Properties

Label 170.2.d
Level 170
Weight 2
Character orbit d
Rep. character \(\chi_{170}(169,\cdot)\)
Character field \(\Q\)
Dimension 8
Newforms 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: \(\Q\)
Newforms: \( 3 \)
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

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

Decomposition of \(S_{2}^{\mathrm{new}}(170, [\chi])\) into irreducible Hecke orbits

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

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