Properties

Label 70.2.g
Level $70$
Weight $2$
Character orbit 70.g
Rep. character $\chi_{70}(13,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $8$
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.g (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 35 \)
Character field: \(\Q(i)\)
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 32 8 24
Cusp forms 16 8 8
Eisenstein series 16 0 16

Trace form

\( 8q - 8q^{7} + O(q^{10}) \) \( 8q - 8q^{7} - 16q^{15} - 8q^{16} + 8q^{18} + 16q^{21} - 16q^{22} - 8q^{23} + 8q^{28} + 16q^{30} - 8q^{35} + 8q^{36} + 32q^{37} + 32q^{43} - 16q^{46} + 32q^{50} - 32q^{51} - 32q^{53} - 8q^{56} - 8q^{57} - 16q^{58} - 8q^{60} + 8q^{65} + 16q^{67} - 24q^{70} - 16q^{71} + 8q^{72} - 16q^{77} - 40q^{78} + 24q^{81} - 48q^{85} + 16q^{88} + 16q^{91} - 8q^{92} - 16q^{93} + 64q^{95} + 32q^{98} + O(q^{100}) \)

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.g.a \(8\) \(0.559\) \(\Q(\zeta_{16})\) None \(0\) \(0\) \(0\) \(-8\) \(q-\zeta_{16}^{6}q^{2}+(\zeta_{16}-\zeta_{16}^{3})q^{3}-\zeta_{16}^{4}q^{4}+\cdots\)

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

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