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Properties

Label 737.1.w
Level $737$
Weight $1$
Character orbit 737.w
Rep. character $\chi_{737}(10,\cdot)$
Character field $\Q(\zeta_{66})$
Dimension $20$
Newform subspaces $1$
Sturm bound $68$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 737 = 11 \cdot 67 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 737.w (of order \(66\) and degree \(20\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 737 \)
Character field: \(\Q(\zeta_{66})\)
Newform subspaces: \( 1 \)
Sturm bound: \(68\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(737, [\chi])\).

Total New Old
Modular forms 60 60 0
Cusp forms 20 20 0
Eisenstein series 40 40 0

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 20 0 0 0

Trace form

\( 20 q - 4 q^{3} + q^{4} + 2 q^{5} - 6 q^{9} + O(q^{10}) \) \( 20 q - 4 q^{3} + q^{4} + 2 q^{5} - 6 q^{9} + q^{11} + 2 q^{12} + 4 q^{15} + q^{16} - q^{20} - 9 q^{23} - 8 q^{27} - q^{31} - 9 q^{33} + 3 q^{36} - q^{37} + q^{44} - 5 q^{45} - q^{47} - 9 q^{48} + q^{49} + 2 q^{53} + 21 q^{55} + 2 q^{59} - 2 q^{60} - 2 q^{64} + q^{67} + 4 q^{69} + 2 q^{71} - 12 q^{80} + 12 q^{81} + 2 q^{89} - 4 q^{92} - 13 q^{93} - q^{97} + 3 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(737, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
737.1.w.a 737.w 737.w $20$ $0.368$ \(\Q(\zeta_{33})\) $D_{33}$ \(\Q(\sqrt{-11}) \) None \(0\) \(-4\) \(2\) \(0\) \(q+(\zeta_{66}^{12}+\zeta_{66}^{30})q^{3}-\zeta_{66}^{7}q^{4}+\cdots\)