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

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

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
170.2.r.a \(32\) \(1.357\) None \(0\) \(0\) \(0\) \(0\)
170.2.r.b \(40\) \(1.357\) None \(0\) \(0\) \(0\) \(0\)

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

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