Properties

Label 3479.1.db
Level $3479$
Weight $1$
Character orbit 3479.db
Rep. character $\chi_{3479}(1097,\cdot)$
Character field $\Q(\zeta_{42})$
Dimension $12$
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.db (of order \(42\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 497 \)
Character field: \(\Q(\zeta_{42})\)
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 108 60 48
Cusp forms 12 12 0
Eisenstein series 96 48 48

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 12 0 0 0

Trace form

\( 12 q + 2 q^{2} + 3 q^{4} - 8 q^{8} + q^{9} + O(q^{10}) \) \( 12 q + 2 q^{2} + 3 q^{4} - 8 q^{8} + q^{9} + 2 q^{11} - 2 q^{16} - 5 q^{18} - 8 q^{22} + 2 q^{23} - 6 q^{25} + 10 q^{29} - q^{32} - 6 q^{36} + 2 q^{37} + 10 q^{43} - q^{44} - 10 q^{46} - 4 q^{50} + 2 q^{53} - 3 q^{58} + 2 q^{67} - 2 q^{71} + 4 q^{72} + 4 q^{74} + 2 q^{79} + q^{81} + 4 q^{86} - 6 q^{88} + 2 q^{92} - 4 q^{99} + O(q^{100}) \)

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.db.a 3479.db 497.x $12$ $1.736$ \(\Q(\zeta_{21})\) $D_{7}$ \(\Q(\sqrt{-7}) \) None \(2\) \(0\) \(0\) \(0\) \(q+(\zeta_{42}^{2}+\zeta_{42}^{8})q^{2}+(\zeta_{42}^{4}+\zeta_{42}^{10}+\cdots)q^{4}+\cdots\)