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Properties

Label 651.1.co
Level $651$
Weight $1$
Character orbit 651.co
Rep. character $\chi_{651}(17,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $8$
Newform subspaces $1$
Sturm bound $85$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 651 = 3 \cdot 7 \cdot 31 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 651.co (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 651 \)
Character field: \(\Q(\zeta_{30})\)
Newform subspaces: \( 1 \)
Sturm bound: \(85\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(651, [\chi])\).

Total New Old
Modular forms 40 40 0
Cusp forms 8 8 0
Eisenstein series 32 32 0

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 8 0 0 0

Trace form

\( 8 q - 2 q^{3} + q^{4} - q^{7} - 2 q^{9} + O(q^{10}) \) \( 8 q - 2 q^{3} + q^{4} - q^{7} - 2 q^{9} + q^{12} + q^{13} + q^{16} + 4 q^{21} - 8 q^{25} - 2 q^{27} - q^{28} - q^{31} - 4 q^{36} + 3 q^{37} + 6 q^{39} - 5 q^{43} + q^{48} + q^{49} + q^{52} + 2 q^{61} - q^{63} - 2 q^{64} + q^{67} - q^{73} + 2 q^{75} + 5 q^{76} - 2 q^{79} - 2 q^{81} - q^{84} - q^{91} - q^{93} - 5 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(651, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
651.1.co.a 651.co 651.bo $8$ $0.325$ \(\Q(\zeta_{15})\) $D_{30}$ \(\Q(\sqrt{-3}) \) None \(0\) \(-2\) \(0\) \(-1\) \(q-\zeta_{30}^{9}q^{3}-\zeta_{30}^{7}q^{4}+\zeta_{30}q^{7}-\zeta_{30}^{3}q^{9}+\cdots\)