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Properties

Label 1519.1.n
Level $1519$
Weight $1$
Character orbit 1519.n
Rep. character $\chi_{1519}(30,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $10$
Newform subspaces $3$
Sturm bound $149$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 1519 = 7^{2} \cdot 31 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1519.n (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 217 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 3 \)
Sturm bound: \(149\)
Trace bound: \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1519, [\chi])\).

Total New Old
Modular forms 38 18 20
Cusp forms 22 10 12
Eisenstein series 16 8 8

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 10 0 0 0

Trace form

\( 10 q + 2 q^{2} - 3 q^{4} - 2 q^{8} - 5 q^{9} + O(q^{10}) \) \( 10 q + 2 q^{2} - 3 q^{4} - 2 q^{8} - 5 q^{9} - 3 q^{10} - q^{16} + 2 q^{18} - 12 q^{20} - 3 q^{25} + 3 q^{31} + 3 q^{32} + 6 q^{36} - 3 q^{38} - 3 q^{40} - 3 q^{47} - 6 q^{50} + 4 q^{64} - q^{67} - 4 q^{71} + q^{72} + 6 q^{76} + 3 q^{80} - 5 q^{81} + 6 q^{82} + 6 q^{90} + q^{95} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(1519, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1519.1.n.a 1519.n 217.n $2$ $0.758$ \(\Q(\sqrt{-3}) \) $D_{3}$ \(\Q(\sqrt{-31}) \) None \(1\) \(0\) \(-1\) \(0\) \(q-\zeta_{6}^{2}q^{2}+\zeta_{6}^{2}q^{5}+q^{8}+\zeta_{6}^{2}q^{9}+\cdots\)
1519.1.n.b 1519.n 217.n $2$ $0.758$ \(\Q(\sqrt{-3}) \) $D_{3}$ \(\Q(\sqrt{-31}) \) None \(1\) \(0\) \(1\) \(0\) \(q-\zeta_{6}^{2}q^{2}-\zeta_{6}^{2}q^{5}+q^{8}+\zeta_{6}^{2}q^{9}+\cdots\)
1519.1.n.c 1519.n 217.n $6$ $0.758$ \(\Q(\zeta_{18})\) $D_{9}$ \(\Q(\sqrt{-31}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(-\zeta_{18}^{7}+\zeta_{18}^{8})q^{2}+(-\zeta_{18}^{5}+\zeta_{18}^{6}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(1519, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(1519, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(217, [\chi])\)\(^{\oplus 2}\)