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Properties

Label 170.2.r
Level $170$
Weight $2$
Character orbit 170.r
Rep. character $\chi_{170}(23,\cdot)$
Character field $\Q(\zeta_{16})$
Dimension $72$
Newform subspaces $2$
Sturm bound $54$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 170 = 2 \cdot 5 \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 170.r (of order \(16\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 85 \)
Character field: \(\Q(\zeta_{16})\)
Newform subspaces: \( 2 \)
Sturm bound: \(54\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(170, [\chi])\).

Total New Old
Modular forms 248 72 176
Cusp forms 184 72 112
Eisenstein series 64 0 64

Trace form

\( 72 q + O(q^{10}) \) \( 72 q - 24 q^{10} - 48 q^{15} - 16 q^{25} + 48 q^{27} - 16 q^{28} - 32 q^{31} + 32 q^{33} + 32 q^{34} - 32 q^{37} - 64 q^{39} - 40 q^{41} - 48 q^{42} - 32 q^{50} - 32 q^{52} + 32 q^{53} - 16 q^{55} - 144 q^{57} - 64 q^{59} + 48 q^{60} - 48 q^{62} - 48 q^{63} + 32 q^{67} + 32 q^{70} + 32 q^{71} + 40 q^{72} + 120 q^{73} + 40 q^{74} - 48 q^{75} + 48 q^{77} + 64 q^{78} - 32 q^{79} + 16 q^{80} + 96 q^{81} + 64 q^{82} + 32 q^{83} + 144 q^{85} + 32 q^{86} + 176 q^{87} + 32 q^{88} + 48 q^{90} + 96 q^{91} + 16 q^{92} - 16 q^{93} - 80 q^{95} - 32 q^{97} + 72 q^{98} + 96 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(170, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
170.2.r.a 170.r 85.r $32$ $1.357$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{16}]$
170.2.r.b 170.r 85.r $40$ $1.357$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{16}]$

Decomposition of \(S_{2}^{\mathrm{old}}(170, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(170, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(85, [\chi])\)\(^{\oplus 2}\)