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Properties

Label 1944.1.e
Level $1944$
Weight $1$
Character orbit 1944.e
Rep. character $\chi_{1944}(1457,\cdot)$
Character field $\Q$
Dimension $2$
Newform subspaces $1$
Sturm bound $324$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 1944 = 2^{3} \cdot 3^{5} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1944.e (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(324\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1944, [\chi])\).

Total New Old
Modular forms 52 2 50
Cusp forms 16 2 14
Eisenstein series 36 0 36

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

\( 2 q + O(q^{10}) \) \( 2 q + 2 q^{13} - 2 q^{19} - 2 q^{25} - 2 q^{31} + 2 q^{43} - 2 q^{49} - 4 q^{55} + 2 q^{61} - 2 q^{67} + 2 q^{73} + 2 q^{79} + 4 q^{85} - 2 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(1944, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1944.1.e.a 1944.e 3.b $2$ $0.970$ \(\Q(\sqrt{-2}) \) $S_{4}$ None None \(0\) \(0\) \(0\) \(0\) \(q-\beta q^{5}-\beta q^{11}+q^{13}+\beta q^{17}-q^{19}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(1944, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(1944, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(243, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(324, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(486, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(648, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(972, [\chi])\)\(^{\oplus 2}\)