Properties

Label 70.2.i
Level $70$
Weight $2$
Character orbit 70.i
Rep. character $\chi_{70}(9,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $8$
Newform subspaces $2$
Sturm bound $24$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 70 = 2 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 70.i (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 35 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(24\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(70, [\chi])\).

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

Trace form

\( 8q + 4q^{4} + 2q^{5} - 12q^{6} + 6q^{9} + O(q^{10}) \) \( 8q + 4q^{4} + 2q^{5} - 12q^{6} + 6q^{9} + 2q^{10} - 6q^{11} - 2q^{14} - 24q^{15} - 4q^{16} - 14q^{19} + 4q^{20} + 6q^{21} - 6q^{24} + 14q^{26} + 20q^{29} + 6q^{30} - 16q^{31} + 16q^{34} + 26q^{35} + 12q^{36} + 12q^{39} - 2q^{40} + 6q^{44} + 24q^{45} + 16q^{46} - 26q^{49} - 32q^{50} - 12q^{51} - 18q^{54} - 24q^{55} + 2q^{56} - 4q^{59} - 12q^{60} + 6q^{61} - 8q^{64} - 2q^{65} - 12q^{69} - 2q^{70} - 14q^{74} + 24q^{75} - 28q^{76} + 8q^{79} + 2q^{80} - 36q^{81} - 24q^{84} + 8q^{85} - 14q^{86} - 10q^{89} + 60q^{90} + 20q^{91} + 2q^{94} + 16q^{95} + 6q^{96} + 36q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(70, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
70.2.i.a \(4\) \(0.559\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(-2\) \(0\) \(q+\zeta_{12}q^{2}+(-3\zeta_{12}+3\zeta_{12}^{3})q^{3}+\cdots\)
70.2.i.b \(4\) \(0.559\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(4\) \(0\) \(q+\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+(2-\zeta_{12}-2\zeta_{12}^{2}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(70, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(70, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 2}\)