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Properties

Label 160.3.w
Level $160$
Weight $3$
Character orbit 160.w
Rep. character $\chi_{160}(11,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $128$
Newform subspaces $1$
Sturm bound $72$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 160 = 2^{5} \cdot 5 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 160.w (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 32 \)
Character field: \(\Q(\zeta_{8})\)
Newform subspaces: \( 1 \)
Sturm bound: \(72\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(160, [\chi])\).

Total New Old
Modular forms 200 128 72
Cusp forms 184 128 56
Eisenstein series 16 0 16

Trace form

\( 128 q + O(q^{10}) \) \( 128 q + 40 q^{10} + 16 q^{14} - 40 q^{16} - 120 q^{18} - 80 q^{20} - 72 q^{22} + 128 q^{23} - 352 q^{24} + 192 q^{27} - 120 q^{28} + 40 q^{32} + 120 q^{34} + 264 q^{36} + 280 q^{38} - 384 q^{39} + 840 q^{42} - 192 q^{43} + 368 q^{44} + 64 q^{46} - 192 q^{51} - 848 q^{52} + 320 q^{53} - 904 q^{54} - 776 q^{56} - 360 q^{58} - 128 q^{59} + 64 q^{61} - 408 q^{62} + 48 q^{64} + 560 q^{66} + 320 q^{67} + 240 q^{68} - 192 q^{69} + 256 q^{71} + 648 q^{72} + 88 q^{74} + 512 q^{76} - 448 q^{77} + 312 q^{78} + 512 q^{79} - 480 q^{80} + 960 q^{83} - 616 q^{84} - 1160 q^{86} - 560 q^{88} - 360 q^{90} + 384 q^{91} + 152 q^{92} + 808 q^{94} - 408 q^{96} + 1136 q^{98} - 256 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(160, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
160.3.w.a 160.w 32.h $128$ $4.360$ None 160.3.w.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{8}]$

Decomposition of \(S_{3}^{\mathrm{old}}(160, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(160, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 2}\)