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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

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

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
165.2.w.a 165.w 55.l $96$ $1.318$ None \(0\) \(0\) \(-8\) \(-20\) $\mathrm{SU}(2)[C_{20}]$

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

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