Properties

Label 3479.1.ea
Level $3479$
Weight $1$
Character orbit 3479.ea
Rep. character $\chi_{3479}(99,\cdot)$
Character field $\Q(\zeta_{70})$
Dimension $24$
Newform subspaces $1$
Sturm bound $336$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 3479 = 7^{2} \cdot 71 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 3479.ea (of order \(70\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 71 \)
Character field: \(\Q(\zeta_{70})\)
Newform subspaces: \( 1 \)
Sturm bound: \(336\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(3479, [\chi])\).

Total New Old
Modular forms 216 144 72
Cusp forms 24 24 0
Eisenstein series 192 120 72

The following table gives the dimensions of subspaces with specified projective image type.

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 24 0 0 0

Trace form

\( 24 q - 3 q^{2} - 2 q^{4} - q^{8} - q^{9} + O(q^{10}) \) \( 24 q - 3 q^{2} - 2 q^{4} - q^{8} - q^{9} - 7 q^{16} + 5 q^{18} - 5 q^{22} + 6 q^{25} + 5 q^{29} - 11 q^{32} - 3 q^{36} - 2 q^{37} - 5 q^{43} - 12 q^{44} - 2 q^{50} + 13 q^{58} - 10 q^{64} + 5 q^{67} + q^{71} - 4 q^{72} + q^{74} + 3 q^{79} + q^{81} + 4 q^{86} + 35 q^{88} - 12 q^{92} + 5 q^{99} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(3479, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
3479.1.ea.a 3479.ea 71.h $24$ $1.736$ \(\Q(\zeta_{35})\) $D_{70}$ \(\Q(\sqrt{-7}) \) None \(-3\) \(0\) \(0\) \(0\) \(q+(\zeta_{70}^{10}-\zeta_{70}^{27})q^{2}+(\zeta_{70}^{2}-\zeta_{70}^{19}+\cdots)q^{4}+\cdots\)