Properties

Label 1444.1.c
Level $1444$
Weight $1$
Character orbit 1444.c
Rep. character $\chi_{1444}(721,\cdot)$
Character field $\Q$
Dimension $2$
Newform subspaces $1$
Sturm bound $190$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 1444 = 2^{2} \cdot 19^{2} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1444.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 19 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(190\)
Trace bound: \(0\)

Dimensions

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

Total New Old
Modular forms 34 2 32
Cusp forms 4 2 2
Eisenstein series 30 0 30

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

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

Trace form

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

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.c.a \(2\) \(0.721\) \(\Q(\sqrt{-2}) \) \(S_{4}\) None None \(0\) \(0\) \(2\) \(2\) \(q-\beta q^{3}+q^{5}+q^{7}-q^{9}-q^{11}-\beta q^{15}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(1444, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(1444, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(76, [\chi])\)\(^{\oplus 2}\)