Properties

Label 3997.1.cj
Level $3997$
Weight $1$
Character orbit 3997.cj
Rep. character $\chi_{3997}(6,\cdot)$
Character field $\Q(\zeta_{190})$
Dimension $72$
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.cj (of order \(190\) and degree \(72\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3997 \)
Character field: \(\Q(\zeta_{190})\)
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 216 216 0
Cusp forms 72 72 0
Eisenstein series 144 144 0

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 72 0 0 0

Trace form

\( 72 q + 2 q^{2} - 2 q^{4} + q^{7} - 15 q^{8} + q^{9} + O(q^{10}) \) \( 72 q + 2 q^{2} - 2 q^{4} + q^{7} - 15 q^{8} + q^{9} - 3 q^{11} + 2 q^{14} - 3 q^{18} - 15 q^{22} - 3 q^{23} + q^{25} - 2 q^{28} - 8 q^{29} - 4 q^{32} + 3 q^{36} + 2 q^{37} - 3 q^{43} - 4 q^{44} - 20 q^{46} + q^{49} + 2 q^{50} - 3 q^{53} - q^{56} + 4 q^{58} + q^{63} - 17 q^{64} - 17 q^{67} - 3 q^{71} - 20 q^{72} - 20 q^{74} + 2 q^{77} - 3 q^{79} + q^{81} - q^{86} + 3 q^{88} - 18 q^{92} - 3 q^{98} + 2 q^{99} + O(q^{100}) \)

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.cj.a 3997.cj 3997.bj $72$ $1.995$ \(\Q(\zeta_{95})\) $D_{95}$ \(\Q(\sqrt{-7}) \) None \(2\) \(0\) \(0\) \(1\) \(q+(-\zeta_{190}^{29}-\zeta_{190}^{71})q^{2}+(-\zeta_{190}^{5}+\cdots)q^{4}+\cdots\)