↑

Properties

Label 1191.1.bb
Level $1191$
Weight $1$
Character orbit 1191.bb
Rep. character $\chi_{1191}(110,\cdot)$
Character field $\Q(\zeta_{66})$
Dimension $20$
Newform subspaces $1$
Sturm bound $132$
Trace bound $0$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1191 = 3 \cdot 397 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1191.bb (of order \(66\) and degree \(20\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1191 \)
Character field: \(\Q(\zeta_{66})\)
Newform subspaces: \( 1 \)
Sturm bound: \(132\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1191, [\chi])\).

Total New Old
Modular forms 60 60 0
Cusp forms 20 20 0
Eisenstein series 40 40 0

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 20 0 0 0

Trace form

\( 20 q + q^{3} - 2 q^{4} - q^{7} + q^{9} + O(q^{10}) \) \( 20 q + q^{3} - 2 q^{4} - q^{7} + q^{9} + q^{12} - q^{13} - 2 q^{16} - q^{19} - q^{21} + q^{25} - 2 q^{27} - q^{28} + 2 q^{31} + q^{36} + 2 q^{37} + 21 q^{39} - 9 q^{43} + q^{48} - q^{52} - q^{57} - q^{61} - 20 q^{63} - 2 q^{64} + 2 q^{67} - q^{73} + q^{75} - q^{76} - q^{79} + q^{81} - q^{84} + q^{91} - q^{93} - q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(1191, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1191.1.bb.a 1191.bb 1191.ab $20$ $0.594$ \(\Q(\zeta_{33})\) $D_{33}$ \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(0\) \(-1\) \(q-\zeta_{66}^{17}q^{3}+\zeta_{66}^{24}q^{4}-\zeta_{66}^{32}q^{7}+\cdots\)