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Properties

Label 740.1.bu
Level $740$
Weight $1$
Character orbit 740.bu
Rep. character $\chi_{740}(99,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $12$
Newform subspaces $2$
Sturm bound $114$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 740 = 2^{2} \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 740.bu (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 740 \)
Character field: \(\Q(\zeta_{18})\)
Newform subspaces: \( 2 \)
Sturm bound: \(114\)
Trace bound: \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(740, [\chi])\).

Total New Old
Modular forms 36 36 0
Cusp forms 12 12 0
Eisenstein series 24 24 0

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

\( 12 q + 3 q^{5} + O(q^{10}) \) \( 12 q + 3 q^{5} - 3 q^{20} - 3 q^{25} - 6 q^{26} + 6 q^{34} - 12 q^{36} + 6 q^{40} - 6 q^{41} + 6 q^{50} + 12 q^{61} - 6 q^{64} - 3 q^{65} - 6 q^{74} - 3 q^{85} - 12 q^{89} + 3 q^{90} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(740, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
740.1.bu.a 740.bu 740.au $6$ $0.369$ \(\Q(\zeta_{18})\) $D_{18}$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{18}^{8}q^{2}-\zeta_{18}^{7}q^{4}-\zeta_{18}^{5}q^{5}+\cdots\)
740.1.bu.b 740.bu 740.au $6$ $0.369$ \(\Q(\zeta_{18})\) $D_{18}$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(3\) \(0\) \(q-\zeta_{18}^{8}q^{2}-\zeta_{18}^{7}q^{4}+\zeta_{18}^{3}q^{5}+\cdots\)