Properties

Label 23.3.b
Level 23
Weight 3
Character orbit b
Rep. character \(\chi_{23}(22,\cdot)\)
Character field \(\Q\)
Dimension 3
Newform subspaces 1
Sturm bound 6
Trace bound 0

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Defining parameters

Level: \( N \) = \( 23 \)
Weight: \( k \) = \( 3 \)
Character orbit: \([\chi]\) = 23.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 23 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(6\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(23, [\chi])\).

Total New Old
Modular forms 5 5 0
Cusp forms 3 3 0
Eisenstein series 2 2 0

Trace form

\( 3q + 12q^{4} - 33q^{6} - 21q^{8} + 27q^{9} + O(q^{10}) \) \( 3q + 12q^{4} - 33q^{6} - 21q^{8} + 27q^{9} + 3q^{12} + 48q^{16} + 39q^{18} - 69q^{23} - 132q^{24} + 75q^{25} + 87q^{26} - 114q^{27} - 84q^{32} + 255q^{36} - 42q^{39} + 231q^{48} + 147q^{49} - 309q^{52} - 297q^{54} - 273q^{58} + 78q^{59} + 303q^{62} - 45q^{64} - 33q^{72} + 399q^{78} + 243q^{81} - 129q^{82} + 246q^{87} - 276q^{92} - 546q^{93} - 57q^{94} - 21q^{96} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(23, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
23.3.b.a \(3\) \(0.627\) 3.3.621.1 \(\Q(\sqrt{-23}) \) \(0\) \(0\) \(0\) \(0\) \(q+(\beta _{1}+\beta _{2})q^{2}+(-2\beta _{1}-\beta _{2})q^{3}+(4+\cdots)q^{4}+\cdots\)

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ \( 1 + 7 T^{3} + 64 T^{6} \)
$3$ \( 1 + 38 T^{3} + 729 T^{6} \)
$5$ \( ( 1 - 5 T )^{3}( 1 + 5 T )^{3} \)
$7$ \( ( 1 - 7 T )^{3}( 1 + 7 T )^{3} \)
$11$ \( ( 1 - 11 T )^{3}( 1 + 11 T )^{3} \)
$13$ \( 1 - 1082 T^{3} + 4826809 T^{6} \)
$17$ \( ( 1 - 17 T )^{3}( 1 + 17 T )^{3} \)
$19$ \( ( 1 - 19 T )^{3}( 1 + 19 T )^{3} \)
$23$ \( ( 1 + 23 T )^{3} \)
$29$ \( 1 - 30746 T^{3} + 594823321 T^{6} \)
$31$ \( 1 - 58754 T^{3} + 887503681 T^{6} \)
$37$ \( ( 1 - 37 T )^{3}( 1 + 37 T )^{3} \)
$41$ \( 1 - 43634 T^{3} + 4750104241 T^{6} \)
$43$ \( ( 1 - 43 T )^{3}( 1 + 43 T )^{3} \)
$47$ \( 1 + 205342 T^{3} + 10779215329 T^{6} \)
$53$ \( ( 1 - 53 T )^{3}( 1 + 53 T )^{3} \)
$59$ \( ( 1 - 26 T + 3481 T^{2} )^{3} \)
$61$ \( ( 1 - 61 T )^{3}( 1 + 61 T )^{3} \)
$67$ \( ( 1 - 67 T )^{3}( 1 + 67 T )^{3} \)
$71$ \( 1 - 667154 T^{3} + 128100283921 T^{6} \)
$73$ \( 1 - 725042 T^{3} + 151334226289 T^{6} \)
$79$ \( ( 1 - 79 T )^{3}( 1 + 79 T )^{3} \)
$83$ \( ( 1 - 83 T )^{3}( 1 + 83 T )^{3} \)
$89$ \( ( 1 - 89 T )^{3}( 1 + 89 T )^{3} \)
$97$ \( ( 1 - 97 T )^{3}( 1 + 97 T )^{3} \)
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