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Properties

Label 23.2.a
Level 23
Weight 2
Character orbit a
Rep. character \(\chi_{23}(1,\cdot)\)
Character field \(\Q\)
Dimension 2
Newform subspaces 1
Sturm bound 4
Trace bound 0

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Defining parameters

Level: \( N \) \(=\) \( 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 23.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(4\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(23))\).

Total New Old
Modular forms 3 3 0
Cusp forms 2 2 0
Eisenstein series 1 1 0

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(23\)Dim.
\(-\)\(2\)

Trace form

\( 2q - q^{2} - q^{4} - 2q^{5} - 5q^{6} + 2q^{7} + 4q^{9} + O(q^{10}) \) \( 2q - q^{2} - q^{4} - 2q^{5} - 5q^{6} + 2q^{7} + 4q^{9} + 6q^{10} - 6q^{11} + 5q^{12} + 6q^{13} + 4q^{14} - 10q^{15} - 3q^{16} + 6q^{17} - 2q^{18} - 4q^{19} - 4q^{20} - 10q^{21} - 2q^{22} + 2q^{23} + 10q^{24} + 2q^{25} - 3q^{26} - 6q^{28} - 6q^{29} + 10q^{30} + 9q^{32} + 10q^{33} - 8q^{34} + 8q^{35} - 2q^{36} + 2q^{37} + 2q^{38} - 10q^{40} + 2q^{41} + 8q^{44} - 4q^{45} - q^{46} - 15q^{48} - 2q^{49} - 11q^{50} + 10q^{51} - 3q^{52} - 8q^{53} + 5q^{54} - 4q^{55} - 10q^{56} + 3q^{58} + 4q^{59} + 4q^{61} + 15q^{62} + 4q^{63} + 4q^{64} - 6q^{65} + 10q^{66} - 10q^{67} + 2q^{68} - 4q^{70} + 20q^{71} + 22q^{73} - 6q^{74} + 20q^{75} + 2q^{76} - 16q^{77} - 15q^{78} - 4q^{79} + 18q^{80} - 22q^{81} - 11q^{82} - 22q^{83} + 10q^{84} - 16q^{85} + 10q^{88} - 12q^{89} + 12q^{90} + 6q^{91} - q^{92} - 30q^{93} - 5q^{94} + 4q^{95} - 5q^{96} + 22q^{97} + 11q^{98} - 12q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(23))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 23
23.2.a.a \(2\) \(0.184\) \(\Q(\sqrt{5}) \) None \(-1\) \(0\) \(-2\) \(2\) \(-\) \(q-\beta q^{2}+(-1+2\beta )q^{3}+(-1+\beta )q^{4}+\cdots\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( 1 + T + 3 T^{2} + 2 T^{3} + 4 T^{4} \)
$3$ \( 1 + T^{2} + 9 T^{4} \)
$5$ \( 1 + 2 T + 6 T^{2} + 10 T^{3} + 25 T^{4} \)
$7$ \( 1 - 2 T + 10 T^{2} - 14 T^{3} + 49 T^{4} \)
$11$ \( 1 + 6 T + 26 T^{2} + 66 T^{3} + 121 T^{4} \)
$13$ \( ( 1 - 3 T + 13 T^{2} )^{2} \)
$17$ \( 1 - 6 T + 38 T^{2} - 102 T^{3} + 289 T^{4} \)
$19$ \( ( 1 + 2 T + 19 T^{2} )^{2} \)
$23$ \( ( 1 - T )^{2} \)
$29$ \( ( 1 + 3 T + 29 T^{2} )^{2} \)
$31$ \( 1 + 17 T^{2} + 961 T^{4} \)
$37$ \( 1 - 2 T + 70 T^{2} - 74 T^{3} + 1369 T^{4} \)
$41$ \( 1 - 2 T + 63 T^{2} - 82 T^{3} + 1681 T^{4} \)
$43$ \( ( 1 + 43 T^{2} )^{2} \)
$47$ \( 1 + 89 T^{2} + 2209 T^{4} \)
$53$ \( 1 + 8 T + 102 T^{2} + 424 T^{3} + 2809 T^{4} \)
$59$ \( 1 - 4 T + 102 T^{2} - 236 T^{3} + 3481 T^{4} \)
$61$ \( 1 - 4 T + 46 T^{2} - 244 T^{3} + 3721 T^{4} \)
$67$ \( 1 + 10 T + 154 T^{2} + 670 T^{3} + 4489 T^{4} \)
$71$ \( 1 - 20 T + 237 T^{2} - 1420 T^{3} + 5041 T^{4} \)
$73$ \( 1 - 22 T + 247 T^{2} - 1606 T^{3} + 5329 T^{4} \)
$79$ \( 1 + 4 T + 82 T^{2} + 316 T^{3} + 6241 T^{4} \)
$83$ \( 1 + 22 T + 282 T^{2} + 1826 T^{3} + 6889 T^{4} \)
$89$ \( 1 + 12 T + 194 T^{2} + 1068 T^{3} + 7921 T^{4} \)
$97$ \( 1 - 22 T + 270 T^{2} - 2134 T^{3} + 9409 T^{4} \)
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