Properties

Label 648.1.r
Level $648$
Weight $1$
Character orbit 648.r
Rep. character $\chi_{648}(19,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $6$
Newform subspaces $1$
Sturm bound $108$
Trace bound $0$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 648 = 2^{3} \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 648.r (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 216 \)
Character field: \(\Q(\zeta_{18})\)
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 18 36
Cusp forms 18 6 12
Eisenstein series 36 12 24

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

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

Trace form

\( 6q + 3q^{8} + O(q^{10}) \) \( 6q + 3q^{8} + 3q^{11} - 3q^{22} - 3q^{34} - 6q^{38} + 3q^{41} - 3q^{43} - 6q^{59} - 3q^{64} - 3q^{67} - 6q^{68} + 6q^{76} + 3q^{86} + 6q^{88} - 3q^{89} - 3q^{97} + 3q^{98} + O(q^{100}) \)

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.r.a \(6\) \(0.323\) \(\Q(\zeta_{18})\) \(D_{9}\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{18}^{4}q^{2}+\zeta_{18}^{8}q^{4}+\zeta_{18}^{3}q^{8}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(648, [\chi])\) into lower level spaces

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