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Properties

Label 3132.1.o
Level $3132$
Weight $1$
Character orbit 3132.o
Rep. character $\chi_{3132}(1855,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $12$
Newform subspaces $2$
Sturm bound $540$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 3132 = 2^{2} \cdot 3^{3} \cdot 29 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 3132.o (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1044 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(540\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(3132, [\chi])\).

Total New Old
Modular forms 60 20 40
Cusp forms 36 12 24
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 12 0 0 0

Trace form

\( 12 q - 6 q^{4} + O(q^{10}) \) \( 12 q - 6 q^{4} - 6 q^{16} - 6 q^{25} + 6 q^{29} - 6 q^{38} - 6 q^{49} + 12 q^{64} - 6 q^{65} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(3132, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
3132.1.o.a 3132.o 1044.o $6$ $1.563$ \(\Q(\zeta_{18})\) $D_{9}$ \(\Q(\sqrt{-29}) \) None 1044.1.o.a \(-3\) \(0\) \(0\) \(0\) \(q+\zeta_{18}^{6}q^{2}-\zeta_{18}^{3}q^{4}+(-\zeta_{18}^{2}-\zeta_{18}^{4}+\cdots)q^{5}+\cdots\)
3132.1.o.b 3132.o 1044.o $6$ $1.563$ \(\Q(\zeta_{18})\) $D_{9}$ \(\Q(\sqrt{-29}) \) None 1044.1.o.a \(3\) \(0\) \(0\) \(0\) \(q-\zeta_{18}^{6}q^{2}-\zeta_{18}^{3}q^{4}+(-\zeta_{18}^{2}-\zeta_{18}^{4}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(3132, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(3132, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(1044, [\chi])\)\(^{\oplus 2}\)