Properties

Label 504.2.ch
Level 504
Weight 2
Character orbit ch
Rep. character \(\chi_{504}(269,\cdot)\)
Character field \(\Q(\zeta_{6})\)
Dimension 64
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.ch (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 168 \)
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 208 64 144
Cusp forms 176 64 112
Eisenstein series 32 0 32

Trace form

\( 64q + O(q^{10}) \) \( 64q + 4q^{16} - 16q^{22} + 32q^{25} + 44q^{28} + 60q^{40} - 16q^{46} + 16q^{49} + 36q^{52} - 44q^{58} - 24q^{64} - 60q^{70} + 48q^{73} + 16q^{79} - 132q^{82} + 4q^{88} - 108q^{94} + O(q^{100}) \)

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.ch.a \(8\) \(4.024\) 8.0.4857532416.2 None \(0\) \(0\) \(0\) \(20\) \(q+\beta _{2}q^{2}+(2-2\beta _{3})q^{4}-\beta _{5}q^{5}+(3+\cdots)q^{7}+\cdots\)
504.2.ch.b \(56\) \(4.024\) None \(0\) \(0\) \(0\) \(-20\)

Decomposition of \(S_{2}^{\mathrm{old}}(504, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(504, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(168, [\chi])\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ (\( ( 1 - 2 T^{2} + 4 T^{4} )^{2} \))
$3$ 1
$5$ (\( ( 1 - 3 T + 4 T^{2} - 15 T^{3} + 25 T^{4} )^{2}( 1 + 3 T + 4 T^{2} + 15 T^{3} + 25 T^{4} )^{2} \))
$7$ (\( ( 1 - 5 T + 7 T^{2} )^{4} \))
$11$ (\( ( 1 + 11 T^{2} )^{4}( 1 - 11 T^{2} + 121 T^{4} )^{2} \))
$13$ (\( ( 1 + 4 T^{2} + 169 T^{4} )^{4} \))
$17$ (\( ( 1 - 28 T^{2} + 495 T^{4} - 8092 T^{6} + 83521 T^{8} )^{2} \))
$19$ (\( ( 1 - 16 T^{2} - 105 T^{4} - 5776 T^{6} + 130321 T^{8} )^{2} \))
$23$ (\( ( 1 + 44 T^{2} + 1407 T^{4} + 23276 T^{6} + 279841 T^{8} )^{2} \))
$29$ (\( ( 1 + 25 T^{2} + 841 T^{4} )^{4} \))
$31$ (\( ( 1 - 9 T + 58 T^{2} - 279 T^{3} + 961 T^{4} )^{4} \))
$37$ (\( ( 1 + 8 T^{2} - 1305 T^{4} + 10952 T^{6} + 1874161 T^{8} )^{2} \))
$41$ (\( ( 1 - 14 T^{2} + 1681 T^{4} )^{4} \))
$43$ (\( ( 1 - 20 T^{2} + 1849 T^{4} )^{4} \))
$47$ (\( ( 1 - 40 T^{2} - 609 T^{4} - 88360 T^{6} + 4879681 T^{8} )^{2} \))
$53$ (\( ( 1 - 73 T^{2} + 2520 T^{4} - 205057 T^{6} + 7890481 T^{8} )^{2} \))
$59$ (\( ( 1 - 15 T + 166 T^{2} - 885 T^{3} + 3481 T^{4} )^{2}( 1 + 15 T + 166 T^{2} + 885 T^{3} + 3481 T^{4} )^{2} \))
$61$ (\( ( 1 - 100 T^{2} + 6279 T^{4} - 372100 T^{6} + 13845841 T^{8} )^{2} \))
$67$ (\( ( 1 + 67 T^{2} + 4489 T^{4} )^{4} \))
$71$ (\( ( 1 - 140 T^{2} + 5041 T^{4} )^{4} \))
$73$ (\( ( 1 + 6 T + 85 T^{2} + 438 T^{3} + 5329 T^{4} )^{4} \))
$79$ (\( ( 1 - 7 T - 30 T^{2} - 553 T^{3} + 6241 T^{4} )^{4} \))
$83$ (\( ( 1 - 155 T^{2} + 6889 T^{4} )^{4} \))
$89$ (\( ( 1 - 82 T^{2} - 1197 T^{4} - 649522 T^{6} + 62742241 T^{8} )^{2} \))
$97$ (\( ( 1 - 191 T^{2} + 9409 T^{4} )^{4} \))
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