Properties

Label 740.1.t
Level $740$
Weight $1$
Character orbit 740.t
Rep. character $\chi_{740}(549,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $4$
Newform subspaces $2$
Sturm bound $114$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 740 = 2^{2} \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 740.t (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 185 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 2 \)
Sturm bound: \(114\)
Trace bound: \(3\)

Dimensions

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

Total New Old
Modular forms 16 4 12
Cusp forms 4 4 0
Eisenstein series 12 0 12

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 0 0 4 0

Trace form

\( 4 q + 2 q^{5} + O(q^{10}) \) \( 4 q + 2 q^{5} - 2 q^{15} + 4 q^{31} - 2 q^{35} + 2 q^{55} - 4 q^{61} - 4 q^{71} - 4 q^{75} + 4 q^{79} - 4 q^{81} - 4 q^{89} + O(q^{100}) \)

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

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
740.1.t.a \(2\) \(0.369\) \(\Q(\sqrt{-1}) \) \(S_{4}\) None None \(0\) \(-2\) \(2\) \(0\) \(q-q^{3}+q^{5}-iq^{7}-iq^{11}-q^{15}+\cdots\)
740.1.t.b \(2\) \(0.369\) \(\Q(\sqrt{-1}) \) \(S_{4}\) None None \(0\) \(2\) \(0\) \(0\) \(q+q^{3}+iq^{5}+iq^{7}-iq^{11}+iq^{15}+\cdots\)