Properties

Label 170.2.b
Level $170$
Weight $2$
Character orbit 170.b
Rep. character $\chi_{170}(101,\cdot)$
Character field $\Q$
Dimension $6$
Newform subspaces $3$
Sturm bound $54$
Trace bound $9$

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Defining parameters

Level: \( N \) \(=\) \( 170 = 2 \cdot 5 \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 170.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 17 \)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(54\)
Trace bound: \(9\)
Distinguishing \(T_p\): \(3\)

Dimensions

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

Total New Old
Modular forms 30 6 24
Cusp forms 22 6 16
Eisenstein series 8 0 8

Trace form

\( 6q + 2q^{2} + 6q^{4} + 2q^{8} - 2q^{9} + O(q^{10}) \) \( 6q + 2q^{2} + 6q^{4} + 2q^{8} - 2q^{9} - 12q^{13} - 8q^{15} + 6q^{16} - 2q^{17} - 10q^{18} + 4q^{19} + 24q^{21} - 6q^{25} + 8q^{26} - 4q^{30} + 2q^{32} - 24q^{33} - 18q^{34} + 4q^{35} - 2q^{36} - 8q^{38} + 24q^{42} - 40q^{43} + 32q^{47} + 2q^{49} - 2q^{50} + 4q^{51} - 12q^{52} - 4q^{53} - 8q^{55} - 20q^{59} - 8q^{60} + 6q^{64} - 8q^{67} - 2q^{68} + 32q^{69} + 4q^{70} - 10q^{72} + 4q^{76} + 32q^{77} + 38q^{81} + 16q^{83} + 24q^{84} + 8q^{85} - 24q^{86} - 16q^{87} + 56q^{93} + 4q^{94} - 26q^{98} + O(q^{100}) \)

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.b.a \(2\) \(1.357\) \(\Q(\sqrt{-1}) \) None \(-2\) \(0\) \(0\) \(0\) \(q-q^{2}+iq^{3}+q^{4}+iq^{5}-iq^{6}-q^{8}+\cdots\)
170.2.b.b \(2\) \(1.357\) \(\Q(\sqrt{-1}) \) None \(2\) \(0\) \(0\) \(0\) \(q+q^{2}+3iq^{3}+q^{4}+iq^{5}+3iq^{6}+\cdots\)
170.2.b.c \(2\) \(1.357\) \(\Q(\sqrt{-1}) \) None \(2\) \(0\) \(0\) \(0\) \(q+q^{2}+q^{4}+iq^{5}+2iq^{7}+q^{8}+3q^{9}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(170, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(34, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(85, [\chi])\)\(^{\oplus 2}\)