Properties

Label 1480.1.de
Level $1480$
Weight $1$
Character orbit 1480.de
Rep. character $\chi_{1480}(219,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $12$
Newform subspaces $2$
Sturm bound $228$
Trace bound $8$

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Defining parameters

Level: \( N \) \(=\) \( 1480 = 2^{3} \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1480.de (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1480 \)
Character field: \(\Q(\zeta_{18})\)
Newform subspaces: \( 2 \)
Sturm bound: \(228\)
Trace bound: \(8\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1480, [\chi])\).

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

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 12 0 0 0

Trace form

\( 12 q + O(q^{10}) \) \( 12 q - 6 q^{10} + 6 q^{14} - 6 q^{19} + 12 q^{36} - 6 q^{44} - 6 q^{46} + 12 q^{59} - 6 q^{64} - 6 q^{65} - 6 q^{76} - 6 q^{89} + 6 q^{91} - 6 q^{94} - 6 q^{99} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1480, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1480.1.de.a 1480.de 1480.ce $6$ $0.739$ \(\Q(\zeta_{18})\) $D_{9}$ \(\Q(\sqrt{-10}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{18}^{4}q^{2}+\zeta_{18}^{8}q^{4}+\zeta_{18}^{2}q^{5}+\cdots\)
1480.1.de.b 1480.de 1480.ce $6$ $0.739$ \(\Q(\zeta_{18})\) $D_{9}$ \(\Q(\sqrt{-10}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{18}^{4}q^{2}+\zeta_{18}^{8}q^{4}-\zeta_{18}^{2}q^{5}+\cdots\)