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Properties

Label 36.2.b
Level 36
Weight 2
Character orbit b
Rep. character \(\chi_{36}(35,\cdot)\)
Character field \(\Q\)
Dimension 2
Newform subspaces 1
Sturm bound 12
Trace bound 0

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Defining parameters

Level: \( N \) = \( 36 = 2^{2} \cdot 3^{2} \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 36.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 12 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(12\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(36, [\chi])\).

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

Trace form

\( 2q - 4q^{4} + O(q^{10}) \) \( 2q - 4q^{4} + 4q^{10} - 8q^{13} + 8q^{16} + 6q^{25} - 20q^{34} + 4q^{37} - 8q^{40} + 14q^{49} + 16q^{52} + 28q^{58} - 20q^{61} - 16q^{64} - 32q^{73} + 4q^{82} + 20q^{85} + 16q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(36, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
36.2.b.a \(2\) \(0.287\) \(\Q(\sqrt{-2}) \) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(0\) \(0\) \(q+\beta q^{2}-2q^{4}-\beta q^{5}-2\beta q^{8}+2q^{10}+\cdots\)

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ \( 1 + 2 T^{2} \)
$3$ 1
$5$ \( 1 - 8 T^{2} + 25 T^{4} \)
$7$ \( ( 1 - 7 T^{2} )^{2} \)
$11$ \( ( 1 + 11 T^{2} )^{2} \)
$13$ \( ( 1 + 4 T + 13 T^{2} )^{2} \)
$17$ \( 1 + 16 T^{2} + 289 T^{4} \)
$19$ \( ( 1 - 19 T^{2} )^{2} \)
$23$ \( ( 1 + 23 T^{2} )^{2} \)
$29$ \( 1 + 40 T^{2} + 841 T^{4} \)
$31$ \( ( 1 - 31 T^{2} )^{2} \)
$37$ \( ( 1 - 2 T + 37 T^{2} )^{2} \)
$41$ \( 1 - 80 T^{2} + 1681 T^{4} \)
$43$ \( ( 1 - 43 T^{2} )^{2} \)
$47$ \( ( 1 + 47 T^{2} )^{2} \)
$53$ \( 1 - 56 T^{2} + 2809 T^{4} \)
$59$ \( ( 1 + 59 T^{2} )^{2} \)
$61$ \( ( 1 + 10 T + 61 T^{2} )^{2} \)
$67$ \( ( 1 - 67 T^{2} )^{2} \)
$71$ \( ( 1 + 71 T^{2} )^{2} \)
$73$ \( ( 1 + 16 T + 73 T^{2} )^{2} \)
$79$ \( ( 1 - 79 T^{2} )^{2} \)
$83$ \( ( 1 + 83 T^{2} )^{2} \)
$89$ \( 1 + 160 T^{2} + 7921 T^{4} \)
$97$ \( ( 1 - 8 T + 97 T^{2} )^{2} \)
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