Properties

Label 64.2.e
Level 64
Weight 2
Character orbit e
Rep. character \(\chi_{64}(17,\cdot)\)
Character field \(\Q(\zeta_{4})\)
Dimension 2
Newform subspaces 1
Sturm bound 16
Trace bound 0

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Defining parameters

Level: \( N \) \(=\) \( 64 = 2^{6} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 64.e (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 16 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 1 \)
Sturm bound: \(16\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(64, [\chi])\).

Total New Old
Modular forms 24 6 18
Cusp forms 8 2 6
Eisenstein series 16 4 12

Trace form

\( 2q + 2q^{3} - 2q^{5} + O(q^{10}) \) \( 2q + 2q^{3} - 2q^{5} - 2q^{11} - 2q^{13} - 4q^{15} - 4q^{17} - 6q^{19} + 4q^{21} + 8q^{27} + 6q^{29} + 16q^{31} - 4q^{33} + 4q^{35} + 6q^{37} - 10q^{43} + 2q^{45} - 16q^{47} + 6q^{49} - 4q^{51} - 10q^{53} + 6q^{59} - 18q^{61} - 4q^{63} + 4q^{65} + 10q^{67} - 12q^{69} - 6q^{75} + 4q^{77} + 10q^{81} + 2q^{83} + 4q^{85} - 4q^{91} + 16q^{93} + 12q^{95} - 4q^{97} + 2q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(64, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
64.2.e.a \(2\) \(0.511\) \(\Q(\sqrt{-1}) \) None \(0\) \(2\) \(-2\) \(0\) \(q+(1-i)q^{3}+(-1-i)q^{5}+2iq^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(64, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(64, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 3}\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ 1
$3$ \( 1 - 2 T + 2 T^{2} - 6 T^{3} + 9 T^{4} \)
$5$ \( ( 1 - 2 T + 5 T^{2} )( 1 + 4 T + 5 T^{2} ) \)
$7$ \( 1 - 10 T^{2} + 49 T^{4} \)
$11$ \( 1 + 2 T + 2 T^{2} + 22 T^{3} + 121 T^{4} \)
$13$ \( ( 1 - 4 T + 13 T^{2} )( 1 + 6 T + 13 T^{2} ) \)
$17$ \( ( 1 + 2 T + 17 T^{2} )^{2} \)
$19$ \( 1 + 6 T + 18 T^{2} + 114 T^{3} + 361 T^{4} \)
$23$ \( 1 - 10 T^{2} + 529 T^{4} \)
$29$ \( ( 1 - 10 T + 29 T^{2} )( 1 + 4 T + 29 T^{2} ) \)
$31$ \( ( 1 - 8 T + 31 T^{2} )^{2} \)
$37$ \( 1 - 6 T + 18 T^{2} - 222 T^{3} + 1369 T^{4} \)
$41$ \( ( 1 - 41 T^{2} )^{2} \)
$43$ \( 1 + 10 T + 50 T^{2} + 430 T^{3} + 1849 T^{4} \)
$47$ \( ( 1 + 8 T + 47 T^{2} )^{2} \)
$53$ \( ( 1 - 4 T + 53 T^{2} )( 1 + 14 T + 53 T^{2} ) \)
$59$ \( 1 - 6 T + 18 T^{2} - 354 T^{3} + 3481 T^{4} \)
$61$ \( 1 + 18 T + 162 T^{2} + 1098 T^{3} + 3721 T^{4} \)
$67$ \( 1 - 10 T + 50 T^{2} - 670 T^{3} + 4489 T^{4} \)
$71$ \( 1 - 42 T^{2} + 5041 T^{4} \)
$73$ \( 1 - 130 T^{2} + 5329 T^{4} \)
$79$ \( ( 1 + 79 T^{2} )^{2} \)
$83$ \( 1 - 2 T + 2 T^{2} - 166 T^{3} + 6889 T^{4} \)
$89$ \( 1 - 162 T^{2} + 7921 T^{4} \)
$97$ \( ( 1 + 2 T + 97 T^{2} )^{2} \)
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