Properties

Label 1444.1.b
Level $1444$
Weight $1$
Character orbit 1444.b
Rep. character $\chi_{1444}(723,\cdot)$
Character field $\Q$
Dimension $4$
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.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 4 \)
Character field: \(\Q\)
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 24 21 3
Cusp forms 4 4 0
Eisenstein series 20 17 3

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

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

Trace form

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

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.b.a \(2\) \(0.721\) \(\Q(\sqrt{5}) \) \(D_{5}\) \(\Q(\sqrt{-1}) \) None \(-2\) \(0\) \(-1\) \(0\) \(q-q^{2}+q^{4}+(-1+\beta )q^{5}-q^{8}+q^{9}+\cdots\)
1444.1.b.b \(2\) \(0.721\) \(\Q(\sqrt{5}) \) \(D_{5}\) \(\Q(\sqrt{-1}) \) None \(2\) \(0\) \(-1\) \(0\) \(q+q^{2}+q^{4}+(-1+\beta )q^{5}+q^{8}+q^{9}+\cdots\)