Properties

Label 165.1.l
Level $165$
Weight $1$
Character orbit 165.l
Rep. character $\chi_{165}(32,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $4$
Newform subspaces $2$
Sturm bound $24$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 165 = 3 \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 165.l (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 165 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 2 \)
Sturm bound: \(24\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(165, [\chi])\).

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

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 4 0 0 0

Trace form

\( 4q - 2q^{3} + O(q^{10}) \) \( 4q - 2q^{3} + 2q^{12} - 2q^{15} - 4q^{16} - 4q^{25} - 2q^{27} + 2q^{33} + 4q^{37} + 2q^{48} + 4q^{55} + 2q^{60} - 4q^{67} + 2q^{75} + 4q^{81} - 4q^{97} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(165, [\chi])\) into newform subspaces

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
165.1.l.a \(2\) \(0.082\) \(\Q(\sqrt{-1}) \) \(D_{4}\) \(\Q(\sqrt{-11}) \) None \(0\) \(-2\) \(0\) \(0\) \(q-q^{3}+iq^{4}+iq^{5}+q^{9}-iq^{11}+\cdots\)
165.1.l.b \(2\) \(0.082\) \(\Q(\sqrt{-1}) \) \(D_{4}\) \(\Q(\sqrt{-11}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{3}+iq^{4}-iq^{5}-q^{9}+iq^{11}+\cdots\)