Properties

Label 504.2.cz
Level 504
Weight 2
Character orbit cz
Rep. character \(\chi_{504}(187,\cdot)\)
Character field \(\Q(\zeta_{6})\)
Dimension 184
Newform subspaces 2
Sturm bound 192
Trace bound 1

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Defining parameters

Level: \( N \) = \( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 504.cz (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 504 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(192\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(504, [\chi])\).

Total New Old
Modular forms 200 200 0
Cusp forms 184 184 0
Eisenstein series 16 16 0

Trace form

\( 184q + q^{2} - 6q^{3} + q^{4} + 6q^{6} - 8q^{8} - 2q^{9} + O(q^{10}) \) \( 184q + q^{2} - 6q^{3} + q^{4} + 6q^{6} - 8q^{8} - 2q^{9} - 6q^{10} - 4q^{11} - 3q^{12} + 5q^{14} + q^{16} - 12q^{17} - 7q^{18} - 12q^{19} - 24q^{20} - 6q^{22} - 12q^{24} + 148q^{25} + 4q^{30} + 21q^{32} - 6q^{33} + 6q^{34} - 18q^{35} + 2q^{36} + 25q^{42} - 4q^{43} - 21q^{44} + 2q^{46} + 9q^{48} - 2q^{49} + 19q^{50} - 54q^{51} - 30q^{54} - 20q^{56} - 20q^{57} - 10q^{58} - 6q^{59} - 50q^{60} - 8q^{64} - 18q^{65} - 21q^{66} + 2q^{67} - 24q^{70} - 7q^{72} - 12q^{73} - 94q^{74} - 36q^{75} + 12q^{76} - 39q^{78} - 63q^{80} - 10q^{81} - 12q^{82} - 60q^{83} - 41q^{84} + 62q^{86} - 18q^{88} - 36q^{89} + 33q^{90} + 20q^{91} - 32q^{92} - 3q^{94} - 54q^{96} + 27q^{98} - 26q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(504, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
504.2.cz.a \(4\) \(4.024\) \(\Q(\zeta_{12})\) None \(-2\) \(-6\) \(0\) \(0\) \(q+(-\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{2}+(-1+\cdots)q^{3}+\cdots\)
504.2.cz.b \(180\) \(4.024\) None \(3\) \(0\) \(0\) \(0\)

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ (\( 1 + 2 T + 2 T^{2} + 4 T^{3} + 4 T^{4} \))
$3$ (\( ( 1 + 3 T + 3 T^{2} )^{2} \))
$5$ (\( ( 1 + 7 T^{2} + 25 T^{4} )^{2} \))
$7$ (\( 1 + 11 T^{2} + 49 T^{4} \))
$11$ (\( ( 1 + 5 T + 11 T^{2} )^{4} \))
$13$ (\( ( 1 - 22 T^{2} + 169 T^{4} )( 1 - T^{2} + 169 T^{4} ) \))
$17$ (\( ( 1 - 3 T + 20 T^{2} - 51 T^{3} + 289 T^{4} )^{2} \))
$19$ (\( ( 1 + 3 T + 22 T^{2} + 57 T^{3} + 361 T^{4} )^{2} \))
$23$ (\( ( 1 + 3 T^{2} + 529 T^{4} )^{2} \))
$29$ (\( 1 + 9 T^{2} - 760 T^{4} + 7569 T^{6} + 707281 T^{8} \))
$31$ (\( 1 - 14 T^{2} - 765 T^{4} - 13454 T^{6} + 923521 T^{8} \))
$37$ (\( ( 1 + 26 T^{2} + 1369 T^{4} )( 1 + 47 T^{2} + 1369 T^{4} ) \))
$41$ (\( ( 1 + 21 T + 188 T^{2} + 861 T^{3} + 1681 T^{4} )^{2} \))
$43$ (\( ( 1 + 9 T + 38 T^{2} + 387 T^{3} + 1849 T^{4} )^{2} \))
$47$ (\( 1 - 82 T^{2} + 4515 T^{4} - 181138 T^{6} + 4879681 T^{8} \))
$53$ (\( 1 - 15 T^{2} - 2584 T^{4} - 42135 T^{6} + 7890481 T^{8} \))
$59$ (\( ( 1 + 12 T + 107 T^{2} + 708 T^{3} + 3481 T^{4} )^{2} \))
$61$ (\( 1 - 110 T^{2} + 8379 T^{4} - 409310 T^{6} + 13845841 T^{8} \))
$67$ (\( ( 1 - 8 T - 3 T^{2} - 536 T^{3} + 4489 T^{4} )^{2} \))
$71$ (\( ( 1 - 42 T^{2} + 5041 T^{4} )^{2} \))
$73$ (\( ( 1 + 15 T + 148 T^{2} + 1095 T^{3} + 5329 T^{4} )^{2} \))
$79$ (\( 1 + 122 T^{2} + 8643 T^{4} + 761402 T^{6} + 38950081 T^{8} \))
$83$ (\( ( 1 + 27 T + 326 T^{2} + 2241 T^{3} + 6889 T^{4} )^{2} \))
$89$ (\( ( 1 - 15 T + 164 T^{2} - 1335 T^{3} + 7921 T^{4} )^{2} \))
$97$ (\( ( 1 + 3 T + 100 T^{2} + 291 T^{3} + 9409 T^{4} )^{2} \))
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