Properties

Label 170.2.d
Level $170$
Weight $2$
Character orbit 170.d
Rep. character $\chi_{170}(169,\cdot)$
Character field $\Q$
Dimension $8$
Newform subspaces $3$
Sturm bound $54$
Trace bound $3$

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Defining parameters

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

Dimensions

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

Total New Old
Modular forms 32 8 24
Cusp forms 24 8 16
Eisenstein series 8 0 8

Trace form

\( 8q - 8q^{4} + 12q^{9} + O(q^{10}) \) \( 8q - 8q^{4} + 12q^{9} + 16q^{15} + 8q^{16} - 12q^{19} - 40q^{21} - 4q^{25} + 20q^{26} - 20q^{30} - 4q^{34} + 4q^{35} - 12q^{36} + 32q^{49} + 4q^{50} + 36q^{51} - 68q^{59} - 16q^{60} - 8q^{64} - 32q^{69} + 44q^{70} + 12q^{76} + 8q^{81} + 40q^{84} + 16q^{85} - 48q^{86} + 68q^{89} + 28q^{94} + O(q^{100}) \)

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.d.a \(2\) \(1.357\) \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(-4\) \(-4\) \(q+iq^{2}-q^{3}-q^{4}+(-2+i)q^{5}-iq^{6}+\cdots\)
170.2.d.b \(2\) \(1.357\) \(\Q(\sqrt{-1}) \) None \(0\) \(2\) \(4\) \(4\) \(q+iq^{2}+q^{3}-q^{4}+(2-i)q^{5}+iq^{6}+\cdots\)
170.2.d.c \(4\) \(1.357\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{8}^{2}q^{2}+(-2\zeta_{8}+2\zeta_{8}^{3})q^{3}-q^{4}+\cdots\)

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

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