Properties

Label 108.2.b
Level 108
Weight 2
Character orbit b
Rep. character \(\chi_{108}(107,\cdot)\)
Character field \(\Q\)
Dimension 8
Newform subspaces 2
Sturm bound 36
Trace bound 4

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Defining parameters

Level: \( N \) = \( 108 = 2^{2} \cdot 3^{3} \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 108.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 12 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(36\)
Trace bound: \(4\)
Distinguishing \(T_p\): \(5\)

Dimensions

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

Total New Old
Modular forms 24 8 16
Cusp forms 12 8 4
Eisenstein series 12 0 12

Trace form

\( 8q + 2q^{4} + O(q^{10}) \) \( 8q + 2q^{4} - 2q^{10} + 4q^{13} - 22q^{16} - 18q^{22} - 12q^{25} + 18q^{28} + 28q^{34} - 20q^{37} + 22q^{40} - 16q^{49} - 8q^{52} + 4q^{58} + 28q^{61} - 10q^{64} + 54q^{70} + 16q^{73} + 36q^{76} - 56q^{82} + 8q^{85} - 18q^{88} - 36q^{94} - 8q^{97} + O(q^{100}) \)

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.b.a \(4\) \(0.862\) \(\Q(\sqrt{3}, \sqrt{-5})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+\beta _{2}q^{4}+(\beta _{1}+\beta _{3})q^{5}+(-1+\cdots)q^{7}+\cdots\)
108.2.b.b \(4\) \(0.862\) \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-\beta _{1}-\beta _{3})q^{5}+\cdots\)

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

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

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ (\( 1 + T^{2} + 4 T^{4} \))(\( 1 - 2 T^{2} + 4 T^{4} \))
$3$ 1
$5$ (\( ( 1 - 5 T^{2} + 25 T^{4} )^{2} \))(\( ( 1 - 2 T^{2} + 25 T^{4} )^{2} \))
$7$ (\( ( 1 + T^{2} + 49 T^{4} )^{2} \))(\( ( 1 - 5 T + 7 T^{2} )^{2}( 1 + 5 T + 7 T^{2} )^{2} \))
$11$ (\( ( 1 + 19 T^{2} + 121 T^{4} )^{2} \))(\( ( 1 - 2 T^{2} + 121 T^{4} )^{2} \))
$13$ (\( ( 1 - 2 T + 13 T^{2} )^{4} \))(\( ( 1 + T + 13 T^{2} )^{4} \))
$17$ (\( ( 1 - 14 T^{2} + 289 T^{4} )^{2} \))(\( ( 1 - 26 T^{2} + 289 T^{4} )^{2} \))
$19$ (\( ( 1 - 19 T^{2} )^{4} \))(\( ( 1 - 7 T + 19 T^{2} )^{2}( 1 + 7 T + 19 T^{2} )^{2} \))
$23$ (\( ( 1 - 2 T^{2} + 529 T^{4} )^{2} \))(\( ( 1 + 22 T^{2} + 529 T^{4} )^{2} \))
$29$ (\( ( 1 - 38 T^{2} + 841 T^{4} )^{2} \))(\( ( 1 - 26 T^{2} + 841 T^{4} )^{2} \))
$31$ (\( ( 1 - 47 T^{2} + 961 T^{4} )^{2} \))(\( ( 1 - 50 T^{2} + 961 T^{4} )^{2} \))
$37$ (\( ( 1 + 4 T + 37 T^{2} )^{4} \))(\( ( 1 + T + 37 T^{2} )^{4} \))
$41$ (\( ( 1 - 2 T^{2} + 1681 T^{4} )^{2} \))(\( ( 1 - 50 T^{2} + 1681 T^{4} )^{2} \))
$43$ (\( ( 1 - 26 T^{2} + 1849 T^{4} )^{2} \))(\( ( 1 - 74 T^{2} + 1849 T^{4} )^{2} \))
$47$ (\( ( 1 + 82 T^{2} + 2209 T^{4} )^{2} \))(\( ( 1 + 70 T^{2} + 2209 T^{4} )^{2} \))
$53$ (\( ( 1 - 101 T^{2} + 2809 T^{4} )^{2} \))(\( ( 1 - 74 T^{2} + 2809 T^{4} )^{2} \))
$59$ (\( ( 1 + 106 T^{2} + 3481 T^{4} )^{2} \))(\( ( 1 + 94 T^{2} + 3481 T^{4} )^{2} \))
$61$ (\( ( 1 + 4 T + 61 T^{2} )^{4} \))(\( ( 1 - 11 T + 61 T^{2} )^{4} \))
$67$ (\( ( 1 - 74 T^{2} + 4489 T^{4} )^{2} \))(\( ( 1 - 11 T + 67 T^{2} )^{2}( 1 + 11 T + 67 T^{2} )^{2} \))
$71$ (\( ( 1 + 34 T^{2} + 5041 T^{4} )^{2} \))(\( ( 1 + 71 T^{2} )^{4} \))
$73$ (\( ( 1 - 5 T + 73 T^{2} )^{4} \))(\( ( 1 + T + 73 T^{2} )^{4} \))
$79$ (\( ( 1 - 16 T + 79 T^{2} )^{2}( 1 + 16 T + 79 T^{2} )^{2} \))(\( ( 1 - 155 T^{2} + 6241 T^{4} )^{2} \))
$83$ (\( ( 1 + 19 T^{2} + 6889 T^{4} )^{2} \))(\( ( 1 + 70 T^{2} + 6889 T^{4} )^{2} \))
$89$ (\( ( 1 - 158 T^{2} + 7921 T^{4} )^{2} \))(\( ( 1 - 170 T^{2} + 7921 T^{4} )^{2} \))
$97$ (\( ( 1 - 11 T + 97 T^{2} )^{4} \))(\( ( 1 + 13 T + 97 T^{2} )^{4} \))
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