Properties

Label 1444.1.j
Level $1444$
Weight $1$
Character orbit 1444.j
Rep. character $\chi_{1444}(333,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $18$
Newform subspaces $2$
Sturm bound $190$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 1444 = 2^{2} \cdot 19^{2} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1444.j (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 19 \)
Character field: \(\Q(\zeta_{18})\)
Newform subspaces: \( 2 \)
Sturm bound: \(190\)
Trace bound: \(1\)

Dimensions

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

Total New Old
Modular forms 198 18 180
Cusp forms 18 18 0
Eisenstein series 180 0 180

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 6 0 12 0

Trace form

\( 18q - 3q^{7} + O(q^{10}) \) \( 18q - 3q^{7} + 9q^{11} + 9q^{45} - 6q^{77} - 6q^{83} - 12q^{87} + O(q^{100}) \)

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.j.a \(6\) \(0.721\) \(\Q(\zeta_{18})\) \(D_{3}\) \(\Q(\sqrt{-19}) \) None \(0\) \(0\) \(0\) \(3\) \(q-\zeta_{18}^{8}q^{5}+\zeta_{18}^{3}q^{7}+\zeta_{18}^{4}q^{9}+\cdots\)
1444.1.j.b \(12\) \(0.721\) 12.0.\(\cdots\).1 \(S_{4}\) None None \(0\) \(0\) \(0\) \(-6\) \(q+(-\beta _{5}+\beta _{11})q^{3}+(\beta _{2}-\beta _{8})q^{5}+(-1+\cdots)q^{7}+\cdots\)