Properties

Label 1260.1.bt
Level $1260$
Weight $1$
Character orbit 1260.bt
Rep. character $\chi_{1260}(349,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $8$
Newform subspaces $4$
Sturm bound $288$
Trace bound $11$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1260 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1260.bt (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 315 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 4 \)
Sturm bound: \(288\)
Trace bound: \(11\)

Dimensions

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

Total New Old
Modular forms 44 8 36
Cusp forms 20 8 12
Eisenstein series 24 0 24

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

\( 8 q - 4 q^{9} + O(q^{10}) \) \( 8 q - 4 q^{9} - 2 q^{11} + 2 q^{15} + 2 q^{21} - 4 q^{25} + 4 q^{29} + 8 q^{35} + 10 q^{39} - 4 q^{49} - 2 q^{51} - 2 q^{65} - 8 q^{71} - 2 q^{79} - 4 q^{81} - 2 q^{85} + 4 q^{91} - 8 q^{99} + O(q^{100}) \)

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.bt.a 1260.bt 315.ag $2$ $0.629$ \(\Q(\sqrt{-3}) \) $D_{3}$ \(\Q(\sqrt{-35}) \) None \(0\) \(-1\) \(-1\) \(-1\) \(q-\zeta_{6}q^{3}-\zeta_{6}q^{5}+\zeta_{6}^{2}q^{7}+\zeta_{6}^{2}q^{9}+\cdots\)
1260.1.bt.b 1260.bt 315.ag $2$ $0.629$ \(\Q(\sqrt{-3}) \) $D_{3}$ \(\Q(\sqrt{-35}) \) None \(0\) \(-1\) \(-1\) \(-1\) \(q+\zeta_{6}^{2}q^{3}-\zeta_{6}q^{5}+\zeta_{6}^{2}q^{7}-\zeta_{6}q^{9}+\cdots\)
1260.1.bt.c 1260.bt 315.ag $2$ $0.629$ \(\Q(\sqrt{-3}) \) $D_{3}$ \(\Q(\sqrt{-35}) \) None \(0\) \(1\) \(1\) \(1\) \(q+\zeta_{6}q^{3}+\zeta_{6}q^{5}-\zeta_{6}^{2}q^{7}+\zeta_{6}^{2}q^{9}+\cdots\)
1260.1.bt.d 1260.bt 315.ag $2$ $0.629$ \(\Q(\sqrt{-3}) \) $D_{3}$ \(\Q(\sqrt{-35}) \) None \(0\) \(1\) \(1\) \(1\) \(q-\zeta_{6}^{2}q^{3}+\zeta_{6}q^{5}-\zeta_{6}^{2}q^{7}-\zeta_{6}q^{9}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(1260, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(1260, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(315, [\chi])\)\(^{\oplus 3}\)