Properties

Label 165.2.s
Level $165$
Weight $2$
Character orbit 165.s
Rep. character $\chi_{165}(4,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $48$
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.s (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 55 \)
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 48 64
Cusp forms 80 48 32
Eisenstein series 32 0 32

Trace form

\( 48q + 12q^{4} - 4q^{5} + 4q^{6} + 12q^{9} + O(q^{10}) \) \( 48q + 12q^{4} - 4q^{5} + 4q^{6} + 12q^{9} - 12q^{10} - 4q^{14} + 10q^{15} - 44q^{16} - 16q^{19} + 46q^{20} - 32q^{21} - 12q^{24} + 14q^{25} - 76q^{26} + 4q^{30} - 20q^{31} - 24q^{34} - 40q^{35} - 12q^{36} - 8q^{39} - 72q^{40} + 60q^{41} - 48q^{44} + 4q^{45} + 108q^{46} - 28q^{49} - 38q^{50} + 28q^{51} + 16q^{54} - 20q^{55} + 24q^{56} + 60q^{59} + 48q^{60} + 40q^{61} + 64q^{64} + 20q^{65} + 12q^{66} + 20q^{69} + 86q^{70} - 32q^{71} - 32q^{74} - 40q^{75} - 136q^{76} - 52q^{79} + 42q^{80} - 12q^{81} - 70q^{85} - 104q^{86} + 40q^{89} - 8q^{90} - 40q^{91} + 72q^{94} - 2q^{95} + 28q^{96} + O(q^{100}) \)

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.s.a \(48\) \(1.318\) None \(0\) \(0\) \(-4\) \(0\)

Decomposition of \(S_{2}^{\mathrm{old}}(165, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(165, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 2}\)