Properties

Label 663.1.g
Level $663$
Weight $1$
Character orbit 663.g
Rep. character $\chi_{663}(662,\cdot)$
Character field $\Q$
Dimension $6$
Newform subspaces $4$
Sturm bound $84$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 663 = 3 \cdot 13 \cdot 17 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 663.g (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 663 \)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(84\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(663, [\chi])\).

Total New Old
Modular forms 10 10 0
Cusp forms 6 6 0
Eisenstein series 4 4 0

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

\( 6q + 2q^{4} + 6q^{9} + O(q^{10}) \) \( 6q + 2q^{4} + 6q^{9} - 2q^{13} - 2q^{16} + 6q^{25} + 2q^{36} - 8q^{42} - 4q^{43} + 2q^{49} - 2q^{51} - 6q^{52} - 6q^{64} - 4q^{69} + 6q^{81} - 4q^{87} - 8q^{94} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(663, [\chi])\) into newform subspaces

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
663.1.g.a \(1\) \(0.331\) \(\Q\) \(D_{2}\) \(\Q(\sqrt{-51}) \), \(\Q(\sqrt{-663}) \) \(\Q(\sqrt{13}) \) \(0\) \(-1\) \(0\) \(0\) \(q-q^{3}-q^{4}+q^{9}+q^{12}+q^{13}+q^{16}+\cdots\)
663.1.g.b \(1\) \(0.331\) \(\Q\) \(D_{2}\) \(\Q(\sqrt{-51}) \), \(\Q(\sqrt{-663}) \) \(\Q(\sqrt{13}) \) \(0\) \(1\) \(0\) \(0\) \(q+q^{3}-q^{4}+q^{9}-q^{12}+q^{13}+q^{16}+\cdots\)
663.1.g.c \(2\) \(0.331\) \(\Q(\sqrt{2}) \) \(D_{4}\) \(\Q(\sqrt{-663}) \) None \(0\) \(-2\) \(0\) \(0\) \(q-\beta q^{2}-q^{3}+q^{4}+\beta q^{6}-\beta q^{7}+q^{9}+\cdots\)
663.1.g.d \(2\) \(0.331\) \(\Q(\sqrt{2}) \) \(D_{4}\) \(\Q(\sqrt{-663}) \) None \(0\) \(2\) \(0\) \(0\) \(q-\beta q^{2}+q^{3}+q^{4}-\beta q^{6}+\beta q^{7}+q^{9}+\cdots\)