Properties

Label 504.2.i
Level 504
Weight 2
Character orbit i
Rep. character \(\chi_{504}(125,\cdot)\)
Character field \(\Q\)
Dimension 32
Newform subspaces 2
Sturm bound 192
Trace bound 1

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 504.i (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 168 \)
Character field: \(\Q\)
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 104 32 72
Cusp forms 88 32 56
Eisenstein series 16 0 16

Trace form

\( 32q + O(q^{10}) \) \( 32q - 4q^{16} + 28q^{22} - 32q^{25} + 4q^{28} - 44q^{46} - 16q^{49} - 4q^{58} + 96q^{64} - 24q^{70} - 16q^{79} - 76q^{88} + O(q^{100}) \)

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.i.a \(8\) \(4.024\) 8.0.157351936.1 \(\Q(\sqrt{-7}) \) \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+\beta _{2}q^{4}+(\beta _{2}-\beta _{5})q^{7}+\beta _{3}q^{8}+\cdots\)
504.2.i.b \(24\) \(4.024\) None \(0\) \(0\) \(0\) \(0\)

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

$p$ $F_p(T)$
$2$ (\( 1 + T^{4} + 16 T^{8} \))
$3$ 1
$5$ (\( ( 1 - 5 T^{2} )^{8} \))
$7$ (\( ( 1 - 7 T^{2} )^{4} \))
$11$ (\( ( 1 - 206 T^{4} + 14641 T^{8} )^{2} \))
$13$ (\( ( 1 + 13 T^{2} )^{8} \))
$17$ (\( ( 1 + 17 T^{2} )^{8} \))
$19$ (\( ( 1 + 19 T^{2} )^{8} \))
$23$ (\( ( 1 - 734 T^{4} + 279841 T^{8} )^{2} \))
$29$ (\( ( 1 + 1234 T^{4} + 707281 T^{8} )^{2} \))
$31$ (\( ( 1 - 31 T^{2} )^{8} \))
$37$ (\( ( 1 - 38 T^{2} + 1369 T^{4} )^{4} \))
$41$ (\( ( 1 + 41 T^{2} )^{8} \))
$43$ (\( ( 1 + 58 T^{2} + 1849 T^{4} )^{4} \))
$47$ (\( ( 1 + 47 T^{2} )^{8} \))
$53$ (\( ( 1 - 5582 T^{4} + 7890481 T^{8} )^{2} \))
$59$ (\( ( 1 - 59 T^{2} )^{8} \))
$61$ (\( ( 1 + 61 T^{2} )^{8} \))
$67$ (\( ( 1 - 4 T + 67 T^{2} )^{4}( 1 + 4 T + 67 T^{2} )^{4} \))
$71$ (\( ( 1 + 2914 T^{4} + 25411681 T^{8} )^{2} \))
$73$ (\( ( 1 - 73 T^{2} )^{8} \))
$79$ (\( ( 1 + 8 T + 79 T^{2} )^{8} \))
$83$ (\( ( 1 - 83 T^{2} )^{8} \))
$89$ (\( ( 1 + 89 T^{2} )^{8} \))
$97$ (\( ( 1 - 97 T^{2} )^{8} \))
show more
show less