Properties

Label 63.2.e
Level 63
Weight 2
Character orbit e
Rep. character \(\chi_{63}(37,\cdot)\)
Character field \(\Q(\zeta_{3})\)
Dimension 4
Newform subspaces 2
Sturm bound 16
Trace bound 2

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Defining parameters

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

Dimensions

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

Total New Old
Modular forms 24 8 16
Cusp forms 8 4 4
Eisenstein series 16 4 12

Trace form

\( 4q + 2q^{2} - 2q^{5} - 6q^{7} + O(q^{10}) \) \( 4q + 2q^{2} - 2q^{5} - 6q^{7} + 4q^{10} - 2q^{11} - 12q^{13} - 2q^{14} + 6q^{19} + 8q^{20} - 8q^{22} + 6q^{25} + 2q^{26} + 16q^{28} - 8q^{29} - 2q^{31} - 8q^{32} + 2q^{35} - 2q^{37} + 2q^{38} + 20q^{41} + 20q^{43} - 4q^{44} - 6q^{47} - 2q^{49} + 4q^{50} - 16q^{52} + 12q^{53} + 8q^{55} - 8q^{58} - 12q^{59} - 24q^{61} - 36q^{62} - 32q^{64} - 2q^{65} - 6q^{67} - 16q^{70} + 12q^{71} + 10q^{73} + 6q^{74} + 32q^{76} + 8q^{77} + 14q^{79} + 8q^{80} + 20q^{82} - 12q^{83} + 10q^{86} + 16q^{89} + 2q^{91} + 12q^{94} - 2q^{95} + 16q^{97} - 4q^{98} + O(q^{100}) \)

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.e.a \(2\) \(0.503\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(-1\) \(q+2\zeta_{6}q^{4}+(1-3\zeta_{6})q^{7}-7q^{13}+(-4+\cdots)q^{16}+\cdots\)
63.2.e.b \(2\) \(0.503\) \(\Q(\sqrt{-3}) \) None \(2\) \(0\) \(-2\) \(-5\) \(q+(2-2\zeta_{6})q^{2}-2\zeta_{6}q^{4}+(-2+2\zeta_{6})q^{5}+\cdots\)

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

$p$ $F_p(T)$
$2$ (\( 1 - 2 T^{2} + 4 T^{4} \))(\( 1 - 2 T + 2 T^{2} - 4 T^{3} + 4 T^{4} \))
$3$ (\( \))(\( \))
$5$ (\( 1 - 5 T^{2} + 25 T^{4} \))(\( 1 + 2 T - T^{2} + 10 T^{3} + 25 T^{4} \))
$7$ (\( 1 + T + 7 T^{2} \))(\( 1 + 5 T + 7 T^{2} \))
$11$ (\( 1 - 11 T^{2} + 121 T^{4} \))(\( 1 + 2 T - 7 T^{2} + 22 T^{3} + 121 T^{4} \))
$13$ (\( ( 1 + 7 T + 13 T^{2} )^{2} \))(\( ( 1 - T + 13 T^{2} )^{2} \))
$17$ (\( 1 - 17 T^{2} + 289 T^{4} \))(\( 1 - 17 T^{2} + 289 T^{4} \))
$19$ (\( ( 1 - 8 T + 19 T^{2} )( 1 + T + 19 T^{2} ) \))(\( ( 1 - 7 T + 19 T^{2} )( 1 + 8 T + 19 T^{2} ) \))
$23$ (\( 1 - 23 T^{2} + 529 T^{4} \))(\( 1 - 23 T^{2} + 529 T^{4} \))
$29$ (\( ( 1 + 29 T^{2} )^{2} \))(\( ( 1 + 4 T + 29 T^{2} )^{2} \))
$31$ (\( ( 1 - 11 T + 31 T^{2} )( 1 + 4 T + 31 T^{2} ) \))(\( 1 + 9 T + 50 T^{2} + 279 T^{3} + 961 T^{4} \))
$37$ (\( ( 1 - 11 T + 37 T^{2} )( 1 + 10 T + 37 T^{2} ) \))(\( 1 + 3 T - 28 T^{2} + 111 T^{3} + 1369 T^{4} \))
$41$ (\( ( 1 + 41 T^{2} )^{2} \))(\( ( 1 - 10 T + 41 T^{2} )^{2} \))
$43$ (\( ( 1 - 5 T + 43 T^{2} )^{2} \))(\( ( 1 - 5 T + 43 T^{2} )^{2} \))
$47$ (\( 1 - 47 T^{2} + 2209 T^{4} \))(\( 1 + 6 T - 11 T^{2} + 282 T^{3} + 2209 T^{4} \))
$53$ (\( 1 - 53 T^{2} + 2809 T^{4} \))(\( 1 - 12 T + 91 T^{2} - 636 T^{3} + 2809 T^{4} \))
$59$ (\( 1 - 59 T^{2} + 3481 T^{4} \))(\( 1 + 12 T + 85 T^{2} + 708 T^{3} + 3481 T^{4} \))
$61$ (\( ( 1 + T + 61 T^{2} )( 1 + 13 T + 61 T^{2} ) \))(\( 1 + 10 T + 39 T^{2} + 610 T^{3} + 3721 T^{4} \))
$67$ (\( ( 1 - 5 T + 67 T^{2} )( 1 + 16 T + 67 T^{2} ) \))(\( ( 1 - 16 T + 67 T^{2} )( 1 + 11 T + 67 T^{2} ) \))
$71$ (\( ( 1 + 71 T^{2} )^{2} \))(\( ( 1 - 6 T + 71 T^{2} )^{2} \))
$73$ (\( ( 1 - 17 T + 73 T^{2} )( 1 + 10 T + 73 T^{2} ) \))(\( 1 - 3 T - 64 T^{2} - 219 T^{3} + 5329 T^{4} \))
$79$ (\( ( 1 - 17 T + 79 T^{2} )( 1 + 4 T + 79 T^{2} ) \))(\( 1 - T - 78 T^{2} - 79 T^{3} + 6241 T^{4} \))
$83$ (\( ( 1 + 83 T^{2} )^{2} \))(\( ( 1 + 6 T + 83 T^{2} )^{2} \))
$89$ (\( 1 - 89 T^{2} + 7921 T^{4} \))(\( 1 - 16 T + 167 T^{2} - 1424 T^{3} + 7921 T^{4} \))
$97$ (\( ( 1 - 14 T + 97 T^{2} )^{2} \))(\( ( 1 + 6 T + 97 T^{2} )^{2} \))
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