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Properties

Label 70.3.b
Level $70$
Weight $3$
Character orbit 70.b
Rep. character $\chi_{70}(41,\cdot)$
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.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
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

\( 8 q + 16 q^{4} - 4 q^{7} - 36 q^{9} + O(q^{10}) \) \( 8 q + 16 q^{4} - 4 q^{7} - 36 q^{9} + 20 q^{11} - 4 q^{14} + 20 q^{15} + 32 q^{16} + 32 q^{18} - 64 q^{21} - 48 q^{22} - 72 q^{23} - 40 q^{25} - 8 q^{28} + 12 q^{29} - 40 q^{30} + 40 q^{35} - 72 q^{36} + 136 q^{37} + 36 q^{39} + 80 q^{42} + 128 q^{43} + 40 q^{44} - 56 q^{46} + 4 q^{49} + 268 q^{51} - 208 q^{53} - 8 q^{56} - 24 q^{57} - 224 q^{58} + 40 q^{60} + 380 q^{63} + 64 q^{64} - 100 q^{65} - 112 q^{67} + 60 q^{70} - 376 q^{71} + 64 q^{72} - 208 q^{74} - 408 q^{77} + 320 q^{78} + 188 q^{79} + 344 q^{81} - 128 q^{84} + 180 q^{85} + 200 q^{86} - 96 q^{88} - 244 q^{91} - 144 q^{92} - 824 q^{93} - 40 q^{95} + 48 q^{98} - 576 q^{99} + O(q^{100}) \)

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.b.a 70.b 7.b $8$ $1.907$ \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(0\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{6}q^{2}+(-\beta _{1}+\beta _{2})q^{3}+2q^{4}-\beta _{2}q^{5}+\cdots\)

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

\( S_{3}^{\mathrm{old}}(70, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(14, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 2}\)