24} + 6 q^{25} + 10 q^{30} - 20 q^{31} - 56 q^{34} + 2 q^{36} - 50 q^{39} + 60 q^{40} - 92 q^{45} - 40 q^{46} + 72 q^{49} + 30 q^{51} + 4 q^{55} + 54 q^{60} + 96 q^{64} - 42 q^{66} + 30 q^{69} - 86 q^{70} + 2 q^{75} - 66 q^{81} + 140 q^{84} - 30 q^{85} + 120 q^{90} + 48 q^{91} + 60 q^{94} - 70 q^{96} + 60 q^{99} + O(q^{100}) \)

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.r.a \(80\) \(1.318\) None \(0\) \(0\) \(0\) \(0\)