Properties

Label 540.1.p
Level $540$
Weight $1$
Character orbit 540.p
Rep. character $\chi_{540}(19,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $4$
Newform subspaces $2$
Sturm bound $108$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 540 = 2^{2} \cdot 3^{3} \cdot 5 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 540.p (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 180 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(108\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(540, [\chi])\).

Total New Old
Modular forms 36 12 24
Cusp forms 12 4 8
Eisenstein series 24 8 16

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

\( 4 q - 2 q^{4} + 2 q^{5} + O(q^{10}) \) \( 4 q - 2 q^{4} + 2 q^{5} - 2 q^{14} - 2 q^{16} + 2 q^{20} - 2 q^{25} - 2 q^{29} - 2 q^{41} - 4 q^{46} - 2 q^{56} + 2 q^{61} + 4 q^{64} + 2 q^{70} - 4 q^{80} + 4 q^{86} + 4 q^{89} + 2 q^{94} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(540, [\chi])\) into newform subspaces

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
540.1.p.a $2$ $0.269$ \(\Q(\sqrt{-3}) \) $D_{3}$ \(\Q(\sqrt{-5}) \) None \(-1\) \(0\) \(1\) \(-1\) \(q-\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}-\zeta_{6}^{2}q^{5}-\zeta_{6}q^{7}+\cdots\)
540.1.p.b $2$ $0.269$ \(\Q(\sqrt{-3}) \) $D_{3}$ \(\Q(\sqrt{-5}) \) None \(1\) \(0\) \(1\) \(1\) \(q+\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}-\zeta_{6}^{2}q^{5}+\zeta_{6}q^{7}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(540, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(540, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(180, [\chi])\)\(^{\oplus 2}\)