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Properties

Label 832.1.bb
Level $832$
Weight $1$
Character orbit 832.bb
Rep. character $\chi_{832}(191,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $6$
Newform subspaces $2$
Sturm bound $112$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 832 = 2^{6} \cdot 13 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 832.bb (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 52 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(112\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(832, [\chi])\).

Total New Old
Modular forms 48 10 38
Cusp forms 24 6 18
Eisenstein series 24 4 20

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 2 4 0 0

Trace form

\( 6 q + 2 q^{5} - q^{9} + O(q^{10}) \) \( 6 q + 2 q^{5} - q^{9} - 3 q^{13} - q^{17} + 4 q^{21} - 4 q^{25} - 3 q^{29} + 2 q^{33} + q^{37} - q^{41} - q^{45} - q^{49} + 2 q^{53} - 4 q^{57} - 3 q^{61} + q^{65} + 2 q^{69} - 2 q^{73} + 4 q^{77} + q^{81} + q^{85} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(832, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
832.1.bb.a 832.bb 52.j $2$ $0.415$ \(\Q(\sqrt{-3}) \) $D_{3}$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(2\) \(0\) \(q+q^{5}-\zeta_{6}q^{9}-\zeta_{6}^{2}q^{13}+\zeta_{6}q^{17}+\cdots\)
832.1.bb.b 832.bb 52.j $4$ $0.415$ \(\Q(\zeta_{12})\) $A_{4}$ None None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{12}^{5}q^{3}+\zeta_{12}q^{7}-\zeta_{12}^{5}q^{11}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(832, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(832, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(52, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(104, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(208, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(416, [\chi])\)\(^{\oplus 2}\)