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Properties

Label 1380.1.bn
Level $1380$
Weight $1$
Character orbit 1380.bn
Rep. character $\chi_{1380}(359,\cdot)$
Character field $\Q(\zeta_{22})$
Dimension $80$
Newform subspaces $4$
Sturm bound $288$
Trace bound $10$

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Defining parameters

Level: \( N \) \(=\) \( 1380 = 2^{2} \cdot 3 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1380.bn (of order \(22\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1380 \)
Character field: \(\Q(\zeta_{22})\)
Newform subspaces: \( 4 \)
Sturm bound: \(288\)
Trace bound: \(10\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1380, [\chi])\).

Total New Old
Modular forms 160 160 0
Cusp forms 80 80 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 80 0 0 0

Trace form

\( 80 q + 8 q^{4} + 8 q^{9} + O(q^{10}) \) \( 80 q + 8 q^{4} + 8 q^{9} - 8 q^{16} - 22 q^{34} - 8 q^{36} - 22 q^{40} - 36 q^{49} - 22 q^{60} + 8 q^{64} - 8 q^{69} + 8 q^{70} - 8 q^{81} + 22 q^{84} + 8 q^{85} - 16 q^{94} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(1380, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1380.1.bn.a 1380.bn 1380.an $20$ $0.689$ \(\Q(\zeta_{44})\) $D_{22}$ \(\Q(\sqrt{-5}) \) None \(0\) \(0\) \(-2\) \(0\) \(q+\zeta_{44}^{21}q^{2}+\zeta_{44}^{13}q^{3}-\zeta_{44}^{20}q^{4}+\cdots\)
1380.1.bn.b 1380.bn 1380.an $20$ $0.689$ \(\Q(\zeta_{44})\) $D_{22}$ \(\Q(\sqrt{-15}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{44}^{13}q^{2}+\zeta_{44}^{3}q^{3}-\zeta_{44}^{4}q^{4}+\cdots\)
1380.1.bn.c 1380.bn 1380.an $20$ $0.689$ \(\Q(\zeta_{44})\) $D_{22}$ \(\Q(\sqrt{-15}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{44}^{7}q^{2}+\zeta_{44}^{3}q^{3}+\zeta_{44}^{14}q^{4}+\cdots\)
1380.1.bn.d 1380.bn 1380.an $20$ $0.689$ \(\Q(\zeta_{44})\) $D_{22}$ \(\Q(\sqrt{-5}) \) None \(0\) \(0\) \(2\) \(0\) \(q+\zeta_{44}^{21}q^{2}-\zeta_{44}^{15}q^{3}-\zeta_{44}^{20}q^{4}+\cdots\)