Properties

Label 1521.1.bd
Level $1521$
Weight $1$
Character orbit 1521.bd
Rep. character $\chi_{1521}(19,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $16$
Newform subspaces $4$
Sturm bound $182$
Trace bound $7$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1521 = 3^{2} \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1521.bd (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
Character field: \(\Q(\zeta_{12})\)
Newform subspaces: \( 4 \)
Sturm bound: \(182\)
Trace bound: \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1521, [\chi])\).

Total New Old
Modular forms 128 36 92
Cusp forms 16 16 0
Eisenstein series 112 20 92

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

\( 16 q + O(q^{10}) \) \( 16 q - 8 q^{22} + 8 q^{55} - 8 q^{94} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1521, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1521.1.bd.a 1521.bd 13.f $4$ $0.759$ \(\Q(\zeta_{12})\) $D_{4}$ \(\Q(\sqrt{-39}) \) None \(-2\) \(0\) \(-4\) \(0\) \(q+(-\zeta_{12}^{2}-\zeta_{12}^{5})q^{2}-\zeta_{12}q^{4}+(-1+\cdots)q^{5}+\cdots\)
1521.1.bd.b 1521.bd 13.f $4$ $0.759$ \(\Q(\zeta_{12})\) $D_{4}$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(-2\) \(q+\zeta_{12}q^{4}+(\zeta_{12}+\zeta_{12}^{4})q^{7}+\zeta_{12}^{2}q^{16}+\cdots\)
1521.1.bd.c 1521.bd 13.f $4$ $0.759$ \(\Q(\zeta_{12})\) $D_{4}$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(2\) \(q+\zeta_{12}q^{4}+(-\zeta_{12}-\zeta_{12}^{4})q^{7}+\zeta_{12}^{2}q^{16}+\cdots\)
1521.1.bd.d 1521.bd 13.f $4$ $0.759$ \(\Q(\zeta_{12})\) $D_{4}$ \(\Q(\sqrt{-39}) \) None \(2\) \(0\) \(4\) \(0\) \(q+(\zeta_{12}^{2}+\zeta_{12}^{5})q^{2}-\zeta_{12}q^{4}+(1+\zeta_{12}^{3}+\cdots)q^{5}+\cdots\)