Properties

Label 1944.1.r
Level $1944$
Weight $1$
Character orbit 1944.r
Rep. character $\chi_{1944}(379,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $24$
Newform subspaces $4$
Sturm bound $324$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 1944 = 2^{3} \cdot 3^{5} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1944.r (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 216 \)
Character field: \(\Q(\zeta_{18})\)
Newform subspaces: \( 4 \)
Sturm bound: \(324\)
Trace bound: \(11\)

Dimensions

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

Total New Old
Modular forms 162 72 90
Cusp forms 54 24 30
Eisenstein series 108 48 60

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 24 0 0 0

Trace form

\( 24q + O(q^{10}) \) \( 24q + 6q^{22} + 6q^{34} + 6q^{43} - 12q^{64} + 6q^{67} - 12q^{76} - 12q^{88} + 6q^{97} + O(q^{100}) \)

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.r.a \(6\) \(0.970\) \(\Q(\zeta_{18})\) \(D_{9}\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{18}^{4}q^{2}+\zeta_{18}^{8}q^{4}-\zeta_{18}^{3}q^{8}+\cdots\)
1944.1.r.b \(6\) \(0.970\) \(\Q(\zeta_{18})\) \(D_{9}\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{18}^{4}q^{2}+\zeta_{18}^{8}q^{4}-\zeta_{18}^{3}q^{8}+\cdots\)
1944.1.r.c \(6\) \(0.970\) \(\Q(\zeta_{18})\) \(D_{9}\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{18}^{4}q^{2}+\zeta_{18}^{8}q^{4}+\zeta_{18}^{3}q^{8}+\cdots\)
1944.1.r.d \(6\) \(0.970\) \(\Q(\zeta_{18})\) \(D_{9}\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{18}^{4}q^{2}+\zeta_{18}^{8}q^{4}+\zeta_{18}^{3}q^{8}+\cdots\)

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

\( S_{1}^{\mathrm{old}}(1944, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(216, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(648, [\chi])\)\(^{\oplus 2}\)