Properties

Label 504.2.cc
Level 504
Weight 2
Character orbit cc
Rep. character \(\chi_{504}(293,\cdot)\)
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.cc (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

\( 184q - 6q^{2} - 2q^{4} - 2q^{7} - 8q^{9} + O(q^{10}) \) \( 184q - 6q^{2} - 2q^{4} - 2q^{7} - 8q^{9} + 12q^{14} - 20q^{15} - 2q^{16} - 18q^{18} + 6q^{22} - 12q^{23} + 72q^{25} + 4q^{28} - 20q^{30} + 24q^{32} - 26q^{36} + 4q^{39} - 16q^{46} - 2q^{49} - 36q^{50} - 24q^{56} - 32q^{57} + 6q^{58} - 20q^{60} - 30q^{63} - 8q^{64} - 12q^{65} - 6q^{70} - 12q^{72} + 48q^{74} - 56q^{78} - 4q^{79} - 24q^{81} - 72q^{84} - 144q^{86} - 18q^{88} + 54q^{92} - 72q^{95} + O(q^{100}) \)

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.cc.a \(16\) \(4.024\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) \(\Q(\sqrt{-14}) \) \(0\) \(0\) \(0\) \(0\) \(q+\beta _{11}q^{2}-\beta _{14}q^{3}+(2-2\beta _{4})q^{4}+\cdots\)
504.2.cc.b \(168\) \(4.024\) None \(-6\) \(0\) \(0\) \(-2\)

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ (\( ( 1 - 2 T^{2} + 4 T^{4} )^{4} \))
$3$ (\( ( 1 - 10 T^{4} + 81 T^{8} )^{2} \))
$5$ (\( ( 1 + 22 T^{4} + 625 T^{8} )^{2}( 1 - 22 T^{4} - 141 T^{8} - 13750 T^{12} + 390625 T^{16} ) \))
$7$ (\( ( 1 + 7 T^{2} + 49 T^{4} )^{4} \))
$11$ (\( ( 1 - 11 T^{2} + 121 T^{4} )^{8} \))
$13$ (\( ( 1 - 310 T^{4} + 67539 T^{8} - 8853910 T^{12} + 815730721 T^{16} )^{2} \))
$17$ (\( ( 1 + 17 T^{2} )^{16} \))
$19$ (\( ( 1 + 650 T^{4} + 292179 T^{8} + 84708650 T^{12} + 16983563041 T^{16} )^{2} \))
$23$ (\( ( 1 - 6 T + 23 T^{2} )^{8}( 1 - 6 T + 13 T^{2} - 138 T^{3} + 529 T^{4} )^{4} \))
$29$ (\( ( 1 - 29 T^{2} + 841 T^{4} )^{8} \))
$31$ (\( ( 1 + 31 T^{2} + 961 T^{4} )^{8} \))
$37$ (\( ( 1 - 37 T^{2} )^{16} \))
$41$ (\( ( 1 - 41 T^{2} + 1681 T^{4} )^{8} \))
$43$ (\( ( 1 + 43 T^{2} + 1849 T^{4} )^{8} \))
$47$ (\( ( 1 - 47 T^{2} + 2209 T^{4} )^{8} \))
$53$ (\( ( 1 + 53 T^{2} )^{16} \))
$59$ (\( ( 1 + 1130 T^{4} - 10840461 T^{8} + 13692617930 T^{12} + 146830437604321 T^{16} )^{2} \))
$61$ (\( ( 1 - 7370 T^{4} + 13845841 T^{8} )^{2}( 1 + 7370 T^{4} + 40471059 T^{8} + 102043848170 T^{12} + 191707312997281 T^{16} ) \))
$67$ (\( ( 1 + 67 T^{2} + 4489 T^{4} )^{8} \))
$71$ (\( ( 1 + 110 T^{2} + 7059 T^{4} + 554510 T^{6} + 25411681 T^{8} )^{4} \))
$73$ (\( ( 1 - 73 T^{2} )^{16} \))
$79$ (\( ( 1 + 130 T^{2} + 6241 T^{4} )^{4}( 1 - 130 T^{2} + 10659 T^{4} - 811330 T^{6} + 38950081 T^{8} )^{2} \))
$83$ (\( ( 1 + 13130 T^{4} + 124938579 T^{8} + 623127754730 T^{12} + 2252292232139041 T^{16} )^{2} \))
$89$ (\( ( 1 + 89 T^{2} )^{16} \))
$97$ (\( ( 1 + 97 T^{2} + 9409 T^{4} )^{8} \))
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