Properties

Label 18.4.a
Level 18
Weight 4
Character orbit a
Rep. character \(\chi_{18}(1,\cdot)\)
Character field \(\Q\)
Dimension 1
Newform subspaces 1
Sturm bound 12
Trace bound 0

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Defining parameters

Level: \( N \) = \( 18 = 2 \cdot 3^{2} \)
Weight: \( k \) = \( 4 \)
Character orbit: \([\chi]\) = 18.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(12\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(18))\).

Total New Old
Modular forms 13 1 12
Cusp forms 5 1 4
Eisenstein series 8 0 8

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

\(2\)\(3\)FrickeDim.
\(-\)\(-\)\(+\)\(1\)
Plus space\(+\)\(1\)
Minus space\(-\)\(0\)

Trace form

\( q + 2q^{2} + 4q^{4} - 6q^{5} - 16q^{7} + 8q^{8} + O(q^{10}) \) \( q + 2q^{2} + 4q^{4} - 6q^{5} - 16q^{7} + 8q^{8} - 12q^{10} - 12q^{11} + 38q^{13} - 32q^{14} + 16q^{16} + 126q^{17} + 20q^{19} - 24q^{20} - 24q^{22} - 168q^{23} - 89q^{25} + 76q^{26} - 64q^{28} - 30q^{29} - 88q^{31} + 32q^{32} + 252q^{34} + 96q^{35} + 254q^{37} + 40q^{38} - 48q^{40} - 42q^{41} - 52q^{43} - 48q^{44} - 336q^{46} + 96q^{47} - 87q^{49} - 178q^{50} + 152q^{52} - 198q^{53} + 72q^{55} - 128q^{56} - 60q^{58} + 660q^{59} - 538q^{61} - 176q^{62} + 64q^{64} - 228q^{65} + 884q^{67} + 504q^{68} + 192q^{70} - 792q^{71} + 218q^{73} + 508q^{74} + 80q^{76} + 192q^{77} - 520q^{79} - 96q^{80} - 84q^{82} + 492q^{83} - 756q^{85} - 104q^{86} - 96q^{88} - 810q^{89} - 608q^{91} - 672q^{92} + 192q^{94} - 120q^{95} + 1154q^{97} - 174q^{98} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(18))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 3
18.4.a.a \(1\) \(1.062\) \(\Q\) None \(2\) \(0\) \(-6\) \(-16\) \(-\) \(-\) \(q+2q^{2}+4q^{4}-6q^{5}-2^{4}q^{7}+8q^{8}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(18))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(18)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_0(6))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(9))\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ \( 1 - 2 T \)
$3$ \( \)
$5$ \( 1 + 6 T + 125 T^{2} \)
$7$ \( 1 + 16 T + 343 T^{2} \)
$11$ \( 1 + 12 T + 1331 T^{2} \)
$13$ \( 1 - 38 T + 2197 T^{2} \)
$17$ \( 1 - 126 T + 4913 T^{2} \)
$19$ \( 1 - 20 T + 6859 T^{2} \)
$23$ \( 1 + 168 T + 12167 T^{2} \)
$29$ \( 1 + 30 T + 24389 T^{2} \)
$31$ \( 1 + 88 T + 29791 T^{2} \)
$37$ \( 1 - 254 T + 50653 T^{2} \)
$41$ \( 1 + 42 T + 68921 T^{2} \)
$43$ \( 1 + 52 T + 79507 T^{2} \)
$47$ \( 1 - 96 T + 103823 T^{2} \)
$53$ \( 1 + 198 T + 148877 T^{2} \)
$59$ \( 1 - 660 T + 205379 T^{2} \)
$61$ \( 1 + 538 T + 226981 T^{2} \)
$67$ \( 1 - 884 T + 300763 T^{2} \)
$71$ \( 1 + 792 T + 357911 T^{2} \)
$73$ \( 1 - 218 T + 389017 T^{2} \)
$79$ \( 1 + 520 T + 493039 T^{2} \)
$83$ \( 1 - 492 T + 571787 T^{2} \)
$89$ \( 1 + 810 T + 704969 T^{2} \)
$97$ \( 1 - 1154 T + 912673 T^{2} \)
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