Properties

Label 63.2.p
Level 63
Weight 2
Character orbit p
Rep. character \(\chi_{63}(17,\cdot)\)
Character field \(\Q(\zeta_{6})\)
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.p (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 21 \)
Character field: \(\Q(\zeta_{6})\)
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 24 4 20
Cusp forms 8 4 4
Eisenstein series 16 0 16

Trace form

\( 4q - 2q^{7} + O(q^{10}) \) \( 4q - 2q^{7} - 12q^{10} + 8q^{16} + 6q^{19} - 8q^{22} - 2q^{25} + 6q^{31} + 2q^{37} + 24q^{40} - 4q^{43} + 16q^{46} - 26q^{49} - 8q^{58} - 12q^{61} - 32q^{64} - 22q^{67} + 24q^{70} + 6q^{73} - 10q^{79} - 36q^{82} + 48q^{85} + 8q^{88} + 54q^{91} + 60q^{94} + O(q^{100}) \)

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.p.a \(4\) \(0.503\) \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(0\) \(0\) \(0\) \(-2\) \(q+\beta _{1}q^{2}+(-\beta _{1}+2\beta _{3})q^{5}+(1-3\beta _{2}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(63, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(63, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ \( ( 1 + 2 T^{2} )^{2}( 1 - 2 T^{2} + 4 T^{4} ) \)
$3$ \( \)
$5$ \( 1 - 4 T^{2} - 9 T^{4} - 100 T^{6} + 625 T^{8} \)
$7$ \( ( 1 + T + 7 T^{2} )^{2} \)
$11$ \( 1 + 20 T^{2} + 279 T^{4} + 2420 T^{6} + 14641 T^{8} \)
$13$ \( ( 1 - 5 T + 13 T^{2} )^{2}( 1 + 5 T + 13 T^{2} )^{2} \)
$17$ \( 1 - 10 T^{2} - 189 T^{4} - 2890 T^{6} + 83521 T^{8} \)
$19$ \( ( 1 - 3 T + 22 T^{2} - 57 T^{3} + 361 T^{4} )^{2} \)
$23$ \( 1 + 14 T^{2} - 333 T^{4} + 7406 T^{6} + 279841 T^{8} \)
$29$ \( ( 1 - 50 T^{2} + 841 T^{4} )^{2} \)
$31$ \( ( 1 - 7 T + 31 T^{2} )^{2}( 1 + 4 T + 31 T^{2} )^{2} \)
$37$ \( ( 1 - 11 T + 37 T^{2} )^{2}( 1 + 10 T + 37 T^{2} )^{2} \)
$41$ \( ( 1 + 28 T^{2} + 1681 T^{4} )^{2} \)
$43$ \( ( 1 + T + 43 T^{2} )^{4} \)
$47$ \( 1 + 56 T^{2} + 927 T^{4} + 123704 T^{6} + 4879681 T^{8} \)
$53$ \( 1 + 98 T^{2} + 6795 T^{4} + 275282 T^{6} + 7890481 T^{8} \)
$59$ \( 1 - 94 T^{2} + 5355 T^{4} - 327214 T^{6} + 12117361 T^{8} \)
$61$ \( ( 1 + 6 T + 73 T^{2} + 366 T^{3} + 3721 T^{4} )^{2} \)
$67$ \( ( 1 - 5 T + 67 T^{2} )^{2}( 1 + 16 T + 67 T^{2} )^{2} \)
$71$ \( ( 1 - 92 T^{2} + 5041 T^{4} )^{2} \)
$73$ \( ( 1 - 10 T + 73 T^{2} )^{2}( 1 + 7 T + 73 T^{2} )^{2} \)
$79$ \( ( 1 + 5 T - 54 T^{2} + 395 T^{3} + 6241 T^{4} )^{2} \)
$83$ \( ( 1 + 112 T^{2} + 6889 T^{4} )^{2} \)
$89$ \( 1 - 154 T^{2} + 15795 T^{4} - 1219834 T^{6} + 62742241 T^{8} \)
$97$ \( ( 1 - 86 T^{2} + 9409 T^{4} )^{2} \)
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