Properties

Label 1444.1.l
Level $1444$
Weight $1$
Character orbit 1444.l
Rep. character $\chi_{1444}(99,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $24$
Newform subspaces $2$
Sturm bound $190$
Trace bound $8$

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Defining parameters

Level: \( N \) \(=\) \( 1444 = 2^{2} \cdot 19^{2} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1444.l (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 76 \)
Character field: \(\Q(\zeta_{18})\)
Newform subspaces: \( 2 \)
Sturm bound: \(190\)
Trace bound: \(8\)

Dimensions

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

Total New Old
Modular forms 144 120 24
Cusp forms 24 24 0
Eisenstein series 120 96 24

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 24 0 0 0

Trace form

\( 24q + O(q^{10}) \) \( 24q - 12q^{20} + 6q^{26} + 6q^{45} - 12q^{49} - 12q^{58} - 12q^{64} + 6q^{68} + O(q^{100}) \)

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.l.a \(12\) \(0.721\) 12.0.\(\cdots\).1 \(D_{5}\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(-\beta _{3}+\beta _{9})q^{2}+(-\beta _{5}+\beta _{11})q^{4}+\cdots\)
1444.1.l.b \(12\) \(0.721\) 12.0.\(\cdots\).1 \(D_{5}\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(\beta _{3}-\beta _{9})q^{2}+(-\beta _{5}+\beta _{11})q^{4}+(\beta _{1}+\cdots)q^{5}+\cdots\)