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Properties

Label 165.4.w
Level $165$
Weight $4$
Character orbit 165.w
Rep. character $\chi_{165}(7,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $288$
Newform subspaces $1$
Sturm bound $96$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 165 = 3 \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 4 \)
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: \(96\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(165, [\chi])\).

Total New Old
Modular forms 608 288 320
Cusp forms 544 288 256
Eisenstein series 64 0 64

Trace form

\( 288 q + 32 q^{5} - 40 q^{7} - 56 q^{11} + 48 q^{12} - 252 q^{15} + 1264 q^{16} - 640 q^{17} + 1140 q^{20} + 356 q^{22} - 224 q^{23} - 232 q^{25} + 240 q^{26} + 720 q^{28} - 2040 q^{30} - 432 q^{31} - 228 q^{33}+ \cdots + 9744 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{4}^{\mathrm{new}}(165, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
165.4.w.a 165.w 55.l $288$ $9.735$ None 165.4.w.a \(0\) \(0\) \(32\) \(-40\) $\mathrm{SU}(2)[C_{20}]$

Decomposition of \(S_{4}^{\mathrm{old}}(165, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(165, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 2}\)