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Properties

Label 1260.1.cw
Level $1260$
Weight $1$
Character orbit 1260.cw
Rep. character $\chi_{1260}(499,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $8$
Newform subspaces $4$
Sturm bound $288$
Trace bound $7$

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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.cw (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1260 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 4 \)
Sturm bound: \(288\)
Trace bound: \(7\)

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

\( 8 q + 8 q^{4} - 4 q^{5} - 4 q^{6} - 4 q^{9} + O(q^{10}) \) \( 8 q + 8 q^{4} - 4 q^{5} - 4 q^{6} - 4 q^{9} + 2 q^{14} + 8 q^{16} - 4 q^{20} - 4 q^{21} - 4 q^{24} - 4 q^{25} - 2 q^{29} + 2 q^{30} - 4 q^{36} - 2 q^{41} + 2 q^{45} - 2 q^{46} + 2 q^{49} + 8 q^{54} + 2 q^{56} + 4 q^{61} + 8 q^{64} - 8 q^{69} - 4 q^{70} - 4 q^{80} - 4 q^{81} - 4 q^{84} + 4 q^{86} - 2 q^{89} - 8 q^{94} - 4 q^{96} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1260.1.cw.a 1260.cw 1260.bw $2$ $0.629$ \(\Q(\sqrt{-3}) \) $D_{3}$ \(\Q(\sqrt{-5}) \) None \(-2\) \(1\) \(-1\) \(-2\) \(q-q^{2}+\zeta_{6}q^{3}+q^{4}+\zeta_{6}^{2}q^{5}-\zeta_{6}q^{6}+\cdots\)
1260.1.cw.b 1260.cw 1260.bw $2$ $0.629$ \(\Q(\sqrt{-3}) \) $D_{3}$ \(\Q(\sqrt{-5}) \) None \(-2\) \(1\) \(-1\) \(1\) \(q-q^{2}-\zeta_{6}^{2}q^{3}+q^{4}+\zeta_{6}^{2}q^{5}+\zeta_{6}^{2}q^{6}+\cdots\)
1260.1.cw.c 1260.cw 1260.bw $2$ $0.629$ \(\Q(\sqrt{-3}) \) $D_{3}$ \(\Q(\sqrt{-5}) \) None \(2\) \(-1\) \(-1\) \(-1\) \(q+q^{2}+\zeta_{6}^{2}q^{3}+q^{4}+\zeta_{6}^{2}q^{5}+\zeta_{6}^{2}q^{6}+\cdots\)
1260.1.cw.d 1260.cw 1260.bw $2$ $0.629$ \(\Q(\sqrt{-3}) \) $D_{3}$ \(\Q(\sqrt{-5}) \) None \(2\) \(-1\) \(-1\) \(2\) \(q+q^{2}-\zeta_{6}q^{3}+q^{4}+\zeta_{6}^{2}q^{5}-\zeta_{6}q^{6}+\cdots\)