Properties

Label 54.2.c
Level 54
Weight 2
Character orbit c
Rep. character \(\chi_{54}(19,\cdot)\)
Character field \(\Q(\zeta_{3})\)
Dimension 2
Newform subspaces 1
Sturm bound 18
Trace bound 0

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Defining parameters

Level: \( N \) = \( 54 = 2 \cdot 3^{3} \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 54.c (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 9 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 1 \)
Sturm bound: \(18\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(54, [\chi])\).

Total New Old
Modular forms 30 2 28
Cusp forms 6 2 4
Eisenstein series 24 0 24

Trace form

\( 2q + q^{2} - q^{4} - 2q^{7} - 2q^{8} + O(q^{10}) \) \( 2q + q^{2} - q^{4} - 2q^{7} - 2q^{8} - 3q^{11} - 2q^{13} + 2q^{14} - q^{16} + 6q^{17} - 2q^{19} + 3q^{22} - 6q^{23} + 5q^{25} - 4q^{26} + 4q^{28} + 6q^{29} + 4q^{31} + q^{32} + 3q^{34} - 8q^{37} - q^{38} + 9q^{41} + q^{43} + 6q^{44} - 12q^{46} - 6q^{47} + 3q^{49} - 5q^{50} - 2q^{52} - 24q^{53} + 2q^{56} - 6q^{58} + 3q^{59} - 8q^{61} + 8q^{62} + 2q^{64} - 5q^{67} - 3q^{68} + 24q^{71} + 22q^{73} - 4q^{74} + q^{76} - 6q^{77} + 4q^{79} + 18q^{82} + 12q^{83} - q^{86} + 3q^{88} - 12q^{89} + 8q^{91} - 6q^{92} + 6q^{94} - 5q^{97} + 6q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(54, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
54.2.c.a \(2\) \(0.431\) \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(0\) \(-2\) \(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}+(-2+2\zeta_{6})q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(54, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(54, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ \( 1 - T + T^{2} \)
$3$ 1
$5$ \( 1 - 5 T^{2} + 25 T^{4} \)
$7$ \( 1 + 2 T - 3 T^{2} + 14 T^{3} + 49 T^{4} \)
$11$ \( 1 + 3 T - 2 T^{2} + 33 T^{3} + 121 T^{4} \)
$13$ \( ( 1 - 5 T + 13 T^{2} )( 1 + 7 T + 13 T^{2} ) \)
$17$ \( ( 1 - 3 T + 17 T^{2} )^{2} \)
$19$ \( ( 1 + T + 19 T^{2} )^{2} \)
$23$ \( 1 + 6 T + 13 T^{2} + 138 T^{3} + 529 T^{4} \)
$29$ \( 1 - 6 T + 7 T^{2} - 174 T^{3} + 841 T^{4} \)
$31$ \( ( 1 - 11 T + 31 T^{2} )( 1 + 7 T + 31 T^{2} ) \)
$37$ \( ( 1 + 4 T + 37 T^{2} )^{2} \)
$41$ \( 1 - 9 T + 40 T^{2} - 369 T^{3} + 1681 T^{4} \)
$43$ \( 1 - T - 42 T^{2} - 43 T^{3} + 1849 T^{4} \)
$47$ \( 1 + 6 T - 11 T^{2} + 282 T^{3} + 2209 T^{4} \)
$53$ \( ( 1 + 12 T + 53 T^{2} )^{2} \)
$59$ \( 1 - 3 T - 50 T^{2} - 177 T^{3} + 3481 T^{4} \)
$61$ \( 1 + 8 T + 3 T^{2} + 488 T^{3} + 3721 T^{4} \)
$67$ \( ( 1 - 11 T + 67 T^{2} )( 1 + 16 T + 67 T^{2} ) \)
$71$ \( ( 1 - 12 T + 71 T^{2} )^{2} \)
$73$ \( ( 1 - 11 T + 73 T^{2} )^{2} \)
$79$ \( ( 1 - 17 T + 79 T^{2} )( 1 + 13 T + 79 T^{2} ) \)
$83$ \( 1 - 12 T + 61 T^{2} - 996 T^{3} + 6889 T^{4} \)
$89$ \( ( 1 + 6 T + 89 T^{2} )^{2} \)
$97$ \( ( 1 - 14 T + 97 T^{2} )( 1 + 19 T + 97 T^{2} ) \)
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