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Properties

Label 70.4.g
Level $70$
Weight $4$
Character orbit 70.g
Rep. character $\chi_{70}(13,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $24$
Newform subspaces $1$
Sturm bound $48$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 70 = 2 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
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: \(48\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(70, [\chi])\).

Total New Old
Modular forms 80 24 56
Cusp forms 64 24 40
Eisenstein series 16 0 16

Trace form

\( 24 q + 4 q^{7} + O(q^{10}) \) \( 24 q + 4 q^{7} + 40 q^{11} + 504 q^{15} - 384 q^{16} - 16 q^{18} - 432 q^{21} - 192 q^{22} + 336 q^{23} + 520 q^{25} - 16 q^{28} - 384 q^{30} - 628 q^{35} - 896 q^{36} - 456 q^{37} + 1280 q^{42} - 1264 q^{43} + 1792 q^{46} - 448 q^{50} + 2184 q^{51} - 2256 q^{53} - 384 q^{56} + 3584 q^{57} + 992 q^{58} + 352 q^{60} - 60 q^{63} - 3312 q^{65} - 1088 q^{67} + 2016 q^{70} - 2688 q^{71} - 64 q^{72} + 3128 q^{77} - 80 q^{78} - 3208 q^{81} + 5072 q^{85} + 2080 q^{86} + 768 q^{88} - 5472 q^{91} + 1344 q^{92} + 7752 q^{93} - 1976 q^{95} - 4064 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(70, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
70.4.g.a 70.g 35.f $24$ $4.130$ None \(0\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{4}]$

Decomposition of \(S_{4}^{\mathrm{old}}(70, [\chi])\) into lower level spaces

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