Properties

Label 70.3.h
Level $70$
Weight $3$
Character orbit 70.h
Rep. character $\chi_{70}(19,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $16$
Newform subspaces $1$
Sturm bound $36$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 70 = 2 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 70.h (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 35 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(36\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(70, [\chi])\).

Total New Old
Modular forms 56 16 40
Cusp forms 40 16 24
Eisenstein series 16 0 16

Trace form

\( 16q + 16q^{4} - 6q^{5} - 12q^{9} + O(q^{10}) \) \( 16q + 16q^{4} - 6q^{5} - 12q^{9} + 24q^{10} - 12q^{11} + 32q^{14} - 28q^{15} - 32q^{16} - 12q^{19} - 8q^{21} - 24q^{24} - 42q^{25} - 48q^{26} - 136q^{29} + 32q^{30} + 84q^{31} - 190q^{35} - 48q^{36} + 312q^{39} + 48q^{40} + 24q^{44} + 384q^{45} - 68q^{46} + 296q^{49} - 96q^{50} - 76q^{51} - 108q^{54} + 56q^{56} - 372q^{59} - 28q^{60} + 348q^{61} - 128q^{64} - 104q^{65} + 480q^{66} - 296q^{70} - 384q^{71} + 208q^{74} - 150q^{75} + 148q^{79} + 24q^{80} - 140q^{81} + 256q^{84} + 580q^{85} - 188q^{86} - 912q^{89} - 616q^{91} - 600q^{94} - 310q^{95} - 48q^{96} + 176q^{99} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(70, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
70.3.h.a \(16\) \(1.907\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(-6\) \(0\) \(q+\beta _{10}q^{2}+\beta _{1}q^{3}+2\beta _{4}q^{4}+(-\beta _{6}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(70, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(70, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 2}\)