Properties

Label 740.1.g
Level $740$
Weight $1$
Character orbit 740.g
Rep. character $\chi_{740}(739,\cdot)$
Character field $\Q$
Dimension $6$
Newform subspaces $4$
Sturm bound $114$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 740 = 2^{2} \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 740.g (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 740 \)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(114\)
Trace bound: \(2\)

Dimensions

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

Total New Old
Modular forms 10 10 0
Cusp forms 6 6 0
Eisenstein series 4 4 0

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 6 0 0 0

Trace form

\( 6 q + 6 q^{4} + 2 q^{9} + O(q^{10}) \) \( 6 q + 6 q^{4} + 2 q^{9} - 2 q^{10} + 6 q^{16} - 8 q^{21} + 6 q^{25} - 4 q^{26} - 4 q^{34} + 2 q^{36} - 2 q^{40} - 4 q^{41} + 2 q^{49} + 6 q^{64} - 4 q^{65} - 2 q^{74} - 2 q^{81} - 8 q^{84} - 4 q^{85} - 6 q^{90} + O(q^{100}) \)

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.g.a 740.g 740.g $1$ $0.369$ \(\Q\) $D_{2}$ \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-185}) \) \(\Q(\sqrt{185}) \) \(-1\) \(0\) \(-1\) \(0\) \(q-q^{2}+q^{4}-q^{5}-q^{8}-q^{9}+q^{10}+\cdots\)
740.1.g.b 740.g 740.g $1$ $0.369$ \(\Q\) $D_{2}$ \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-185}) \) \(\Q(\sqrt{185}) \) \(1\) \(0\) \(1\) \(0\) \(q+q^{2}+q^{4}+q^{5}+q^{8}-q^{9}+q^{10}+\cdots\)
740.1.g.c 740.g 740.g $2$ $0.369$ \(\Q(\sqrt{2}) \) $D_{4}$ \(\Q(\sqrt{-185}) \) None \(-2\) \(0\) \(2\) \(0\) \(q-q^{2}-\beta q^{3}+q^{4}+q^{5}+\beta q^{6}+\beta q^{7}+\cdots\)
740.1.g.d 740.g 740.g $2$ $0.369$ \(\Q(\sqrt{2}) \) $D_{4}$ \(\Q(\sqrt{-185}) \) None \(2\) \(0\) \(-2\) \(0\) \(q+q^{2}-\beta q^{3}+q^{4}-q^{5}-\beta q^{6}+\beta q^{7}+\cdots\)