Properties

Label 63.2.c
Level 63
Weight 2
Character orbit c
Rep. character \(\chi_{63}(62,\cdot)\)
Character field \(\Q\)
Dimension 4
Newform subspaces 1
Sturm bound 16
Trace bound 0

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Defining parameters

Level: \( N \) = \( 63 = 3^{2} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 63.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 21 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(16\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(63, [\chi])\).

Total New Old
Modular forms 12 4 8
Cusp forms 4 4 0
Eisenstein series 8 0 8

Trace form

\( 4q - 8q^{4} + O(q^{10}) \) \( 4q - 8q^{4} + 12q^{16} + 20q^{22} - 20q^{25} - 28q^{28} + 44q^{46} + 28q^{49} - 52q^{58} - 24q^{64} - 16q^{67} + 32q^{79} + 28q^{88} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(63, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
63.2.c.a \(4\) \(0.503\) \(\Q(\sqrt{-2}, \sqrt{7})\) \(\Q(\sqrt{-7}) \) \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+(-2+\beta _{2})q^{4}-\beta _{2}q^{7}+(-2\beta _{1}+\cdots)q^{8}+\cdots\)

Hecke Characteristic Polynomials

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