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Properties

Label 1444.1.h
Level $1444$
Weight $1$
Character orbit 1444.h
Rep. character $\chi_{1444}(69,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $6$
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.h (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 19 \)
Character field: \(\Q(\zeta_{6})\)
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 66 6 60
Cusp forms 6 6 0
Eisenstein series 60 0 60

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 2 0 4 0

Trace form

\( 6q - q^{5} + 2q^{7} + q^{9} + O(q^{10}) \) \( 6q - q^{5} + 2q^{7} + q^{9} - 6q^{11} - q^{17} - 2q^{23} - 3q^{35} + 3q^{43} - 6q^{45} + 3q^{47} + q^{55} + 3q^{61} + 3q^{63} - q^{73} - 2q^{77} + q^{81} + 4q^{83} - 3q^{85} + 8q^{87} - q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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.h.a \(2\) \(0.721\) \(\Q(\sqrt{-3}) \) \(D_{3}\) \(\Q(\sqrt{-19}) \) None \(0\) \(0\) \(1\) \(-2\) \(q-\zeta_{6}^{2}q^{5}-q^{7}-\zeta_{6}q^{9}-q^{11}-\zeta_{6}^{2}q^{17}+\cdots\)
1444.1.h.b \(4\) \(0.721\) \(\Q(\sqrt{-2}, \sqrt{-3})\) \(S_{4}\) None None \(0\) \(0\) \(-2\) \(4\) \(q+\beta _{1}q^{3}+(-1+\beta _{2})q^{5}+q^{7}+\beta _{2}q^{9}+\cdots\)