Properties

Label 1444.1.g
Level $1444$
Weight $1$
Character orbit 1444.g
Rep. character $\chi_{1444}(1151,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $8$
Newform subspaces $2$
Sturm bound $190$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 1444 = 2^{2} \cdot 19^{2} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1444.g (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 76 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(190\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1444, [\chi])\).

Total New Old
Modular forms 48 40 8
Cusp forms 8 8 0
Eisenstein series 40 32 8

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 8 0 0 0

Trace form

\( 8q - 4q^{4} + 2q^{5} - 4q^{9} + O(q^{10}) \) \( 8q - 4q^{4} + 2q^{5} - 4q^{9} - 4q^{16} + 2q^{17} - 4q^{20} - 2q^{25} - 4q^{26} - 4q^{36} - 4q^{45} + 8q^{49} - 4q^{58} + 2q^{61} + 8q^{64} - 4q^{68} + 2q^{73} + 2q^{74} + 2q^{80} - 4q^{81} + 2q^{82} + 4q^{85} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1444, [\chi])\) into newform subspaces

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1444.1.g.a \(4\) \(0.721\) \(\Q(\sqrt{-3}, \sqrt{5})\) \(D_{5}\) \(\Q(\sqrt{-1}) \) None \(-2\) \(0\) \(1\) \(0\) \(q+(-1-\beta _{3})q^{2}+\beta _{3}q^{4}+(1-\beta _{1}+\beta _{3})q^{5}+\cdots\)
1444.1.g.b \(4\) \(0.721\) \(\Q(\sqrt{-3}, \sqrt{5})\) \(D_{5}\) \(\Q(\sqrt{-1}) \) None \(2\) \(0\) \(1\) \(0\) \(q+(1+\beta _{3})q^{2}+\beta _{3}q^{4}+(1-\beta _{1}+\beta _{3})q^{5}+\cdots\)