Properties

Label 21.2.g
Level 21
Weight 2
Character orbit g
Rep. character \(\chi_{21}(5,\cdot)\)
Character field \(\Q(\zeta_{6})\)
Dimension 2
Newform subspaces 1
Sturm bound 5
Trace bound 0

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Defining parameters

Level: \( N \) \(=\) \( 21 = 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 21.g (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 21 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(5\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(21, [\chi])\).

Total New Old
Modular forms 10 10 0
Cusp forms 2 2 0
Eisenstein series 8 8 0

Trace form

\( 2q - 3q^{3} - 2q^{4} + q^{7} + 3q^{9} + O(q^{10}) \) \( 2q - 3q^{3} - 2q^{4} + q^{7} + 3q^{9} + 6q^{12} - 4q^{16} - 9q^{19} - 6q^{21} + 5q^{25} + 8q^{28} + 15q^{31} - 12q^{36} - q^{37} + 3q^{39} - 10q^{43} - 13q^{49} - 6q^{52} + 18q^{57} + 12q^{61} + 15q^{63} + 16q^{64} - 11q^{67} - 27q^{73} - 15q^{75} + 13q^{79} - 9q^{81} - 6q^{84} + 9q^{91} - 15q^{93} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(21, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
21.2.g.a \(2\) \(0.168\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(-3\) \(0\) \(1\) \(q+(-1-\zeta_{6})q^{3}+(-2+2\zeta_{6})q^{4}+(2+\cdots)q^{7}+\cdots\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( 1 + 2 T^{2} + 4 T^{4} \)
$3$ \( 1 + 3 T + 3 T^{2} \)
$5$ \( 1 - 5 T^{2} + 25 T^{4} \)
$7$ \( 1 - T + 7 T^{2} \)
$11$ \( 1 + 11 T^{2} + 121 T^{4} \)
$13$ \( ( 1 - 7 T + 13 T^{2} )( 1 + 7 T + 13 T^{2} ) \)
$17$ \( 1 - 17 T^{2} + 289 T^{4} \)
$19$ \( ( 1 + T + 19 T^{2} )( 1 + 8 T + 19 T^{2} ) \)
$23$ \( 1 + 23 T^{2} + 529 T^{4} \)
$29$ \( ( 1 - 29 T^{2} )^{2} \)
$31$ \( ( 1 - 11 T + 31 T^{2} )( 1 - 4 T + 31 T^{2} ) \)
$37$ \( ( 1 - 10 T + 37 T^{2} )( 1 + 11 T + 37 T^{2} ) \)
$41$ \( ( 1 + 41 T^{2} )^{2} \)
$43$ \( ( 1 + 5 T + 43 T^{2} )^{2} \)
$47$ \( 1 - 47 T^{2} + 2209 T^{4} \)
$53$ \( 1 + 53 T^{2} + 2809 T^{4} \)
$59$ \( 1 - 59 T^{2} + 3481 T^{4} \)
$61$ \( ( 1 - 13 T + 61 T^{2} )( 1 + T + 61 T^{2} ) \)
$67$ \( ( 1 - 5 T + 67 T^{2} )( 1 + 16 T + 67 T^{2} ) \)
$71$ \( ( 1 - 71 T^{2} )^{2} \)
$73$ \( ( 1 + 10 T + 73 T^{2} )( 1 + 17 T + 73 T^{2} ) \)
$79$ \( ( 1 - 17 T + 79 T^{2} )( 1 + 4 T + 79 T^{2} ) \)
$83$ \( ( 1 + 83 T^{2} )^{2} \)
$89$ \( 1 - 89 T^{2} + 7921 T^{4} \)
$97$ \( ( 1 - 14 T + 97 T^{2} )( 1 + 14 T + 97 T^{2} ) \)
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