Properties

Label 648.1.bf
Level $648$
Weight $1$
Character orbit 648.bf
Rep. character $\chi_{648}(43,\cdot)$
Character field $\Q(\zeta_{54})$
Dimension $18$
Newform subspaces $1$
Sturm bound $108$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 648 = 2^{3} \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 648.bf (of order \(54\) and degree \(18\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 648 \)
Character field: \(\Q(\zeta_{54})\)
Newform subspaces: \( 1 \)
Sturm bound: \(108\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(648, [\chi])\).

Total New Old
Modular forms 54 54 0
Cusp forms 18 18 0
Eisenstein series 36 36 0

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

\( 18q + O(q^{10}) \) \( 18q - 9q^{18} - 9q^{38} - 9q^{51} - 9q^{59} + 18q^{68} - 9q^{76} - 9q^{88} - 9q^{89} + 18q^{96} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(648, [\chi])\) into newform subspaces

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
648.1.bf.a \(18\) \(0.323\) \(\Q(\zeta_{54})\) \(D_{27}\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{54}^{7}q^{2}-\zeta_{54}^{19}q^{3}+\zeta_{54}^{14}q^{4}+\cdots\)