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Properties

Label 1260.1.br
Level $1260$
Weight $1$
Character orbit 1260.br
Rep. character $\chi_{1260}(479,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $8$
Newform subspaces $2$
Sturm bound $288$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 1260 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1260.br (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1260 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(288\)
Trace bound: \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1260, [\chi])\).

Total New Old
Modular forms 24 24 0
Cusp forms 8 8 0
Eisenstein series 16 16 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

\( 8 q - 8 q^{4} + 4 q^{9} - 6 q^{14} + 8 q^{16} + 4 q^{21} - 4 q^{25} + 6 q^{29} + 2 q^{30} - 4 q^{36} - 6 q^{41} - 6 q^{45} + 2 q^{46} - 2 q^{49} + 6 q^{56} - 8 q^{64} - 4 q^{70} - 4 q^{81} - 4 q^{84} + 6 q^{89}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{1}^{\mathrm{new}}(1260, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1260.1.br.a 1260.br 1260.ar $4$ $0.629$ \(\Q(\zeta_{12})\) $D_{6}$ \(\Q(\sqrt{-5}) \) None 1260.1.br.a \(0\) \(0\) \(-2\) \(0\) \(q+\zeta_{12}^{3}q^{2}+\zeta_{12}^{5}q^{3}-q^{4}-\zeta_{12}^{2}q^{5}+\cdots\)
1260.1.br.b 1260.br 1260.ar $4$ $0.629$ \(\Q(\zeta_{12})\) $D_{6}$ \(\Q(\sqrt{-5}) \) None 1260.1.br.b \(0\) \(0\) \(2\) \(0\) \(q+\zeta_{12}^{3}q^{2}-\zeta_{12}q^{3}-q^{4}+\zeta_{12}^{2}q^{5}+\cdots\)