Properties

Label 504.2.k
Level 504
Weight 2
Character orbit k
Rep. character \(\chi_{504}(377,\cdot)\)
Character field \(\Q\)
Dimension 8
Newform subspaces 1
Sturm bound 192
Trace bound 0

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Defining parameters

Level: \( N \) = \( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 504.k (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 21 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(192\)
Trace bound: \(0\)

Dimensions

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

Total New Old
Modular forms 112 8 104
Cusp forms 80 8 72
Eisenstein series 32 0 32

Trace form

\( 8q + 8q^{7} + O(q^{10}) \) \( 8q + 8q^{7} + 24q^{25} + 32q^{37} + 16q^{43} - 8q^{49} - 32q^{67} - 64q^{79} - 64q^{85} + O(q^{100}) \)

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.k.a \(8\) \(4.024\) \(\Q(\zeta_{16})\) None \(0\) \(0\) \(0\) \(8\) \(q-\zeta_{16}^{7}q^{5}+(1+\zeta_{16}^{4})q^{7}+(\zeta_{16}+\zeta_{16}^{2}+\cdots)q^{11}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(504, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(168, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(252, [\chi])\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ \( \)
$3$ \( \)
$5$ \( ( 1 + 4 T^{2} + 22 T^{4} + 100 T^{6} + 625 T^{8} )^{2} \)
$7$ \( ( 1 - 4 T + 10 T^{2} - 28 T^{3} + 49 T^{4} )^{2} \)
$11$ \( ( 1 - 32 T^{2} + 466 T^{4} - 3872 T^{6} + 14641 T^{8} )^{2} \)
$13$ \( ( 1 - 20 T^{2} + 310 T^{4} - 3380 T^{6} + 28561 T^{8} )^{2} \)
$17$ \( ( 1 - 12 T^{2} + 582 T^{4} - 3468 T^{6} + 83521 T^{8} )^{2} \)
$19$ \( ( 1 - 44 T^{2} + 1078 T^{4} - 15884 T^{6} + 130321 T^{8} )^{2} \)
$23$ \( ( 1 - 48 T^{2} + 1346 T^{4} - 25392 T^{6} + 279841 T^{8} )^{2} \)
$29$ \( ( 1 - 80 T^{2} + 3154 T^{4} - 67280 T^{6} + 707281 T^{8} )^{2} \)
$31$ \( ( 1 + 4 T^{2} - 122 T^{4} + 3844 T^{6} + 923521 T^{8} )^{2} \)
$37$ \( ( 1 - 4 T + 37 T^{2} )^{8} \)
$41$ \( ( 1 + 84 T^{2} + 3558 T^{4} + 141204 T^{6} + 2825761 T^{8} )^{2} \)
$43$ \( ( 1 - 4 T + 18 T^{2} - 172 T^{3} + 1849 T^{4} )^{4} \)
$47$ \( ( 1 + 124 T^{2} + 7750 T^{4} + 273916 T^{6} + 4879681 T^{8} )^{2} \)
$53$ \( ( 1 - 176 T^{2} + 13234 T^{4} - 494384 T^{6} + 7890481 T^{8} )^{2} \)
$59$ \( ( 1 + 59 T^{2} )^{8} \)
$61$ \( ( 1 - 61 T^{2} )^{8} \)
$67$ \( ( 1 + 8 T + 118 T^{2} + 536 T^{3} + 4489 T^{4} )^{4} \)
$71$ \( ( 1 - 208 T^{2} + 20610 T^{4} - 1048528 T^{6} + 25411681 T^{8} )^{2} \)
$73$ \( ( 1 - 132 T^{2} + 8742 T^{4} - 703428 T^{6} + 28398241 T^{8} )^{2} \)
$79$ \( ( 1 + 16 T + 190 T^{2} + 1264 T^{3} + 6241 T^{4} )^{4} \)
$83$ \( ( 1 + 12 T^{2} + 13302 T^{4} + 82668 T^{6} + 47458321 T^{8} )^{2} \)
$89$ \( ( 1 + 276 T^{2} + 34854 T^{4} + 2186196 T^{6} + 62742241 T^{8} )^{2} \)
$97$ \( ( 1 - 228 T^{2} + 31686 T^{4} - 2145252 T^{6} + 88529281 T^{8} )^{2} \)
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