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Properties

Label 70.3.d
Level $70$
Weight $3$
Character orbit 70.d
Rep. character $\chi_{70}(69,\cdot)$
Character field $\Q$
Dimension $8$
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.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 35 \)
Character field: \(\Q\)
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 28 8 20
Cusp forms 20 8 12
Eisenstein series 8 0 8

Trace form

\( 8 q - 16 q^{4} + 36 q^{9} + O(q^{10}) \) \( 8 q - 16 q^{4} + 36 q^{9} - 60 q^{11} + 4 q^{14} + 4 q^{15} + 32 q^{16} + 56 q^{21} - 92 q^{29} - 104 q^{30} + 52 q^{35} - 72 q^{36} + 204 q^{39} + 120 q^{44} + 104 q^{46} - 284 q^{49} + 192 q^{50} - 212 q^{51} - 8 q^{56} - 8 q^{60} - 64 q^{64} - 292 q^{65} - 4 q^{70} + 504 q^{71} - 112 q^{74} + 692 q^{79} - 136 q^{81} - 112 q^{84} + 92 q^{85} - 280 q^{86} - 44 q^{91} - 176 q^{95} - 944 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
70.3.d.a 70.d 35.c $8$ $1.907$ 8.0.\(\cdots\).6 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{4}q^{2}-\beta _{5}q^{3}-2q^{4}+(\beta _{2}-\beta _{6}+\cdots)q^{5}+\cdots\)

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

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