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Properties

Label 633.1.m
Level $633$
Weight $1$
Character orbit 633.m
Rep. character $\chi_{633}(71,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $12$
Newform subspaces $2$
Sturm bound $70$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 633 = 3 \cdot 211 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 633.m (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 633 \)
Character field: \(\Q(\zeta_{10})\)
Newform subspaces: \( 2 \)
Sturm bound: \(70\)
Trace bound: \(1\)

Dimensions

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

Total New Old
Modular forms 20 20 0
Cusp forms 12 12 0
Eisenstein series 8 8 0

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 4 0 0 8

Trace form

\( 12 q + q^{3} - 5 q^{4} + q^{7} - 3 q^{9} + O(q^{10}) \) \( 12 q + q^{3} - 5 q^{4} + q^{7} - 3 q^{9} + 4 q^{10} + 8 q^{12} - q^{16} + q^{19} - 2 q^{22} - q^{25} + q^{27} + 9 q^{28} + 6 q^{30} - 6 q^{31} - 8 q^{34} - 5 q^{36} + 3 q^{37} - 4 q^{39} - 8 q^{40} - 10 q^{43} + 4 q^{46} - q^{48} + 2 q^{49} - 8 q^{52} + 4 q^{55} + 12 q^{58} - 8 q^{61} + 6 q^{63} - 7 q^{64} + 2 q^{66} - 2 q^{67} + 4 q^{70} - 10 q^{73} - q^{75} + 9 q^{76} - 2 q^{79} - 3 q^{81} + 2 q^{82} - 3 q^{84} - 4 q^{85} + 4 q^{88} - 6 q^{90} - 2 q^{91} + 7 q^{93} - 12 q^{94} + 3 q^{97} + O(q^{100}) \)

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.m.a 633.m 633.m $4$ $0.316$ \(\Q(\zeta_{10})\) $D_{5}$ \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(0\) \(3\) \(q-\zeta_{10}^{3}q^{3}+\zeta_{10}^{2}q^{4}+(1-\zeta_{10}^{3}+\cdots)q^{7}+\cdots\)
633.1.m.b 633.m 633.m $8$ $0.316$ \(\Q(\zeta_{20})\) $A_{5}$ None None \(0\) \(2\) \(0\) \(-2\) \(q+(\zeta_{20}^{5}+\zeta_{20}^{9})q^{2}+\zeta_{20}^{6}q^{3}+(-1+\cdots)q^{4}+\cdots\)