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Properties

Label 3997.1.cz
Level $3997$
Weight $1$
Character orbit 3997.cz
Rep. character $\chi_{3997}(13,\cdot)$
Character field $\Q(\zeta_{570})$
Dimension $144$
Newform subspaces $1$
Sturm bound $381$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 3997 = 7 \cdot 571 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 3997.cz (of order \(570\) and degree \(144\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3997 \)
Character field: \(\Q(\zeta_{570})\)
Newform subspaces: \( 1 \)
Sturm bound: \(381\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(3997, [\chi])\).

Total New Old
Modular forms 432 432 0
Cusp forms 144 144 0
Eisenstein series 288 288 0

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 144 0 0 0

Trace form

\( 144 q + q^{2} + 5 q^{4} + 2 q^{7} + 21 q^{8} - q^{9} + O(q^{10}) \) \( 144 q + q^{2} + 5 q^{4} + 2 q^{7} + 21 q^{8} - q^{9} + 6 q^{11} + q^{14} + 6 q^{16} - 9 q^{18} + 21 q^{22} + 3 q^{23} - q^{25} - 10 q^{28} - 4 q^{29} - 5 q^{32} - 2 q^{37} - 9 q^{43} - 20 q^{44} - 34 q^{46} + 2 q^{49} - 2 q^{50} + 6 q^{53} - 8 q^{56} - q^{58} - q^{63} + 11 q^{64} + 20 q^{67} + 3 q^{71} + 23 q^{72} - 31 q^{74} + q^{77} + 6 q^{79} - q^{81} + 7 q^{86} - 9 q^{88} + 9 q^{92} + 6 q^{98} - 2 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(3997, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
3997.1.cz.a 3997.cz 3997.bz $144$ $1.995$ \(\Q(\zeta_{570})\) $D_{285}$ \(\Q(\sqrt{-7}) \) None \(1\) \(0\) \(0\) \(2\) \(q+(-\zeta_{570}^{201}+\zeta_{570}^{244})q^{2}+(-\zeta_{570}^{117}+\cdots)q^{4}+\cdots\)