Properties

Label 70.2.c
Level $70$
Weight $2$
Character orbit 70.c
Rep. character $\chi_{70}(29,\cdot)$
Character field $\Q$
Dimension $4$
Newform subspaces $1$
Sturm bound $24$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 70 = 2 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 70.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(24\)
Trace bound: \(0\)

Dimensions

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

Total New Old
Modular forms 16 4 12
Cusp forms 8 4 4
Eisenstein series 8 0 8

Trace form

\( 4q - 4q^{4} + 4q^{5} - 12q^{9} + O(q^{10}) \) \( 4q - 4q^{4} + 4q^{5} - 12q^{9} + 4q^{10} - 4q^{14} + 12q^{15} + 4q^{16} - 16q^{19} - 4q^{20} - 8q^{26} - 8q^{29} + 12q^{30} + 16q^{31} + 8q^{34} + 4q^{35} + 12q^{36} + 24q^{39} - 4q^{40} - 24q^{41} - 12q^{45} + 8q^{46} - 4q^{49} - 4q^{50} - 24q^{55} + 4q^{56} + 16q^{59} - 12q^{60} + 24q^{61} - 4q^{64} - 4q^{65} - 48q^{66} + 48q^{69} - 4q^{70} - 24q^{71} + 8q^{74} + 16q^{76} - 8q^{79} + 4q^{80} - 36q^{81} - 8q^{85} - 16q^{86} + 40q^{89} - 12q^{90} - 8q^{91} + 16q^{94} - 4q^{95} + O(q^{100}) \)

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.c.a \(4\) \(0.559\) \(\Q(i, \sqrt{6})\) None \(0\) \(0\) \(4\) \(0\) \(q+\beta _{2}q^{2}+(\beta _{1}+\beta _{3})q^{3}-q^{4}+(1-\beta _{1}+\cdots)q^{5}+\cdots\)

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

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