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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

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

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
170.2.b.a 170.b 17.b $2$ $1.357$ \(\Q(\sqrt{-1}) \) None 170.2.b.a \(-2\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{2}+i q^{3}+q^{4}+i q^{5}-i q^{6}+\cdots\)
170.2.b.b 170.b 17.b $2$ $1.357$ \(\Q(\sqrt{-1}) \) None 170.2.b.b \(2\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{2}+3 i q^{3}+q^{4}+i q^{5}+3 i q^{6}+\cdots\)
170.2.b.c 170.b 17.b $2$ $1.357$ \(\Q(\sqrt{-1}) \) None 170.2.b.c \(2\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{2}+q^{4}+i q^{5}+2 i q^{7}+q^{8}+\cdots\)

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

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