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Properties

Label 633.1.z
Level $633$
Weight $1$
Character orbit 633.z
Rep. character $\chi_{633}(5,\cdot)$
Character field $\Q(\zeta_{70})$
Dimension $24$
Newform subspaces $1$
Sturm bound $70$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 633 = 3 \cdot 211 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 633.z (of order \(70\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 633 \)
Character field: \(\Q(\zeta_{70})\)
Newform subspaces: \( 1 \)
Sturm bound: \(70\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(633, [\chi])\).

Total New Old
Modular forms 72 72 0
Cusp forms 24 24 0
Eisenstein series 48 48 0

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 24 0 0 0

Trace form

\( 24 q + q^{3} + q^{4} - 3 q^{7} + q^{9} + O(q^{10}) \) \( 24 q + q^{3} + q^{4} - 3 q^{7} + q^{9} - 4 q^{12} + 2 q^{13} + q^{16} - 3 q^{19} - 12 q^{21} + q^{25} + q^{27} - 3 q^{28} + 2 q^{31} + q^{36} - 3 q^{37} - 5 q^{39} - 5 q^{43} + q^{48} - 2 q^{49} + 2 q^{52} + 2 q^{57} + 2 q^{61} + 2 q^{63} + q^{64} - 5 q^{67} - 5 q^{73} + q^{75} - 3 q^{76} + 2 q^{79} + q^{81} - 3 q^{84} + 4 q^{91} - 3 q^{93} - 3 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(633, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
633.1.z.a 633.z 633.z $24$ $0.316$ \(\Q(\zeta_{35})\) $D_{35}$ \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(0\) \(-3\) \(q-\zeta_{70}^{9}q^{3}-\zeta_{70}^{11}q^{4}+(-\zeta_{70}^{5}+\cdots)q^{7}+\cdots\)