Properties

Label 165.2.w
Level $165$
Weight $2$
Character orbit 165.w
Rep. character $\chi_{165}(7,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $96$
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.w (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 55 \)
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 96 128
Cusp forms 160 96 64
Eisenstein series 64 0 64

Trace form

\( 96q - 8q^{5} - 20q^{7} + O(q^{10}) \) \( 96q - 8q^{5} - 20q^{7} + 8q^{11} - 16q^{12} - 12q^{15} + 8q^{16} - 20q^{17} - 60q^{20} - 32q^{22} + 32q^{23} - 32q^{25} - 60q^{28} - 40q^{30} + 16q^{31} - 16q^{33} + 24q^{36} + 8q^{37} + 56q^{38} - 120q^{41} + 12q^{42} - 200q^{46} + 60q^{47} + 48q^{48} + 80q^{50} + 40q^{51} + 40q^{52} + 36q^{53} + 80q^{55} - 80q^{56} + 40q^{57} + 44q^{58} + 48q^{60} + 40q^{61} + 80q^{62} + 20q^{63} + 56q^{66} - 48q^{67} + 80q^{68} - 92q^{70} + 32q^{71} - 60q^{73} - 24q^{77} - 96q^{78} - 80q^{80} + 24q^{81} + 32q^{82} - 200q^{83} - 80q^{85} - 80q^{86} - 144q^{88} + 56q^{91} + 20q^{92} - 72q^{93} + 60q^{95} + 32q^{97} + O(q^{100}) \)

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.w.a \(96\) \(1.318\) None \(0\) \(0\) \(-8\) \(-20\)

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

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