Properties

Label 633.1.m
Level 633
Weight 1
Character orbit 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

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

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

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
633.1.m.a \(4\) \(0.316\) \(\Q(\zeta_{10})\) \(D_{5}\) \(\Q(\sqrt{-3}) \) 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 \(8\) \(0.316\) \(\Q(\zeta_{20})\) \(A_{5}\) None None \(0\) \(2\) \(0\) \(-2\) \(q+(\zeta_{20}^{5}+\zeta_{20}^{9})q^{2}+\zeta_{20}^{6}q^{3}+(-1+\cdots)q^{4}+\cdots\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ (\( ( 1 - T + T^{2} - T^{3} + T^{4} )( 1 + T + T^{2} + T^{3} + T^{4} ) \))(\( ( 1 + T^{2} )^{4}( 1 - T^{2} + T^{4} - T^{6} + T^{8} ) \))
$3$ (\( 1 + T + T^{2} + T^{3} + T^{4} \))(\( ( 1 - T + T^{2} - T^{3} + T^{4} )^{2} \))
$5$ (\( ( 1 - T + T^{2} - T^{3} + T^{4} )( 1 + T + T^{2} + T^{3} + T^{4} ) \))(\( 1 + T^{2} - T^{6} - T^{8} - T^{10} + T^{14} + T^{16} \))
$7$ (\( ( 1 - T )^{4}( 1 + T + T^{2} + T^{3} + T^{4} ) \))(\( ( 1 + T - T^{3} - T^{4} - T^{5} + T^{7} + T^{8} )^{2} \))
$11$ (\( ( 1 - T + T^{2} - T^{3} + T^{4} )( 1 + T + T^{2} + T^{3} + T^{4} ) \))(\( ( 1 + T^{2} )^{4}( 1 - T^{2} + T^{4} - T^{6} + T^{8} ) \))
$13$ (\( ( 1 + T + T^{2} + T^{3} + T^{4} )^{2} \))(\( ( 1 - T + T^{3} - T^{4} + T^{5} - T^{7} + T^{8} )^{2} \))
$17$ (\( ( 1 - T + T^{2} - T^{3} + T^{4} )( 1 + T + T^{2} + T^{3} + T^{4} ) \))(\( ( 1 - T^{2} + T^{4} - T^{6} + T^{8} )^{2} \))
$19$ (\( ( 1 - T )^{4}( 1 + T + T^{2} + T^{3} + T^{4} ) \))(\( ( 1 + T - T^{3} - T^{4} - T^{5} + T^{7} + T^{8} )^{2} \))
$23$ (\( ( 1 - T + T^{2} - T^{3} + T^{4} )( 1 + T + T^{2} + T^{3} + T^{4} ) \))(\( 1 + T^{2} - T^{6} - T^{8} - T^{10} + T^{14} + T^{16} \))
$29$ (\( ( 1 - T + T^{2} - T^{3} + T^{4} )( 1 + T + T^{2} + T^{3} + T^{4} ) \))(\( ( 1 + T^{2} )^{4}( 1 - T^{2} + T^{4} - T^{6} + T^{8} ) \))
$31$ (\( ( 1 + T + T^{2} + T^{3} + T^{4} )^{2} \))(\( ( 1 + T + T^{2} + T^{3} + T^{4} )^{4} \))
$37$ (\( ( 1 - T )^{4}( 1 + T + T^{2} + T^{3} + T^{4} ) \))(\( ( 1 - T^{2} + T^{4} - T^{6} + T^{8} )^{2} \))
$41$ (\( ( 1 - T + T^{2} - T^{3} + T^{4} )( 1 + T + T^{2} + T^{3} + T^{4} ) \))(\( ( 1 + T^{2} )^{4}( 1 - T^{2} + T^{4} - T^{6} + T^{8} ) \))
$43$ (\( ( 1 + T + T^{2} + T^{3} + T^{4} )^{2} \))(\( ( 1 + T + T^{2} )^{8} \))
$47$ (\( ( 1 - T + T^{2} - T^{3} + T^{4} )( 1 + T + T^{2} + T^{3} + T^{4} ) \))(\( ( 1 + T^{2} )^{4}( 1 - T^{2} + T^{4} - T^{6} + T^{8} ) \))
$53$ (\( ( 1 - T + T^{2} - T^{3} + T^{4} )( 1 + T + T^{2} + T^{3} + T^{4} ) \))(\( ( 1 - T + T^{2} - T^{3} + T^{4} )^{2}( 1 + T + T^{2} + T^{3} + T^{4} )^{2} \))
$59$ (\( ( 1 - T + T^{2} - T^{3} + T^{4} )( 1 + T + T^{2} + T^{3} + T^{4} ) \))(\( ( 1 - T + T^{2} - T^{3} + T^{4} )^{2}( 1 + T + T^{2} + T^{3} + T^{4} )^{2} \))
$61$ (\( ( 1 + T + T^{2} + T^{3} + T^{4} )^{2} \))(\( ( 1 + T )^{8}( 1 - T + T^{2} - T^{3} + T^{4} )^{2} \))
$67$ (\( ( 1 + T + T^{2} + T^{3} + T^{4} )^{2} \))(\( ( 1 + T^{2} )^{8} \))
$71$ (\( ( 1 - T + T^{2} - T^{3} + T^{4} )( 1 + T + T^{2} + T^{3} + T^{4} ) \))(\( ( 1 - T^{2} + T^{4} - T^{6} + T^{8} )^{2} \))
$73$ (\( ( 1 + T + T^{2} + T^{3} + T^{4} )^{2} \))(\( ( 1 + T + T^{2} )^{8} \))
$79$ (\( ( 1 + T + T^{2} + T^{3} + T^{4} )^{2} \))(\( ( 1 - T^{2} + T^{4} - T^{6} + T^{8} )^{2} \))
$83$ (\( ( 1 - T + T^{2} - T^{3} + T^{4} )( 1 + T + T^{2} + T^{3} + T^{4} ) \))(\( ( 1 - T^{2} + T^{4} - T^{6} + T^{8} )^{2} \))
$89$ (\( ( 1 - T + T^{2} - T^{3} + T^{4} )( 1 + T + T^{2} + T^{3} + T^{4} ) \))(\( 1 + T^{2} - T^{6} - T^{8} - T^{10} + T^{14} + T^{16} \))
$97$ (\( ( 1 - T )^{4}( 1 + T + T^{2} + T^{3} + T^{4} ) \))(\( ( 1 - T^{2} + T^{4} - T^{6} + T^{8} )^{2} \))
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