Properties

Label 170.2.c
Level $170$
Weight $2$
Character orbit 170.c
Rep. character $\chi_{170}(69,\cdot)$
Character field $\Q$
Dimension $8$
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.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
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 32 8 24
Cusp forms 24 8 16
Eisenstein series 8 0 8

Trace form

\( 8q - 8q^{4} + 4q^{5} - 12q^{9} + O(q^{10}) \) \( 8q - 8q^{4} + 4q^{5} - 12q^{9} - 4q^{10} + 8q^{15} + 8q^{16} + 12q^{19} - 4q^{20} - 24q^{21} + 4q^{25} - 4q^{26} - 24q^{29} + 20q^{30} + 16q^{31} - 4q^{34} + 20q^{35} + 12q^{36} - 40q^{39} + 4q^{40} + 32q^{41} + 12q^{45} - 8q^{46} + 16q^{49} - 12q^{50} + 4q^{51} - 24q^{54} - 8q^{55} - 28q^{59} - 8q^{60} - 24q^{61} - 8q^{64} + 16q^{66} + 48q^{69} + 4q^{70} - 32q^{71} + 8q^{75} - 12q^{76} - 24q^{79} + 4q^{80} + 40q^{81} + 24q^{84} + 4q^{85} + 16q^{86} + 20q^{89} + 20q^{90} - 24q^{91} + 36q^{94} - 56q^{99} + O(q^{100}) \)

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.c.a \(2\) \(1.357\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(2\) \(0\) \(q+iq^{2}+iq^{3}-q^{4}+(1+2i)q^{5}-q^{6}+\cdots\)
170.2.c.b \(6\) \(1.357\) 6.0.5161984.1 None \(0\) \(0\) \(2\) \(0\) \(q+\beta _{4}q^{2}+(-\beta _{1}+\beta _{2}+\beta _{5})q^{3}-q^{4}+\cdots\)

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

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