Properties

Label 1944.1.h
Level $1944$
Weight $1$
Character orbit 1944.h
Rep. character $\chi_{1944}(485,\cdot)$
Character field $\Q$
Dimension $10$
Newform subspaces $3$
Sturm bound $324$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 1944 = 2^{3} \cdot 3^{5} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1944.h (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 24 \)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(324\)
Trace bound: \(2\)

Dimensions

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

Total New Old
Modular forms 34 10 24
Cusp forms 16 10 6
Eisenstein series 18 0 18

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 6 0 4 0

Trace form

\( 10 q + 6 q^{4} + 4 q^{7} + O(q^{10}) \) \( 10 q + 6 q^{4} + 4 q^{7} - 4 q^{10} + 2 q^{16} + 10 q^{25} - 4 q^{31} - 4 q^{34} + 4 q^{40} - 4 q^{46} + 6 q^{49} - 4 q^{52} - 6 q^{55} - 6 q^{58} + 6 q^{64} - 10 q^{70} + 4 q^{76} - 2 q^{79} + 4 q^{82} + 4 q^{97} + O(q^{100}) \)

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

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1944.1.h.a \(3\) \(0.970\) \(\Q(\zeta_{18})^+\) \(D_{9}\) \(\Q(\sqrt{-6}) \) None \(-3\) \(0\) \(0\) \(0\) \(q-q^{2}+q^{4}+\beta _{1}q^{5}+(\beta _{1}-\beta _{2})q^{7}+\cdots\)
1944.1.h.b \(3\) \(0.970\) \(\Q(\zeta_{18})^+\) \(D_{9}\) \(\Q(\sqrt{-6}) \) None \(3\) \(0\) \(0\) \(0\) \(q+q^{2}+q^{4}-\beta _{1}q^{5}+(\beta _{1}-\beta _{2})q^{7}+\cdots\)
1944.1.h.c \(4\) \(0.970\) \(\Q(\zeta_{8})\) \(S_{4}\) None None \(0\) \(0\) \(0\) \(4\) \(q-\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}+(\zeta_{8}-\zeta_{8}^{3})q^{5}+\cdots\)

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

\( S_{1}^{\mathrm{old}}(1944, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(216, [\chi])\)\(^{\oplus 3}\)