Properties

Label 1944.1.bf
Level $1944$
Weight $1$
Character orbit 1944.bf
Rep. character $\chi_{1944}(19,\cdot)$
Character field $\Q(\zeta_{54})$
Dimension $18$
Newform subspaces $1$
Sturm bound $324$
Trace bound $0$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1944 = 2^{3} \cdot 3^{5} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1944.bf (of order \(54\) and degree \(18\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 648 \)
Character field: \(\Q(\zeta_{54})\)
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 162 54 108
Cusp forms 54 18 36
Eisenstein series 108 36 72

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 18 0 0 0

Trace form

\( 18 q + O(q^{10}) \) \( 18 q + 9 q^{38} + 9 q^{59} - 18 q^{68} - 9 q^{76} - 9 q^{88} + 9 q^{89} + O(q^{100}) \)

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.bf.a \(18\) \(0.970\) \(\Q(\zeta_{54})\) \(D_{27}\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{54}^{7}q^{2}+\zeta_{54}^{14}q^{4}+\zeta_{54}^{21}q^{8}+\cdots\)

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

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