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Properties

Label 1265.1.bi
Level $1265$
Weight $1$
Character orbit 1265.bi
Rep. character $\chi_{1265}(43,\cdot)$
Character field $\Q(\zeta_{44})$
Dimension $40$
Newform subspaces $2$
Sturm bound $144$
Trace bound $15$

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Defining parameters

Level: \( N \) \(=\) \( 1265 = 5 \cdot 11 \cdot 23 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1265.bi (of order \(44\) and degree \(20\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1265 \)
Character field: \(\Q(\zeta_{44})\)
Newform subspaces: \( 2 \)
Sturm bound: \(144\)
Trace bound: \(15\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1265, [\chi])\).

Total New Old
Modular forms 120 120 0
Cusp forms 40 40 0
Eisenstein series 80 80 0

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 40 0 0 0

Trace form

\( 40 q - 4 q^{3} + O(q^{10}) \) \( 40 q - 4 q^{3} - 4 q^{12} + 4 q^{16} - 2 q^{23} + 4 q^{25} - 22 q^{33} - 4 q^{36} - 4 q^{47} + 4 q^{48} + 4 q^{55} - 36 q^{71} - 18 q^{75} - 4 q^{81} - 2 q^{92} + 22 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(1265, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1265.1.bi.a 1265.bi 1265.ai $20$ $0.631$ \(\Q(\zeta_{44})\) $D_{44}$ \(\Q(\sqrt{-11}) \) None \(0\) \(-2\) \(0\) \(0\) \(q+(-\zeta_{44}^{2}+\zeta_{44}^{19})q^{3}-\zeta_{44}^{15}q^{4}+\cdots\)
1265.1.bi.b 1265.bi 1265.ai $20$ $0.631$ \(\Q(\zeta_{44})\) $D_{44}$ \(\Q(\sqrt{-11}) \) None \(0\) \(-2\) \(0\) \(0\) \(q+(\zeta_{44}^{8}-\zeta_{44}^{13})q^{3}-\zeta_{44}^{15}q^{4}+\cdots\)