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Properties

Label 1288.1.bi
Level $1288$
Weight $1$
Character orbit 1288.bi
Rep. character $\chi_{1288}(13,\cdot)$
Character field $\Q(\zeta_{22})$
Dimension $60$
Newform subspaces $5$
Sturm bound $192$
Trace bound $36$

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Defining parameters

Level: \( N \) \(=\) \( 1288 = 2^{3} \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1288.bi (of order \(22\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1288 \)
Character field: \(\Q(\zeta_{22})\)
Newform subspaces: \( 5 \)
Sturm bound: \(192\)
Trace bound: \(36\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1288, [\chi])\).

Total New Old
Modular forms 100 100 0
Cusp forms 60 60 0
Eisenstein series 40 40 0

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 60 0 0 0

Trace form

\( 60 q + 2 q^{2} - 6 q^{4} + 2 q^{7} + 2 q^{8} - 2 q^{9} + O(q^{10}) \) \( 60 q + 2 q^{2} - 6 q^{4} + 2 q^{7} + 2 q^{8} - 2 q^{9} - 6 q^{14} - 8 q^{15} - 6 q^{16} + 34 q^{18} - 6 q^{23} - 2 q^{25} + 2 q^{28} + 36 q^{30} + 2 q^{32} - 13 q^{36} - 8 q^{39} - 11 q^{44} + 2 q^{46} - 6 q^{49} + q^{50} - 6 q^{56} - 8 q^{57} + 11 q^{58} - 8 q^{60} - 10 q^{63} - 6 q^{64} - 8 q^{65} + 4 q^{71} - 10 q^{72} - 11 q^{74} - 8 q^{78} + 4 q^{79} + 30 q^{81} - 11 q^{88} - 6 q^{92} - 8 q^{95} - 9 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(1288, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1288.1.bi.a 1288.bi 1288.ai $10$ $0.643$ \(\Q(\zeta_{22})\) $D_{11}$ \(\Q(\sqrt{-14}) \) None \(-1\) \(-9\) \(2\) \(-1\) \(q-\zeta_{22}^{3}q^{2}+(-1-\zeta_{22}^{4})q^{3}+\zeta_{22}^{6}q^{4}+\cdots\)
1288.1.bi.b 1288.bi 1288.ai $10$ $0.643$ \(\Q(\zeta_{22})\) $D_{11}$ \(\Q(\sqrt{-14}) \) None \(-1\) \(9\) \(-2\) \(-1\) \(q-\zeta_{22}^{3}q^{2}+(1+\zeta_{22}^{4})q^{3}+\zeta_{22}^{6}q^{4}+\cdots\)
1288.1.bi.c 1288.bi 1288.ai $10$ $0.643$ \(\Q(\zeta_{22})\) $D_{22}$ \(\Q(\sqrt{-7}) \) None \(1\) \(0\) \(0\) \(1\) \(q+\zeta_{22}^{9}q^{2}-\zeta_{22}^{7}q^{4}+\zeta_{22}q^{7}+\zeta_{22}^{5}q^{8}+\cdots\)
1288.1.bi.d 1288.bi 1288.ai $10$ $0.643$ \(\Q(\zeta_{22})\) $D_{22}$ \(\Q(\sqrt{-7}) \) None \(1\) \(0\) \(0\) \(1\) \(q-\zeta_{22}^{8}q^{2}-\zeta_{22}^{5}q^{4}+\zeta_{22}q^{7}-\zeta_{22}^{2}q^{8}+\cdots\)
1288.1.bi.e 1288.bi 1288.ai $20$ $0.643$ \(\Q(\zeta_{44})\) $D_{22}$ \(\Q(\sqrt{-14}) \) None \(2\) \(0\) \(0\) \(2\) \(q+\zeta_{44}^{18}q^{2}+(\zeta_{44}^{11}+\zeta_{44}^{13})q^{3}+\cdots\)