Properties

Label 180.1.p
Level $180$
Weight $1$
Character orbit 180.p
Rep. character $\chi_{180}(79,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $4$
Newform subspaces $2$
Sturm bound $36$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 180 = 2^{2} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 180.p (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 180 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(36\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(180, [\chi])\).

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

\( 4q - 2q^{4} - 2q^{5} + 4q^{6} - 2q^{9} + O(q^{10}) \) \( 4q - 2q^{4} - 2q^{5} + 4q^{6} - 2q^{9} + 2q^{14} - 2q^{16} - 2q^{20} - 4q^{21} - 2q^{24} - 2q^{25} + 2q^{29} - 2q^{30} + 4q^{36} + 2q^{41} + 4q^{45} - 4q^{46} - 2q^{54} + 2q^{56} + 2q^{61} + 4q^{64} + 2q^{69} + 2q^{70} + 4q^{80} - 2q^{81} + 2q^{84} - 4q^{86} - 4q^{89} + 2q^{94} - 2q^{96} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(180, [\chi])\) into newform subspaces

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
180.1.p.a \(2\) \(0.090\) \(\Q(\sqrt{-3}) \) \(D_{3}\) \(\Q(\sqrt{-5}) \) None \(-1\) \(-1\) \(-1\) \(1\) \(q+\zeta_{6}^{2}q^{2}-\zeta_{6}q^{3}-\zeta_{6}q^{4}-\zeta_{6}q^{5}+\cdots\)
180.1.p.b \(2\) \(0.090\) \(\Q(\sqrt{-3}) \) \(D_{3}\) \(\Q(\sqrt{-5}) \) None \(1\) \(1\) \(-1\) \(-1\) \(q-\zeta_{6}^{2}q^{2}+\zeta_{6}q^{3}-\zeta_{6}q^{4}-\zeta_{6}q^{5}+\cdots\)