Properties

Label 648.1.b
Level $648$
Weight $1$
Character orbit 648.b
Rep. character $\chi_{648}(163,\cdot)$
Character field $\Q$
Dimension $2$
Newform subspaces $2$
Sturm bound $108$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 648 = 2^{3} \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 648.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 8 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(108\)
Trace bound: \(2\)

Dimensions

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

Total New Old
Modular forms 14 6 8
Cusp forms 2 2 0
Eisenstein series 12 4 8

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 2 0 0 0

Trace form

\( 2q + 2q^{4} + O(q^{10}) \) \( 2q + 2q^{4} + 2q^{16} - 2q^{19} - 2q^{22} + 2q^{25} - 2q^{34} - 2q^{43} + 2q^{49} + 2q^{64} - 2q^{67} - 2q^{73} - 2q^{76} - 2q^{82} - 2q^{88} - 2q^{97} + O(q^{100}) \)

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.b.a \(1\) \(0.323\) \(\Q\) \(D_{3}\) \(\Q(\sqrt{-2}) \) None \(-1\) \(0\) \(0\) \(0\) \(q-q^{2}+q^{4}-q^{8}+q^{11}+q^{16}+q^{17}+\cdots\)
648.1.b.b \(1\) \(0.323\) \(\Q\) \(D_{3}\) \(\Q(\sqrt{-2}) \) None \(1\) \(0\) \(0\) \(0\) \(q+q^{2}+q^{4}+q^{8}-q^{11}+q^{16}-q^{17}+\cdots\)