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Properties

Label 2132.1.cs
Level $2132$
Weight $1$
Character orbit 2132.cs
Rep. character $\chi_{2132}(167,\cdot)$
Character field $\Q(\zeta_{24})$
Dimension $8$
Newform subspaces $1$
Sturm bound $294$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 2132 = 2^{2} \cdot 13 \cdot 41 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 2132.cs (of order \(24\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 2132 \)
Character field: \(\Q(\zeta_{24})\)
Newform subspaces: \( 1 \)
Sturm bound: \(294\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(2132, [\chi])\).

Total New Old
Modular forms 40 40 0
Cusp forms 8 8 0
Eisenstein series 32 32 0

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 8 0 0 0

Trace form

\( 8 q - 4 q^{2} - 4 q^{4} + 8 q^{8} + O(q^{10}) \) \( 8 q - 4 q^{2} - 4 q^{4} + 8 q^{8} + 4 q^{13} - 4 q^{16} - 8 q^{25} + 4 q^{26} - 4 q^{32} - 8 q^{41} - 8 q^{45} + 4 q^{50} - 8 q^{52} - 4 q^{53} + 8 q^{61} + 8 q^{64} + 4 q^{82} - 4 q^{85} + 4 q^{90} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(2132, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
2132.1.cs.a 2132.cs 2132.bs $8$ $1.064$ \(\Q(\zeta_{24})\) $D_{24}$ \(\Q(\sqrt{-1}) \) None 2132.1.cs.a \(-4\) \(0\) \(0\) \(0\) \(q-\zeta_{24}^{4}q^{2}+\zeta_{24}^{8}q^{4}+(\zeta_{24}^{5}+\zeta_{24}^{7}+\cdots)q^{5}+\cdots\)