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Properties

Label 1815.1.v
Level $1815$
Weight $1$
Character orbit 1815.v
Rep. character $\chi_{1815}(233,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $16$
Newform subspaces $2$
Sturm bound $264$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 1815 = 3 \cdot 5 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1815.v (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 165 \)
Character field: \(\Q(\zeta_{20})\)
Newform subspaces: \( 2 \)
Sturm bound: \(264\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1815, [\chi])\).

Total New Old
Modular forms 208 144 64
Cusp forms 16 16 0
Eisenstein series 192 128 64

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 16 0 0 0

Trace form

\( 16 q + 2 q^{3} + O(q^{10}) \) \( 16 q + 2 q^{3} + 8 q^{12} + 2 q^{15} + 4 q^{16} + 4 q^{25} + 2 q^{27} - 4 q^{37} - 2 q^{48} - 2 q^{60} - 16 q^{67} - 2 q^{75} - 4 q^{81} + 4 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(1815, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1815.1.v.a 1815.v 165.u $8$ $0.906$ \(\Q(\zeta_{20})\) $D_{4}$ \(\Q(\sqrt{-11}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{20}^{7}q^{3}+\zeta_{20}^{3}q^{4}+\zeta_{20}q^{5}-\zeta_{20}^{4}q^{9}+\cdots\)
1815.1.v.b 1815.v 165.u $8$ $0.906$ \(\Q(\zeta_{20})\) $D_{4}$ \(\Q(\sqrt{-11}) \) None \(0\) \(2\) \(0\) \(0\) \(q+\zeta_{20}^{2}q^{3}+\zeta_{20}^{3}q^{4}-\zeta_{20}q^{5}+\zeta_{20}^{4}q^{9}+\cdots\)