Properties

Label 108.2.e
Level 108
Weight 2
Character orbit e
Rep. character \(\chi_{108}(37,\cdot)\)
Character field \(\Q(\zeta_{3})\)
Dimension 2
Newform subspaces 1
Sturm bound 36
Trace bound 0

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Defining parameters

Level: \( N \) = \( 108 = 2^{2} \cdot 3^{3} \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 108.e (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 9 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 1 \)
Sturm bound: \(36\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(108, [\chi])\).

Total New Old
Modular forms 54 2 52
Cusp forms 18 2 16
Eisenstein series 36 0 36

Trace form

\( 2q + 3q^{5} + q^{7} + O(q^{10}) \) \( 2q + 3q^{5} + q^{7} + 3q^{11} + q^{13} - 12q^{17} - 8q^{19} - 3q^{23} - 4q^{25} + 3q^{29} - 5q^{31} + 6q^{35} + 4q^{37} + 3q^{41} + q^{43} - 9q^{47} + 6q^{49} + 12q^{53} + 18q^{55} - 3q^{59} + 13q^{61} - 3q^{65} + 7q^{67} + 24q^{71} - 20q^{73} - 3q^{77} - 11q^{79} - 9q^{83} - 18q^{85} - 12q^{89} + 2q^{91} - 12q^{95} - 11q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(108, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
108.2.e.a \(2\) \(0.862\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(3\) \(1\) \(q+3\zeta_{6}q^{5}+(1-\zeta_{6})q^{7}+(3-3\zeta_{6})q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(108, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(108, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(54, [\chi])\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ 1
$3$ 1
$5$ \( 1 - 3 T + 4 T^{2} - 15 T^{3} + 25 T^{4} \)
$7$ \( ( 1 - 5 T + 7 T^{2} )( 1 + 4 T + 7 T^{2} ) \)
$11$ \( 1 - 3 T - 2 T^{2} - 33 T^{3} + 121 T^{4} \)
$13$ \( 1 - T - 12 T^{2} - 13 T^{3} + 169 T^{4} \)
$17$ \( ( 1 + 6 T + 17 T^{2} )^{2} \)
$19$ \( ( 1 + 4 T + 19 T^{2} )^{2} \)
$23$ \( 1 + 3 T - 14 T^{2} + 69 T^{3} + 529 T^{4} \)
$29$ \( 1 - 3 T - 20 T^{2} - 87 T^{3} + 841 T^{4} \)
$31$ \( 1 + 5 T - 6 T^{2} + 155 T^{3} + 961 T^{4} \)
$37$ \( ( 1 - 2 T + 37 T^{2} )^{2} \)
$41$ \( 1 - 3 T - 32 T^{2} - 123 T^{3} + 1681 T^{4} \)
$43$ \( 1 - T - 42 T^{2} - 43 T^{3} + 1849 T^{4} \)
$47$ \( 1 + 9 T + 34 T^{2} + 423 T^{3} + 2209 T^{4} \)
$53$ \( ( 1 - 6 T + 53 T^{2} )^{2} \)
$59$ \( 1 + 3 T - 50 T^{2} + 177 T^{3} + 3481 T^{4} \)
$61$ \( ( 1 - 14 T + 61 T^{2} )( 1 + T + 61 T^{2} ) \)
$67$ \( 1 - 7 T - 18 T^{2} - 469 T^{3} + 4489 T^{4} \)
$71$ \( ( 1 - 12 T + 71 T^{2} )^{2} \)
$73$ \( ( 1 + 10 T + 73 T^{2} )^{2} \)
$79$ \( 1 + 11 T + 42 T^{2} + 869 T^{3} + 6241 T^{4} \)
$83$ \( 1 + 9 T - 2 T^{2} + 747 T^{3} + 6889 T^{4} \)
$89$ \( ( 1 + 6 T + 89 T^{2} )^{2} \)
$97$ \( 1 + 11 T + 24 T^{2} + 1067 T^{3} + 9409 T^{4} \)
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