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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

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

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
70.2.c.a 70.c 5.b $4$ $0.559$ \(\Q(i, \sqrt{6})\) None \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{2}+(\beta _{1}+\beta _{3})q^{3}-q^{4}+(1-\beta _{1}+\cdots)q^{5}+\cdots\)

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

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