Properties

Label 55.2.e
Level 55
Weight 2
Character orbit e
Rep. character \(\chi_{55}(32,\cdot)\)
Character field \(\Q(\zeta_{4})\)
Dimension 8
Newform subspaces 2
Sturm bound 12
Trace bound 3

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 55 = 5 \cdot 11 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 55.e (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 55 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 2 \)
Sturm bound: \(12\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(55, [\chi])\).

Total New Old
Modular forms 16 16 0
Cusp forms 8 8 0
Eisenstein series 8 8 0

Trace form

\( 8q - 6q^{3} - 8q^{5} + O(q^{10}) \) \( 8q - 6q^{3} - 8q^{5} + 4q^{11} + 8q^{12} - 4q^{15} - 12q^{16} + 24q^{20} - 20q^{22} + 14q^{23} + 14q^{25} - 40q^{26} + 6q^{27} + 8q^{31} - 26q^{33} + 36q^{36} - 2q^{37} + 40q^{38} - 22q^{45} - 12q^{47} + 4q^{48} - 16q^{53} + 14q^{55} - 40q^{58} - 64q^{60} + 40q^{66} + 38q^{67} - 44q^{71} + 36q^{75} + 40q^{78} - 8q^{80} + 12q^{81} + 40q^{82} - 20q^{88} + 48q^{92} + 58q^{93} - 62q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(55, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
55.2.e.a \(4\) \(0.439\) \(\Q(i, \sqrt{10})\) None \(0\) \(-4\) \(-8\) \(0\) \(q+\beta _{1}q^{2}+(-1-\beta _{2})q^{3}+3\beta _{2}q^{4}+\cdots\)
55.2.e.b \(4\) \(0.439\) \(\Q(i, \sqrt{11})\) \(\Q(\sqrt{-11}) \) \(0\) \(-2\) \(0\) \(0\) \(q+(-1+\beta _{1}-\beta _{3})q^{3}+2\beta _{2}q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ (\( 1 - 7 T^{4} + 16 T^{8} \))(\( ( 1 - 2 T + 2 T^{2} )^{2}( 1 + 2 T + 2 T^{2} )^{2} \))
$3$ (\( ( 1 + 2 T + 2 T^{2} + 6 T^{3} + 9 T^{4} )^{2} \))(\( ( 1 + T + 3 T^{2} )^{2}( 1 - 5 T^{2} + 9 T^{4} ) \))
$5$ (\( ( 1 + 4 T + 5 T^{2} )^{2} \))(\( 1 - T^{2} + 25 T^{4} \))
$7$ (\( ( 1 + 49 T^{4} )^{2} \))(\( ( 1 + 49 T^{4} )^{2} \))
$11$ (\( ( 1 - 2 T + 11 T^{2} )^{2} \))(\( ( 1 - 11 T^{2} )^{2} \))
$13$ (\( ( 1 - 8 T + 32 T^{2} - 104 T^{3} + 169 T^{4} )( 1 + 8 T + 32 T^{2} + 104 T^{3} + 169 T^{4} ) \))(\( ( 1 + 169 T^{4} )^{2} \))
$17$ (\( 1 - 382 T^{4} + 83521 T^{8} \))(\( ( 1 + 289 T^{4} )^{2} \))
$19$ (\( ( 1 - 2 T^{2} + 361 T^{4} )^{2} \))(\( ( 1 + 19 T^{2} )^{4} \))
$23$ (\( ( 1 + 2 T + 2 T^{2} + 46 T^{3} + 529 T^{4} )^{2} \))(\( ( 1 - 9 T + 23 T^{2} )^{2}( 1 + 35 T^{2} + 529 T^{4} ) \))
$29$ (\( ( 1 + 18 T^{2} + 841 T^{4} )^{2} \))(\( ( 1 + 29 T^{2} )^{4} \))
$31$ (\( ( 1 - 2 T + 31 T^{2} )^{4} \))(\( ( 1 - 37 T^{2} + 961 T^{4} )^{2} \))
$37$ (\( ( 1 - 6 T + 18 T^{2} - 222 T^{3} + 1369 T^{4} )^{2} \))(\( ( 1 + 7 T + 37 T^{2} )^{2}( 1 - 25 T^{2} + 1369 T^{4} ) \))
$41$ (\( ( 1 - 42 T^{2} + 1681 T^{4} )^{2} \))(\( ( 1 - 41 T^{2} )^{4} \))
$43$ (\( ( 1 + 1849 T^{4} )^{2} \))(\( ( 1 + 1849 T^{4} )^{2} \))
$47$ (\( ( 1 - 6 T + 18 T^{2} - 282 T^{3} + 2209 T^{4} )^{2} \))(\( ( 1 + 12 T + 47 T^{2} )^{2}( 1 + 50 T^{2} + 2209 T^{4} ) \))
$53$ (\( ( 1 + 2 T + 2 T^{2} + 106 T^{3} + 2809 T^{4} )^{2} \))(\( ( 1 + 6 T + 53 T^{2} )^{2}( 1 - 70 T^{2} + 2809 T^{4} ) \))
$59$ (\( ( 1 - 82 T^{2} + 3481 T^{4} )^{2} \))(\( ( 1 - 15 T + 59 T^{2} )^{2}( 1 + 15 T + 59 T^{2} )^{2} \))
$61$ (\( ( 1 - 82 T^{2} + 3721 T^{4} )^{2} \))(\( ( 1 - 61 T^{2} )^{4} \))
$67$ (\( ( 1 - 6 T + 18 T^{2} - 402 T^{3} + 4489 T^{4} )^{2} \))(\( ( 1 - 13 T + 67 T^{2} )^{2}( 1 + 35 T^{2} + 4489 T^{4} ) \))
$71$ (\( ( 1 + 8 T + 71 T^{2} )^{4} \))(\( ( 1 + 3 T + 71 T^{2} )^{4} \))
$73$ (\( 1 + 5218 T^{4} + 28398241 T^{8} \))(\( ( 1 + 5329 T^{4} )^{2} \))
$79$ (\( ( 1 + 118 T^{2} + 6241 T^{4} )^{2} \))(\( ( 1 + 79 T^{2} )^{4} \))
$83$ (\( 1 - 6382 T^{4} + 47458321 T^{8} \))(\( ( 1 + 6889 T^{4} )^{2} \))
$89$ (\( ( 1 - 142 T^{2} + 7921 T^{4} )^{2} \))(\( ( 1 - 97 T^{2} + 7921 T^{4} )^{2} \))
$97$ (\( ( 1 + 14 T + 98 T^{2} + 1358 T^{3} + 9409 T^{4} )^{2} \))(\( ( 1 + 17 T + 97 T^{2} )^{2}( 1 + 95 T^{2} + 9409 T^{4} ) \))
show more
show less